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SUMMARY:Mathematics and Biology II: Mathematics and Science of Behavior
DESCRIPTION:Mathematics and Biology II: Mathematics and Science of Behavior \nDates: April 27–30\, 2026 \nLocation: Harvard CMSA\, Room G10\, 20 Garden Street\, Cambridge MA \nYoutube Playlist \n\n\nThis meeting will explore the emerging mathematics and science of embodied cognition—the idea that behavior arises not solely from the brain but through the dynamic interaction of brain\, body\, and environment. Understanding how animals sense\, move\, decide\, and coordinate\, from individual sensorimotor loops to collective dynamics\, demands mathematical frameworks that integrate geometry\, dynamics\, stochastic processes\, control theory\, and multiscale physics. The meeting will bring together experimentalists studying behavior across species with theorists and engineers building mathematical models and bio-inspired machines\, to identify shared principles of adaptive behavior. \n\n\nCo-organizers: L. Mahadevan (Harvard)\, Francesco Mori (Harvard CMSA)\, Venkatesh Murthy (Harvard) \nSpeakers \n\nPulkit Agrawal\, MIT\nKristin Branson\, HHMI\nAntonio C. Costa\, Sorbonne University/Paris Brain Institute\nNoah Cowan\, Johns Hopkins University\nRobert Datta\, Harvard Medical School\nBen de Bivort\, Harvard University\nOfer Feinerman\, Weizmann Institute of Science\nDeborah Gordon\, Stanford University\nAlbert Kao\, UMass Boston\nAnn Kennedy\, Scripps Research Institute\nHungtang Ko\, Tufts University\nGeorge Lauder\, Harvard University\nBence Ölveczky\, Harvard University\nKirstin Petersen\, Cornell University\nPavan Ramdya\, EPFL\nElizabeth Tibbetts\, University of Michigan\nRobert Wood\, Harvard University\n\n  \n\nSchedule (pdf) \nMonday\, Apr. 27\, 2026 \n9:00–9:30 am: Breakfast \n9:30–10:15 am: Deborah Gordon\, Stanford University\nTitle: The dynamics of collective behavior in changing environments\nAbstract: Collective behavior operates without central control\, using interactions among participants adjust to changing conditions. There is enormous diversity in the dynamics of collective behavior\, including in the rate of response to conditions\, in feedback regimes that set whether interactions stimulate or inhibit activity\, and the extent of centralization or modularity of information flow. An ecological perspective suggests how this diversity of collective behavior reflects the dynamics of the environment\, including its stability\, the ratio of resources spent to resources gained\, and the distribution of resources in time and space.\nAs examples\, I will discuss field studies and modelling of the regulation of foraging behavior in two species of ants\, Harvester ant colonies in the desert regulate foraging to manage high costs\, in water loss\, to obtain scattered and stable resources. They use a centralized system\, with the default to remain inactive unless stimulated\, that is slow to adjust foraging activity. In contrast\, the turtle ant colonies form trail networks in the canopy of the tropical forest\, in unstable conditions where activity costs are low\, to find and collect ephemeral and patchy resources. They use a highly modular system\, with the default to sustain activity unless inhibited\, that can rapidly adjust trail networks to changing resources and conditions. \n10:15–10:30 am: Discussion \n10:30–11:00 am: Tea Break \n11:00–11:45 am: Hungtang Ko\, Tufts University\nTitle: Collective mechanical intelligence: how fluid environments mediate self-organization of swarms\nAbstract: Biological collectives across scales self-organize within fluid environments. The mechanical coupling between swarming agents and fluid fields provides opportunities for both passive self-assembly and active\, fluid-mediated communication. However\, while sporadic evidence of collective mechanical intelligence exists\, its underlying mechanisms remain elusive. In this talk\, I will focus on two key systems: fire ant rafts and fish schools. Using a combination of experiments and mathematical models\, I will show that fire ant rafts leverage passive interfacial forces for self-assembly and self-stabilization. Furthermore\, I will demonstrate how schools of giant danio utilize mechanically intelligent formations in 3D\, and discuss how swarm robotics may provide the key to future research in collective mechanical intelligence. \n11:45 am–12:00 pm: Discussion \n12:00–1:30 pm: Catered Lunch \n1:30–2:15 pm: Albert Kao\, UMass Boston\nTitle: The limits and potential of collective wisdom\nAbstract: Over the past several years\, many studies have demonstrated\, both in theory and in experiments\, the ability of groups to make better decisions than individuals — a phenomenon known as collective wisdom. However\, the task types and experimental paradigms used vary considerably\, making comparisons across studies\, and consequently a unified theory of collective wisdom\, difficult. Here\, I derive a measure called the effective group size which allows for such comparisons. I use this measure to demonstrate several limitations to collective wisdom\, including when groups are large\, when there are correlations in opinions in the group\, and when information is passed down in chains. In addition\, collective wisdom is fragile in the face of an individual who has a disproportionate amount of power\, even if far from being a dictator. \n2:15–2:30 pm: Discussion \n2:30–3:15 pm: Ann Kennedy\, Scripps Research Institute\nTitle: Neural mechanisms that gate the expression of motivated behaviors\nAbstract: In order to survive and reproduce\, animals must set and weigh off goals in a way that is adaptive and responsive to the context of the environment. Intense evolutionary pressure has wired these algorithms of survival into the connectivity and gene expression patterns of the brain. In this talk\, I will present our lab’s recent work on the structure of animal behavior and its neural correlates\, showing how theory and modeling can uncover the computational mechanisms by which the brain sets survival goals and weighs off competing survival needs. I will first show how at the macroscopic level\, models of behavior as a feedback control system can help uncover control principles by which pressing survival needs can override less urgent drives. Next\, I will present new work exploring how macroscopic drives are translated into moment-to-moment behavioral choices. \n  \n3:15–4:30 pm: Discussion \n4:30–5:30 pm: CMSA Colloquium: Ofer Feinerman\, Weizmann Institute of Science\nTitle: Enacted collective cognition: Brainless problem-solving in weaver ants\nAbstract: Unlike most ants\, weaver ants construct their nests by pulling together leaves. Because individual ants are small relative to the leaves\, they assemble their bodies into temporary tools that bend the leaves into a hollow structure\, later stabilized with larval silk. Remarkably\, they achieve functional nests across a wide range of leaf shapes and configurations\, suggesting that this distributed system is capable of solving complex\, open-ended problems.\nTo understand how this is possible\, we performed laboratory experiments using controlled leaf configurations. In simple cases\, we show that ants can rely on a zipping heuristic that produces closed nests\, and we use differential geometry to demonstrate how flexible leaves are transformed into rigid structures. Crucially\, this zipping behavior forms a feedback loop in which ants continuously read and modify the evolving structure. In this sense\, the nest itself functions as a shared physical information system.\nThis suggests that cognition in this system is not located within individual ants\, but is enacted through the co-dynamics of the colony and the structure it builds. We present preliminary experiments with more complex leaf configurations\, showing that this process can solve increasingly challenging construction problems. Together\, these results point to a distributed\, brainless\, and enactive form of cognition. \n  \nTuesday\, April 28\, 2026 \n9:00–9:30 am: Breakfast \n9:30–10:15 am: Ben de Bivort\, Harvard University\nTitle: Bayesian Inference on biophysical models of connectomes\nAbstract: Recent progress in connectomics has opened new frontiers for understanding the underlying principles of neural circuits. By leveraging high-resolution maps of synaptic connections\, computational models can simulate neural dynamics with unprecedented detail. However\, it remains challenging to parsimoniously integrate circuit activity data with connectomic information to make biological in- sights. We propose a Bayesian framework as a principled method for bringing to bear existing data\, enabling uncertainty quantification for inferring parameters of interest\, as well as for predicted circuit outputs. To demonstrate this approach\, we implement a simple spiking neuron model using leaky- integrate-and-fire dynamics in the Drosophila olfactory circuit\, incorporating available firing rate data. We evaluate how models with varying levels of biological detail fit experimental data and examine how training on different subsets of data influences model predictions. \n10:15–10:30 am: Discussion \n10:30–11:00 am: Trainee talk: Yasuko Isoe\, Harvard University\nTitle: Divergent spatiotemporal integration of whole-field visual motion in medaka and zebrafish larvae\nAbstract: Cross-species comparisons offer powerful leverage for identifying conserved and divergent neural computations underlying innate behavior. Visual motion integration is a fundamental operation that stabilizes an animal’s position relative to its environment\, yet how its underlying algorithms vary across closely related vertebrate brains remains poorly understood. We investigated how zebrafish (Danio rerio) and medaka (Oryzias latipes) larvae implement visual motion integration using both free-swimming behavioral assays and head-fixed\, tail-free preparations\, the latter allowing us to confirm and extend our findings under precise stimulus control. Using whole-field motion stimuli\, we found that the two species employ distinct spatiotemporal filtering strategies. Medaka pool motion signals over larger visual fields and weight peripheral inputs more strongly\, whereas zebrafish rely more on motion signals directly beneath the body. Temporally\, zebrafish respond robustly to brief stimuli\, while medaka require longer stimulus durations and sustain motion-driven activity well after stimulus offset. Decomposition of turning behavior revealed separable control modules for large and small corrective maneuvers\, with species differences arising primarily from prolonged temporal integration in medaka. Together\, our results demonstrate how alterations in basic computational motifs — spatiotemporal pooling\, gain\, and persistence — can generate divergent visuomotor strategies across closely related vertebrate brains\, offering a window into the evolutionary diversification of sensorimotor computation. \n11:00–11:30 am: Trainee Talk: Siddharth Jayakumar\, Harvard University\nTitle: Mice follow scent trails using predictive policies\nAbstract: Animals must extract reliable information from noisy sensory signals. In olfaction\, this is especially challenging\, since cues are sparse and must be actively sampled. We asked how mice navigate odor trails under these conditions. Using an “infinite” paper treadmill\, we find that mice rapidly learn to track trails with high precision. Disrupting bilateral sampling introduces systematic\, lateralized errors\, consistent with a comparison of signals across the two sides. Individual inhalations near the trail trigger rapid corrective movements.\nInterestingly\, we find that mice do not follow trails purely reactively: deviations in tracking at unexpected trail bends reflected recent history\, indicating the use of short-term memory. We have begun to investigate the neural substrates of this behavior\, focusing on how sensory signals and predictive information are represented in the brain. Broadly\, our results suggest that odor-guided navigation depends on combining immediate sensory input with a short-term internal estimate\, enabling reliable tracking despite sparse cues. \n11:30 am–12:00 pm: Discussion \n12:00–1:30 pm: Catered Lunch \n1:30–2:15 pm: Noah Cowan\, Johns Hopkins University\nTitle: Toward a Control Theory for Active Sensing\nAbstract: Active sensing is often defined as “movement for the purpose of sensing.” Here\, I take a different perspective—that active sensing in biological systems is not a distinct class of behaviors\, but rather a set of movement phenomena that arise from a control objective. Biological sensors adapt to persistent stimuli\, acting like high-pass filters that tend to block “DC.” Such “change-detecting” sensors can support efficient coding with a high dynamic range\, and in engineering\, bio-inspired event cameras are similar: they transmit information only when a pixel changes and\, as such\, are extremely fast and make efficient use of bandwidth for the right applications. However\, such “AC” sensors pose technical challenges for control. Specifically\, event-like biological sensors can cause a nonlinear system (1) to lose local linear observability\, and (2) to become impossible to stabilize about an equilibrium point (Biswas\, Sontag\, Cowan\, Eur J Control\, 2025). Active sensing behaviors must emerge for stable control\, even in the somewhat paradoxical setting where the task-level goal is to remain stationary. Here\, I will discuss my lab’s progress in analyzing how animals use active sensing behaviors to format sensory information\, enhancing observability and control. I will also present our efforts to formalize controller synthesis with event-like sensors. \n2:15–2:30 pm: Discussion \n2:30–3:15 pm: Robert Datta\, Harvard Medical School\nTitle: Unveiling structure in natural behavior\nAbstract: Ethologists describing animals in the wild have long appreciated that naturalistic\, self-motivated behavior is built from modules that are linked together over time into predictable sequences. Many such sequences are built to extract information from the environment.\nAnd yet\, it remains unclear how the brain regulates the selection of individual behavioral modules for expression at any given moment\, or how it dynamically composes these modules into the fluid behaviors observed when animals act of their own volition\, and in the absence of experimental restraint\, task structure or explicit reward. Here we use novel methods for characterizing spontaneous mouse behavior to reveal mechanisms used by the brain to create the architecture of self-guided behavior. \n3:15–4:30 pm: Discussion \n  \nWednesday\, April 29\, 2026 \n9:00–9:30 am: Breakfast \n9:30–10:15 am: Kristin Branson\, HHMI\nTitle: How can generative AI help us understand animal behavior?\nAbstract: Understanding animal behavior at an algorithmic level — what animals attend to\, how they form internal world models\, goals\, and plans\, and how state maps to action — remains a central challenge in neuroethology. Large-scale behavioral experiments now produce trajectory datasets of extraordinary scale and complexity\, but existing approaches necessarily compress this complexity to just a few dimensions. We argue that generative AI offers a path toward rich\, query-able models of the data. We adapt transformer-based sequence modeling to multi-agent animal keypoint trajectories\, treating behavior forecasting as analogous to next-token prediction. Our agent-based network inputs biologically-motivated sensory representations and outputs the distribution of future pose velocities. We show that the model captures statistical properties of the behavioral distribution. We have built a Python library that encapsulates the complexity of transforms relating raw keypoints and model inputs and outputs to make these tools extensible by the NeuroAI community and accessible to theorists and experimentalists. Finally\, we argue that mechanistic interpretability methods allow us to query trained models through the natural framework of artificial neuroethology experiments. \n10:15–10:30 am: Discussion \n10:30–11:00 am: Tea Break \n11:00–11:30 am: Trainee talk: Golnar Gharooni Fard\, Harvard University\nTitle: The Geometry and Dynamics of Embodied Cognition: From Collective Architecture to Interspecies Navigation\nAbstract: Biological behavior is fundamentally an emergent property of the coupling between an agent’s physical form\, its environment\, and local interaction rules. In this talk\, I explore the mathematical principles of this “embodied cognition” across two distinct scales: the stigmergic spatial memory of honeybee collectives and the real-time dynamic coordination of human-bird mutualism. I’ll start by discussing static embodied intelligence through the lens of honeycomb construction. Using 3D-printed foundations to introduce controlled geometric frustration (including misalignment angles and lattice shifts) I demonstrate how honeybee collectives resolve structural mismatches through the adaptive placement of topological defects. I will show how these complex behavioral responses can be modeled as a physics-based potential minimization problem\, proving that the hive’s “intelligence” is a distributed response to local geometric cues. In the second part\, I transition to “dynamic” coordination by examining the mutualistic search for honeybee nests between humans and honeyguide birds in Africa. Unlike the persistent memory of the wax comb\, this interspecies cooperation requires real-time processing of noisy\, stochastic signals. I present a data-driven model of this interaction as a coupled tracking problem. By analyzing the interplay between human engagement and a leaky integrator memory constant\, I identify the sweet spots of temporal integration required to successfully filter bird behavior and maintain goal-oriented navigation. Together\, these two projects demonstrate that a data-driven physics-inspired modeling framework\, can uncover the fundamental rules of agent-environment coupling that drive adaptive behavior across biological scales. \n11:30 am–12:00 pm: Trainee talk: Wenyi Zhang\, Harvard University\nTitle: Mechanisms of Setpoint Control in Drosophila Navigation System\nAbstract: Navigation provides a powerful system for studying how animals balance behavioral persistence with flexibility. During navigation\, fruit flies often default to fast straight walking (or “menotaxis”) in a barren environment\, maintaining a stable heading setpoint over a long period of time. Conversely\, when the local environment is enriched with sensory stimuli\, flies often explore the environment with more frequent heading changes\, either through directed steering driven by a sequence of updating setpoints\, or through undirected turning driven by temporarily lifting the setpoint control. Although this framework suggests a central role for the setpoint in guiding navigation\, the neural mechanisms for flexible setpoint control remain unclear.\nHere we identified h∆A\, a central complex cell type involved in setpoint control. In an aversive heat paradigm\, hΔA played an important role in the fly’s sensory-driven deviation from the menotactic goal direction. We characterized hΔA population activity and found that it carries two separable activity components: a bump-like signal that encodes a slowly varying travel-direction-related setpoint\, and a spatially uniform signal associated with turning. We further identified modulatory inputs to hΔA that shape h∆A activity. Together\, these results support a model in which short- and long-timescale setpoints compete for steering control\, and suggest a circuit mechanism by which flies balance directional persistence with flexible reorientation under changing sensory conditions. \n12:00–1:30 pm: Catered Lunch \n1:30–2:15 pm: Bence Ölveczky\, Harvard University\nTitle: Using neuro-biomechanical simulations to probe neural control of learned skills\nAbstract: The goal of my lab is to decipher the circuit logic by which the brain learns and controls motor skills. The standard mechanistic approach is to dissect the underlying circuits brain area-by-brain area\, inferring function by relating recordings and perturbations within each to behavior. This runs into fundamental problems in highly recurrent systems\, where activity in any one node is shaped by the dynamics of the whole\, a problem compounded by the fact that the circuits we probe control a complex biomechanical body and not measurable features of behavior. I will discuss these challenges and present results suggesting that neuro-biomechanical simulation\, leveraging advances in physics simulation and AI\, can offer a powerful alternative window into the neural circuits underlying learned skills. \n2:15–2:30 pm: Discussion \n2:30–3:15 pm: Pavan Ramdya\, EPFL\nTitle: Object manipulation and affordance learning in Drosophila\nAbstract: Many animals must manipulate objects to perform tasks like pushing away debris when navigating over complex\, natural terrain. For previously unseen objects\, efficient manipulation requires that their affordances–the possible actions one can perform upon them–first be learned through experience. However\, the behavioral and neural mechanisms underlying the learning of object affordances remain largely unknown. To address this gap\, we show that adult Drosophila melanogaster flies can learn to push novel spherical objects without being given any explicit reward. To do this\, flies appear to learn the ball’s pushability affordance: pushing is delayed when animals are first exposed to an immobile ball\, and manipulating one ball accelerates pushing of a second one in a new context. Behavioral quantification of a large-scale neural silencing screen reveals that specific visual projection neurons and olfactory sensory neurons regulate initial reactions to the object while dopaminergic neurons and the mushroom bodies\, a center for learning and memory in insects\, are critical for generalizing object affordances. These findings open the door to a mechanistic understanding of object manipulation and affordance learning. \n3:15–4:30 pm: Discussion \n  \nThursday\, April 30\, 2026 \n9:00–9:30 am: Breakfast \n9:30–10:15 am: Pulkit Agrawal\, MIT\nTitle: What Robots Are Missing: Force Intelligence and Lifelong Learning\nAbstract: Modern robots can plan sophisticated motions\, yet they remain slow\, brittle\, and unreliable on tasks humans find effortless. The missing piece is not better planning\, but better force reasoning: knowing when\, where\, and how much force to apply under uncertainty and across diverse tasks. Force intelligence\, I argue\, is a unifying principle for scalable robotics—bridging dexterous manipulation and whole-body control. However\, even a force-aware robot that cannot learn from its own experience will remain brittle. Today’s systems are effectively frozen after training\, unable to adapt once deployed. Real-world autonomy instead demands learning in deployment: the ability to improve continuously from interactions\, failures\, and successes. In this talk\, I will present our lab’s recent work on lifelong learning and outline a future path for how combining it with force-centric design could enable reliable\, useful robots in the real world. \n10:15–10:30 am: Discussion \n10:30–11:00 am: Tea Break \n11:00–11:45 am: Antonio C. Costa\, Sorbonne University/Paris Brain Institute\nTitle: Unraveling the structure of behavioral variation: a dynamical approach to naturalistic data\nAbstract: Animal behavior varies widely\, both within the same individual over time and between individuals. While often overlooked\, this variation reflects hidden control variables and mechanisms that were shaped by evolution. For example\, variation in behavioral traits can help populations withstand environmental change\, while atypical motor patterns in neurological disorders may offer clues for personalized therapies. Comparing such complex behaviors is difficult. When dynamics are nonlinear and unfold over multiple timescales\, standard metrics based on summary statistics often miss meaningful differences. To address this\, we introduce a framework that encodes multiscale dynamics to compare behavior from data. By modeling nonlinear dynamics probabilistically (using transfer operators inferred from time-series data)\, we define a distance metric that captures behavioral differences across timescales. Tailored to finite\, noisy datasets\, our approach identifies principal axes of variation and enables rigorous clustering of individual trajectories. We demonstrate this framework in various biological systems\, including bacterial chemotaxis and larval zebrafish locomotion\, where the inferred axes of behavioral variation reflect underlying physiological variables and developmental histories. \n11:45 am–12:00 pm: Discussion \n12:00–1:30 pm: Catered Lunch \n1:30–2:15 pm: Elizabeth Tibbetts\, University of Michigan\nTitle: What paper wasps can teach us about the evolution of animal minds\nAbstract: Why do animals differ in their cognitive abilities? Some animals fail at apparently simple tasks\, while others have a remarkable capacity to collect\, retain\, and use information from the environment to guide their behavior. Although paper wasps brains are smaller than a grain of rice\, Tibbetts will show that wasps can perform seemingly complex behaviors like individual face recognition\, transitive inference\, social eavesdropping\, and concept learning. She will also describe experiments that take advantage of natural variation in behavior within and among wasp species to test how social interactions shape the development and evolution of cognitive abilities. \n2:15–2:30 pm: Discussion \n2:30–3:15 pm: Robert Wood\, Harvard University\nTitle: The Mechanical Side of Artificial Intelligence\nAbstract: Artificial Intelligence research typically focuses on perception\, learning\, and control methods to enable autonomous agents\, including robots\, to make and act on decisions in real-world scenarios. However\, even the most capable AI without a well-designed physical structure is of minimal use for canonical robotics tasks. Our research is focused on the design\, mechanics\, materials\, and manufacturing of novel robot platforms that make perception\, control\, or action easier or more robust for natural\, unstructured\, and often unpredictable environments. Key principles in this pursuit include bioinspired designs\, smart materials for novel sensors and actuators\, and the development of multi-scale\, multi-material manufacturing methods. This talk will illustrate this philosophy by highlighting the creation of three classes of robots with unique hardware challenges: bioinspired microrobots\, soft-bodied robots for manipulation\, and robots for interacting with delicate marine life. \n3:15–4:00 pm: Discussion \n4:00–5:00 pm: George Lauder\, Harvard University\nTitle: Fish schooling behavior from kinematics to hydrodynamics to energetics\nAbstract: Do fish moving in a school reduce their energetic costs compared to swimming alone? If so\, how does collective motion reduce the energy needed to move? Only within the last two years have experimental studies directly demonstrated that fish swimming in a group have lower energy expenditure than solitary locomotion. Most studies of how fish move in a collective have focused on understanding the potential benefits of swimming in fixed relative positions. But recent experiments on fish schooling behavior have revealed that fish within the school are nearly constantly rearranging their relative positions. In this talk I will show how fish in a school can save energy even if they do not maintain fixed positions. Analyses of water flow patterns within fish schools have been used to resolve this “paradox” and show that fish movement within a school creates hydrodynamic shelters with zones of reduced flow velocity that nearby fish can take advantage of. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/bioshape2_2026/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Programs
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DTSTART;TZID=America/New_York:20260223T090000
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DTSTAMP:20260613T181931
CREATED:20250502T183538Z
LAST-MODIFIED:20260325T134313Z
UID:10003750-1771837200-1773248400@cmsa.fas.harvard.edu
SUMMARY:Mathematics and Biology I: Morphometry\, Morphogenesis and Mathematics
DESCRIPTION:Mathematics and Biology I: Morphometry\, Morphogenesis and Mathematics \nDates: February 23–March 11\, 2026 \nLocation: Harvard CMSA\, Room G10\, 20 Garden Street\, Cambridge MA \nMathematics\, Morphometry and Morphogenesis is a 3-week program at the Harvard CMSA\, which will bring together researchers from a few different communities with a common aim—to understand shape and its development and evolution in living matter. \nThe aim is to bring together those interested in evolutionary and developmental biology\, soft and active matter physics\, and differential\, discrete and computational geometry and topology\, especially with a statistical bent. Although each of these fields has developed powerful tools and deep insights into form\, function\, and dynamics\, opportunities for them to meet and interact are rare. This workshop aims to foster dialogue and discovery across these disciplinary boundaries—where paleontologists\, developmental biologists\, physicists\, computer scientists and mathematicians can exchange ideas\, identify shared challenges\, and spark new collaborations. We envision this as a chance not only to showcase exciting advances within each domain\, but also to chart new directions together at the intersection of evolution\, development\, and geometry. \nThe first week will have a few tutorials on developmental and evolutionary aspects of morphology\, computational geometry\, statistics and dynamical systems\, along with a workshop-style meeting with research talks\, setting the stage for longer stays and new collaborations over the following weeks. \nPlease note that this is an in-person event. \n  \nWeek 1: Feb 23–27\, 2026: Teaching lectures and research seminars \nThe teaching lectures span a broad range of topics\, including statistical shape and morphometric analysis\, dynamical systems\, differential geometry\, and current themes in morphogenesis\, developmental biology\, and evolutionary developmental biology in Week 1. \n  \nWeek 2-3: March 2–5 & 10–11\, 2026: Research seminars and discussion \nWeeks 2 and 3 will cover development\, regeneration\, and evolution from quantitative\, morphometric\, and mathematical perspectives. \n  \nTopics include: \n🧬 Organoids & Tissue-Engineered Models \n🔬 Computational Imaging & Geometry \n⚙️ Biophysics\, Mechanics & Theory \n🌱 Developmental Biology & Evo-Devo \n  \nSpeakers: \n\nSalem al-Mosleh\, University of Maryland Eastern Shore\nVanessa Barone\, Stanford University\nYohannes Bellaiche\, Institut Curie\nAlain Chedotal\, Institut de la Vision\nGary P.T. Choi\, Chinese University of Hong Kong\nStefano Di Talia\, Duke University\nPaul Francois\, McGill University\nJianping Fu\, University of Michigan\nThomas Gregor\, Pasteur Institute & Princeton\nSahand Hormoz\, Harvard\nHelen James\, Smithsonian Institution\nPurnati Khuntia\, Harvard\nAllon Klein\, Harvard Medical School\nElena Kramer\, Harvard University\nThomas Lecuit\, College de France & IBDM\nDaniel Lew\, MIT\nL. Mahadevan\, Harvard\nM. Lisa Manning\, Syracuse\nAdam Martin\, MIT\nSean Megason\, Harvard\nNoah Mitchell\, University of Chicago\nAkankshi Munjal\, Duke\nNipam Patel\, MBL Woods Hole\nOlivier Pourquié\, Harvard Medical School\nAdrienne Roeder\, Cornell University\nMattia Serra\, UC San Diego\nSuraj Shankar\, University of Michigan\nAnuj Srivastava\, Johns Hopkins\nSebastian Streichan\, UC Santa Barbara\nBerta Verd\, University of Oxford\n\n  \nOrganizers: \n\nSalem al-Mosleh\, University of Maryland Eastern Shore\nVanessa Barone\, Stanford\nL. Mahadevan\, Harvard\nAkankshi Munjal\, Duke\nOlivier Pourquie\, Harvard\n\n  \nVideos from the program are available at the CMSA Youtube Channel. \nMathematics and Biology Playlist \nWeek 1: Feb 23–27\, 2026 – Workshop \nMonday\, 2/23/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:30 am: Tutorial: Anuj Srivastava (Johns Hopkins) — Advances in Statistical Shape Analysis of Biological Structures\n\n10:30–11:00 am: Tea Break\n\n11:00 am–12:00 pm: Tutorial: Anuj Srivastava (Johns Hopkins) — Advances in Statistical Shape Analysis of Biological Structures\n\n12:00–1:30 pm: Lunch: CMSA Common Room\, catered\n\n1:30–2:15 pm: Research Talk: Noah Mitchell (University of Chicago) — Mechanical canalization of 3D chiral morphogenesis\n\nTuesday\, 2/24/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:30 am: Tutorial: Mattia Serra (UCSD) —Tissue Flows\, Morphogen Transport and Positional Information: A Dynamical Systems Framework \n\n10:30–11:00 am: Tea Break\n\n11:00 am–12:00 pm: Tutorial: Mattia Serra (UCSD) — Tissue Flows\, Morphogen Transport and Positional Information: A Dynamical Systems Framework \n\n12:00–1:30 pm: Lunch Break\n\n1:30–2:15 pm: Research Talk: Paul Francois (McGill) — Waddington Landscapes in the Age of Machine Learning\n\nWednesday\, 2/25/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:30 am: Tutorial: Olivier Pourquie (Harvard) — Segmentation and body axis\n\n10:30–11:00 am: Tea Break\n\n11:00 am–12:00 pm: Tutorial: Akankshi Munjal (Duke) — Principles of Tissue Morphogenesis\n\n12:00–1:30 pm: Lunch: CMSA Common Room\, catered\n\n1:30–2:15 pm: Research Talk: Allon Klein (Harvard) — Stochastic Cell State Transitions\n2:15–3:00 pm: Research Talk: Salem Al-Mosleh (University of Maryland) — Linking Geometry\, Evolution\, & Development of Bird Beaks\n\nThursday\, 2/26/26 \n\nIn-person discussions\n\nFriday\, 2/27/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:30 am: Tutorial: Vanessa Barone (Stanford)\n\n10:30–11:00 am: Tea Break\n\n11:00 am–12:00 pm: Tutorial: Vanessa Barone (Stanford)\n\n12:00–1:30 pm: Lunch Break\n\n1:30–2:15 pm: Research Talk: Alain Chedotal (Institut de la Vision) — Tridimensional analysis of human development\n\n2:15–3:00 pm: Research Talk: Jianping Fu (University of Michigan) — Bioengineering Human Embryo and Organ Models\n\n\n  \nWeek 2: March 2–5\, 2026 \nMonday\, 3/2/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:30 am: Research Talk: Thomas Lecuit (Collège de France) —Encoding neuronal shape in the stochastic dynamics of branching processes\n\n10:30–11:00 am: Tea Break\n\n11:00 am–12:00 pm: Research Talk: Danny Lew (MIT) — Tuning the Cell Polarity Circuit: location and number of polarity sites\n12:00–1:30 pm: Lunch: CMSA Common Room\, catered\n\n1:30–2:15 pm: Research Talk: Suraj Shankar (University of Michigan)\n2:15–2:50 pm: Trainee Research Talk: Wenhui Tang (Harvard) — Wetting dynamics and mechanics in human vertebrate somite formation\n2:50–3:05 pm: Tea Break\n3:05–3:35 pm: Trainee Research Talk: Ludwig Hoffmann (Harvard) — Shape deformations through mechanochemical feedback\n4:30–5:30 pm: CMSA Colloquium: L Mahadevan (Harvard) — Inverse problems in soft and active matter\n\nTuesday\, 3/3/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:30 am: Research Talk: Adrienne Roeder (Cornell) — Mechanisms generating robustness in flower morphogenesis\n\n10:30–11:00 am: Tea Break\n\n11:00 am–12:00 pm: Research Talk: Gary Choi (Chinese University of Hong Kong) — Quantifying shape variation using quasi-conformal geometry\n\n12:00–1:30 pm: Lunch Break\n\n1:30–2:15 pm: Research Talk: Akankshi Munjal (Duke) — Shaping the inner ear from the Outside in\n\n2:15–2:50 pm: Trainee Research Talk: Sean McGeary (Harvard) — Uncovering principles of tissue organization with massively parallel cell-interaction assays\n2:50–3:05 pm: Tea Break\n3:05–3:35 pm: Trainee Research Talk: Oliver Inge (Harvard) —Combinatorial BMP4 and activin direct the choice between alternate routes to endoderm in a stem cell model of human gastrulation\n3:40–4:10 pm: Trainee Research Talk: Mehrana Raeisian Nejad (Harvard) — Stress-shape misalignment in confluent cell layers\n\nWednesday\, 3/4/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:15 am: Research Talk: Nipam Patel (Marine Biology Lab\, Woods Hole) — Cellular Morphogenesis at the Nanoscale: Structural color in butterflies\n\n10:15–11:00 am: Tea Break\n\n11:00 am–12:00 pm: Research Talk: M. Lisa Manning (Syracuse) — Sparse mesenchymal cell networks as a fluid under tension (and possibly as tunable matter)\n\n12:00–1:30 pm: Lunch Break: CMSA Common Room\, catered\n\n1:30–2:30 pm: Research Talk: Research Talk: Stefano Di Talia (Duke) — Encoding Geometric Memory During Zebrafish Appendage Regeneration \n\n2:30–3:00 pm: Trainee Research Talk: Suhrid Ghosh (Harvard) — One Cell After Another: Mechanical Counting in Reproductive Evolution\n\n3:00–3:15 pm: Tea Break\n3:15–4:05 pm: Research Talk: Sean Megason (Harvard) — Algorithms for Creating Form: How multiscale control systems make development robust\n4:10–4:40 pm: Trainee Research Talk: Alexandru Bacanu (Harvard) — Forcing tissues into shape: mechanical development in the early human brain\n\nThursday\, 3/5/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:30 am: Research Talk: Sebastian Streichen (UCSB) — Physics of Living Systems: From embryos to structured active matter\n\n10:30–11:00 am: Tea Break\n\n11:00 am–12:00 pm: Research Talk: Berta Verd (University of Oxford) — Evolving phenotypic diversity \n\n12:00–1:30 pm: Lunch Break\n\n1:30–2:15 pm: Research Talk: Elena Kramer (Harvard) — Life in a box: Generating developmental complexity while bound by cell walls\n\n2:20–2:50 pm: Trainee Research Talk: Beatrice Steinert (Brown) — Grids and Folds: Morphogenetic Mechanisms of Body Plan Organization\n\n2:50–3:05 pm: Tea Break\n3:05–3:35 pm: Trainee Research Talk: Rikki Garner (Harvard)\n3:40–4:10 pm: Trainee Research Talk: Chaitra Prabhakara (Harvard) — One Morphogen\, Diverse Patterns: Unraveling Muscle Formation Across the Embryonic Gut Axis\n\n  \nWeek 3: March 10–11\, 2026 \nTuesday\, 3/10/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:30 am: Research talk: Adam Martin (MIT) — Getting in shape: geometry\, mechanics\, and signaling in living epithelia\n\n10:30–11:00 am: Tea break\n\n11:00 am–12:00 pm: Research talk: Yohannes Bellaiche (Institut Curie) — How do cells and tissues sense their size to tailor their dynamics during development?\n12:00–1:30 pm: Lunch Break\n\n1:30–2:15 pm: Research talk: Sahand Hormoz (Harvard) — Learning the rules of morphogenesis\n\nWednesday\, 3/11/26 \n\n9:00–9:30 am: Breakfast\n\n9:30–10:15 am: Research talk: Thomas Gregor (Pasteur Institute & Princeton) — From Fluctuations to Form: Empirical Laws and Scaling Principles in Development\n\n10:15–11:00 am: Research talk: Allison Kann (Harvard) — How to rebuild an organ: The cellular choreography of whole-body regeneration\n\n11:00–11:30 am: Tea Break\n11:30 am–12:00 pm: Research talk: Chandra Kuyyamudi Ashwinikumar (Harvard)\n12:00–12:30 pm: Research talk: Purnati Khuntia (Harvard) — Role of Nucleus in Building Epithelial Tissues \n1:00 pm: Lunch: CMSA Common Room\, catered\n\n\n\n  \n  \n  \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/bioshape_2026/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Programs
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Biology1_21926.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250324T090000
DTEND;TZID=America/New_York:20250524T170000
DTSTAMP:20260613T181931
CREATED:20240228T180801Z
LAST-MODIFIED:20250514T204248Z
UID:10002883-1742806800-1748106000@cmsa.fas.harvard.edu
SUMMARY:Program on Classical\, quantum\, and probabilistic integrable systems - novel interactions and applications
DESCRIPTION:Program on Classical\, quantum\, and probabilistic integrable systems – novel interactions and applications \nDates: March 24–May 24\, 2025  \nLocation: CMSA\, 20 Garden Street\, Cambridge MA 02138 \nExactly solvable models have played pivotal roles in mathematics and physics throughout their history. The program is dedicated to exploring and developing a more recent wave of their influence in stochastic models together with accompanying combinatorial\, classical\, and quantum integrable systems. Topics will include: \n\nColored and uncolored interacting particle systems with associated vertex models and line ensembles\nYang-Baxter integrability and its applications in algebraic combinatorics\, quantum systems\, and conformal field theory\nQuantum stochastic models\, quantum exclusion processes\, and free probability\nEmerging new aspects of classical and quantum integrable systems – hydrodynamics\, large deviations of stochastic models\, and random surface models\n\nOrganizers: \n\nAmol Aggarwal\, Columbia University & Clay Mathematics Institute\nGuillaume Barraquand\, École normale supérieure\, Paris\nAlexei Borodin\, MIT\nIvan Corwin\, Columbia University\nPierre Le Doussal\, École normale supérieure\, Paris\nMichael Wheeler\, University of Melbourne\n\nParticipants \n\nDenis Bernard\, Ecole Normale Supérieure Paris\nAlexey Bufetov\, University of Leipzig\nPasquale Calabrese\, SISSA Trieste\nSylvie Corteel\, UC Berkeley\nCesar Cuenca\, Ohio State University\nJan De Gier\, University of Melbourne\nAndrea De Luca\, CNRS\, Cergy Paris University\nBenjamin Doyon\, King’s College London\nPatrik Ferrari\, University of Bonn\nVadim Gorin\, UC Berkeley\nTamara Grava\, SISSA\nJimmy He\, Ohio State University\nJiaoyang Huang\, University of Pennsylvania\nKurt Johansson\, KTH Stockholm\nRichard Kenyon\, Yale\nAlexandre Krajenbrink\, Cambridge Quantum Computing & Quantinuum\nAtsuo Kuniba\, University of Tokyo\nMatteo Mucciconi\, National University of Singapore\nGreta Panova\, University of Southern California\nLeonid Petrov\, University of Virginia\nSylvain Prolhac\, Université Paul Sabatier\, Toulouse\nTomaž Prosen\, University of Ljubljana\nTomohiro Sasamoto\, Tokyo Institute of Technology\nHerbert Spohn\, Technical University of Munich\nLi-Cheng Tsai\, University of Utah\n\nSchedule \nWeek 1\nMonday\, March 24th \n11:00am – 12:00pm Room G-10\, Lecture 1 of 4: Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n12:00 – 2:00pm Common Room: Program Lunch \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 – 5:30pm Common Room\, CMSA colloquium: Amol Aggarwal\, Columbia University: The Toda Lattice as a Soliton Gas \n  \nTuesday\, March 25th \n3:30 – 4:00pm Common Room: Program tea \n4:00 – 5:00pm Room G-10\, Seminar: Patrik Ferrari\, Universität Bonn: Decoupling and decay of two-point functions in a two-species TASEP \n  \nWednesday\, March 26th \n11:00am – 12:00pm Room G-10\, Lecture 1 of 3: Atsuo Kuniba\, University of Tokyo: Multispecies ASEP and t-PushTASEP on a ring and a strange five vertex model \n3:00 – 4:00pm Room G-10\, Lecture 2 of 4: Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, March 27th \n11:00am – 12:00pm Room G-10\, Lecture 1 of 2: Benjamin Doyon\, King’s College London: The equations of generalised hydrodynamics\, and their unusual diffusve corrections \nAbstract: I will discuss the hydrodynamics of one-dimensional many-body integrable models. At the Euler scale\, this is given by “generalised hydrodynamics”\, whose equations only depend on the asymptotic state content and the two-body scattering shift of the model. I will explain how these equations arise\, and mention some of their properties: Hamiltonian structure\, exact solutions\, absence of shocks. At the diffusive scale\, generic one-dimensional models with state-dependent currents display super-diffusion. However\, integrable models are in a special class of “linearly degenerate systems”\, where there is no superdiffusion\, and one might expect a standard derivative expansion. I will explain how the diffusive corrections to the Euler equations are not given by a derivative expansion\, but instead governed by long-range correlations coming from an Euler-scale fluctuation theory. I will give the general ideas behind this fluctuation theory\, where initial fluctuations are deterministically transported by the Euler equation. I will finally provide arguments for the conjecture that\, once long-range correlations are accounted for\, there is no emergent stochasticity at all scales of hydrodynamics in integrable systems. \n3:30 – 4:00pm Common Room: Program tea \n4:00 – 5:00pm Room G-10\, Seminar: Sylvie Corteel\, University of California at Berkeley: Crystal Skeletons \n  \nFriday\, March 28th \n12:00 – 1:00 pm Common Room: Lunch with CMSA Member Seminar \n2:00 – 3:00pm Room G-10\, Lecture 3 of 4 : Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n3:30 – 4:00 pm Common Room: Program tea \n  \n\n \nWeek 2\nMonday\, March 31 \n11:00am – 12:00pm Room G-10\, Lecture 2 of 2: Benjamin Doyon\, King’s College London: The equations of generalised hydrodynamics\, and their unusual diffusve corrections \nAbstract: I will discuss the hydrodynamics of one-dimensional many-body integrable models. At the Euler scale\, this is given by “generalised hydrodynamics”\, whose equations only depend on the asymptotic state content and the two-body scattering shift of the model. I will explain how these equations arise\, and mention some of their properties: Hamiltonian structure\, exact solutions\, absence of shocks. At the diffusive scale\, generic one-dimensional models with state-dependent currents display super-diffusion. However\, integrable models are in a special class of “linearly degenerate systems”\, where there is no superdiffusion\, and one might expect a standard derivative expansion. I will explain how the diffusive corrections to the Euler equations are not given by a derivative expansion\, but instead governed by long-range correlations coming from an Euler-scale fluctuation theory. I will give the general ideas behind this fluctuation theory\, where initial fluctuations are deterministically transported by the Euler equation. I will finally provide arguments for the conjecture that\, once long-range correlations are accounted for\, there is no emergent stochasticity at all scales of hydrodynamics in integrable systems. \n12:00 – 2:00pm Common Room: Program Lunch \n2:00 – 3:00pm Room G-10\, Lecture 2 of 3: Atsuo Kuniba\, University of Tokyo: Solutions of tetrahedron and 3D reflection equations from quantum cluster algebras \n\nAbstract: Tetrahedron and 3D equations are three-dimensional generalizations of the Yang-Baxter and the reflection equations. I will explain how quantum cluster algebras lead to solutions that generalize and unify many known solutions.  \n\n3:30 – 4:00pm Program tea \n  \nTuesday\, April 1 \n11:00am – 12:00pm Room G-10\, Lecture 1 of 2: Kurt Johansson\, KTH Stockholm: Extremal particles in uniform random Gelfand-Tsetlin patterns \nAbstract: I will report on joint work with Elnur Emrah on edge fluctuations in uniform random interlacing patterns with fixed top configuration. The goal is to describe all possible limit processes that can occur\, and the conditions under which they occur. \n3:30pm – 4:00pm\, Common Room: Program tea \n  \nWednesday\, April 2 \n11:00am – 12:00pm Room G-10\, Lecture 4 of 4: Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n3:00 – 4:00pm Room G-10\, Lecture 3 of 3: Atsuo Kuniba\, University of Tokyo: Box-ball systems \nAbstract: Box-ball systems are one-dimensional integrable cellular automata introduced in 1990. This talk surveys major developments that have unfolded consistently over the decades\, enriching the scope of the theory. Topics include ultradiscretization\, crystal theory in quantum groups\, the combinatorial and thermodynamic Bethe ansatz\, as well as generalized hydrodynamics. \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, April 3 \n11:00am – 12:00pm Room G-10\, Lecture 2 of 2: Kurt Johansson\, KTH Stockholm: Extremal particles in uniform random Gelfand-Tsetlin patterns \nAbstract: I will report on joint work with Elnur Emrah on edge fluctuations in uniform random interlacing patterns with fixed top configuration. The goal is to describe all possible limit processes that can occur\, and the conditions under which they occur. \n3:30pm – 4:00pm Common Room: Program tea \n  \nFriday\, April 4 \n12:00 – 1:00pm Common Room: CMSA Member Seminar and Lunch \n3:30 – 4:00pm Common Room: Program tea \n  \n\n \nWeek 3\nMonday\, April 7 \n12:00 – 2:00pm Common Room: Program lunch \n4:00 – 4:30pm Tea with CMSA colloquium \n4:30 – 5:30pm CMSA Colloquium: Ben Webster\, University of Waterloo and Perimeter Institute: 3-D Mirror Symmetry \n  \nTuesday\, April 8 \n11:00am – 2:00pm Room G-10\, Pierre Le Doussal\, École normale supérieure de Paris: Exact results for the macroscopic fluctuation theory of the 1D weakly asymmetric exclusion process. \n3:30 – 4:00pm Common Room: Program tea  \n  \nWednesday\, April 9 \n12:00 – 1:00pm Common Room\, CMSA Q&A Seminar and lunch: Eric Maskin\, Harvard Economics: The Mathematics of Voting \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, April 10 \n3:30 – 4:00pm Common Room: Program tea  \n  \nFriday\, April 11 \n12:00 – 1:00pm Common Room: CMSA member seminar and lunch \n3:30 – 4:00pm Common Room: Program tea \n  \n\nWeek 4\nMonday\, April 14 \n12:00 – 2:00pm Common Room: Program lunch \n4:00 – 4:30pm Tea with CMSA colloquium \n4:30 –5:30pm CMSA colloquium: Andrey Smirnov\, University of North Carolina at Chapel Hill: Quantum K-theory at roots of unity \n  \nTuesday\, April 15 \n11:00 am – 12:00pm Room G-10\, Ivan Corwin\, Columbia University: How Yang-Baxter unravels Kardar-Parisi-Zhang \nAbstract: Over the past few decades\, physicists and then mathematicians have sought to uncover the (conjecturally) universal long time and large space scaling limit for the so-called Kardar-Parisi-Zhang (KPZ) class of stochastically growing interfaces in (1+1)-dimensions. Progress has been marked by several breakthroughs\, starting with the identification of a few free-fermionic integrable models in this class and their single-point limiting distributions\, widening the field to include non-free-fermionic integrable representatives\, evaluating their asymptotics distributions at various levels of generality\, constructing the conjectural full space-time scaling limit\, known as the directed landscape\, and checking convergence to it for a few of the free-fermion representatives. \nIn this talk\, I will describe a method that should prove convergence for all known integrable representatives of the KPZ class to this universal scaling limit. The method has been fully realized for the Asymmetric Simple Exclusion Process and the Stochastic Six Vertex Model. It relies on the Yang-Baxter equation as its only input and unravels the rich complexity of the KPZ class and its asymptotics from first principles. This is based on a few works involving Amol Aggarwal\, Alexei Borodin\, Milind Hegde\, Jiaoyang Huang and me. \n3:30 – 4:00pm Common Room: Program tea  \n  \nWednesday\, April 16 \n11:00am – 12:00pm Room G-10\, Tamara Grava\, University of Bristol: Random solitons and soliton gas \nAbstract: A soliton is a localised travelling wave solution of a nonlinear dispersive equation. When the equation is integrable the interaction of many solitons is elastic. We study the behaviour of a set of N solitons for the Korteweg de Vries equation in the limit N goes to infinity (soliton gas) and the interaction of the soliton gas with a distinct soliton that we call a tracer soliton. We show that the average velocity of the tracer soliton satisfies the Zakharov-El kinetic equations. We then consider a set of random N soliton solution q_N(x\,t) and its limiting soliton gas q(x\,t). We prove a central limit theorem for the difference q_N(x\,t)-q(x\,t) for values of x and t that are bounded by log(N). \n12:00 – 1:00pm Common Room: CMSA Q&A seminar and lunch: Noah Golowich\, MIT: What is length generalization in large language models? \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, April 17 \n11:00am – 12:00pm Room G-10\, Guillaume Barraquand\, École normale supérieure de Paris: Large time cumulants of the open KPZ equation \n12:00 – 1:00pm Common Room: lunch with featured Yip Lecture speaker Scott Aaronson and CMSA residents \n3:30pm Common Room: Program tea  \n4:00 – 5:00pm Science Center Hall A: Fifth Annual Yip Lecture\, Scott Aaronson: How Much Math is Knowable? \n5:00 – 6:00pm Math Department Common Room at the Harvard Science Center: Yip Lecture reception \n  \nFriday\, April 18 \n12:00 – 1:00pm Common Room: CMSA Member Seminar and lunch: Han Shao\, Harvard CMSA\, Topic TBD \n3:30 – 4:00pm Common Room: Program tea \n  \n\nWeek 5\n  \nMonday\, April 21 \n11:00am – 12:00pm Room G-10\, Tomaz Prosen\, University of Ljubljana\, Lecture 1 of 3: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries) \nAbstract: I will introduce Yang-Baxter integrable brickwork quantum circuit models and discuss their integrability structure\, specifically\, the transfer matrix\, conservation laws etc. A paradigmatic example\, XXZ or unitary 6-vertex circuits exhibit an unusual link to KPZ scaling at the isotropic (SU(2) symmetric) point. I will establish the link to corresponding classical integrable Landau-Lifshitz circuits and discuss some aspects of transport and full counting statistics. \n12:00 – 2:00pm Common Room: Program Lunch \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 – 5:30pm  Common Room\, CMSA colloquium: Ila Fiete\, MIT: Modeling the emergence of complex cortical structure from simple precursors in the brain: maps\, hierarchies\, and modules \n  \nTuesday\, April 22 \n11:00am – 12:00pm Room G-10\, Tomohiro Sasamoto\, Tokyo Institute of Technology: Large deviation of symmetric models through classical integrable systems \n3:30pm Common Room: Program tea  \n  \nWednesday\, April 23 \n11:00am – 12:00pm Room G-10\, Tomaz Prosen\, University of Ljubljana: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries) \nAbstract: I will discuss explicit matrix product solutions for quantum many-body Markov chains\, defined for a Yang-Baxter integrable quantum circuit with specific stochastic Kraus processes at its boundaries. In the continuous time limit\, these solutions correspond to steady states of boundary driven Lindbladian dynamics and often yield non-trivial quasi-local conservation laws of integrable spin chains. The specific case of XXZ and Hubbard chain will be discussed. \n12:00 – 1:00pm Common Room: CMSA Q&A seminar and lunch: Alexei Borodin\, MIT: Connections between physics and probability \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, April 24 \n11:00am – 12:00pm Room G-10\, Sylvain Prolhac\, Université Paul Sabatier\, Toulouse: Approach to stationarity for KPZ fluctuations in finite volume \nAbstract: At late times $t$\, the cumulants of the height for the KPZ fixed point in finite volume behave as affine functions of time $c_k(t) = a_k t+b_k$\, up to exponentially small corrections. The constant term $b_k$ is the last remaining information about the initial state observable at long enough times. Two approaches allow us to compute this constant from the totally asymmetric exclusion process\, a discrete version of the KPZ fixed point. First\, an iterated version of the matrix product representation for the stationary state leads\, for arbitrary initial conditions\, to expressions involving extreme value statistics of Brownian paths. On the other hand\, Bethe ansatz leads to rather explicit expressions for simple initial conditions. Comparison between the two approaches then provides conjectures for some generating functions of Brownian paths. \n3:30pm Common Room: Program tea  \n  \nFriday\, April 25 \n11:00am – 12:00pm Room G-10\, Tomaz Prosen\, University of Ljubljana\, Lecture 3 of 3: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries) \nAbstract: In the last lecture I will discuss the possibility of quantum integrability of many-body quantum Markov chain generators\, such as Lindbladians with bulk or boundary dissipation\, and the corresponding circuit (Kraus) counterparts. The paradigmatic example is the XX model with dephasing noise which can be mapped to a Hubbard model with imaginary interaction\, both in the Hamiltonian and circuit formulation. \n3:30 – 4:00pm Common Room: Program tea \n  \n\nWeek 6\n  \nMonday\, April 28 \n11:00am – 12:00pm Room G-10\, Herbert Spohn\, Technische Universitaet Muenchen\, Lecture 1 of 3: Integral many-body systems and GHD \n12:00 – 2:00pm Common Room: Program Lunch \n2:00 – 3:00 pm Room G-10\, Tomohiro Sasamoto\, Tokyo Institute of Technology\, Exact density profile and current fluctuations in a tight-binding chain with dephasing noise \nAbstract: We consider a tight-binding chain with dephasing noise\, whose time evolution is described by the quantum master equation called the Gorini-Kossakowski-Sudarhan-Lindblad (GKSL) equation. By using a connection of this model to the Hubbard model with imaginary coupling [1]\, we study the density profile [2] and the variance of the current [3] exactly for the model on the infinite line by writing down contour integral formulas using Bethe ansatz. The talk is based on collaborations with Taiki Ishiyama and Kazuya Fujimoto.  \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 –5:30pm Room G-10\, CMSA colloquium: Peter Sarnak\, IAS and Princeton University\, Bass-Note Spectra of locally uniform geometries \n  \nTuesday\, April 29 \n11:00 am – 12:00pm Room G-10\, Pasquale Calabrese\, SISSA Trieste\, Lecture 1 of 3: Quantum Mpemba effect \n2:00 – 3:00 pm Room G-10\, Greta Panova\, University of Southern California\, Grothendieck shenanigans: permutons from pipe dreams via integrable probability \nAbstract: Pipe dreams are tiling models originally introduced to study objects related to the Schubert calculus and K-theory of the Grassmannian. They can also be viewed as ensembles of random lattice walks with various interaction constraints. In our quest to understand what the maximal and typical algebraic objects look like\, we revealed some interesting permutons. The proofs use the theory of the Totally Asymmetric Simple Exclusion Process (TASEP). Deeper connections with domino tilings of the Aztec diamond and its frozen boundary allow us to describe the extreme cases of the original algebraic problem. This is based on joint work with A. H. Morales\, L. Petrov\, D. Yeliussizov. \n3:30 – 4:00pm Common Room: Program tea  \n  \nWednesday\, April 30 \n11:00am – 12:00pm Herbert Spohn\, Technische Universitaet Muenchen\, Lecture 2 of 3: Integral many-body systems and GHD \n12:00 – 1:00pm (tentative) Common Room: CMSA Q&A seminar and lunch \n3:00 – 4pm Room G-10\, Pasquale Calabrese\, SISSA Trieste\, Entanglement evolution and quasiparticle picture 1 \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, May 1 \n11:00am – 12:00pm Room G-10\, Herbert Spohn\, Technische Universitaet Muenchen\, Lecture 3 of 3: Integral many-body systems and GHD \n2:00 – 3:00 pm Room G-10\, Li-Cheng Tsai\, University of Utah\, Stochastic heat flow by moments \nAbstract: The Stochastic Heat Flow (SHF) is the scaling limit of the directed polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE)\, at the critical dimension of two and near the critical temperature. The finite-dimensional distributions of the SHF was obtained by Caravenna\, Sun\, and Zygouras (2023) by proving that the discrete polymers converge to a universal (model-independent) limit. In this talk\, I will report a new approach based on axioms. We formulate the SHF as a two-parameter continuous measure-valued process that satisfies a set of axioms\, and prove the uniqueness in law under these axioms. The key feature of the axioms concerns the matching of the first four moments. As an application\, we prove the convergence of the noise-mollified SHE to the SHF\, which only requires moment estimates. \n3:30pm Common Room: Program tea  \n  \nFriday\, May 2 \n11:00am – 12:00pm Room G-10\, Pasquale Calabrese\, SISSA Trieste\, Lecture 3 of 3: Entanglement evolution and quasiparticle picture 2 \n12:00 – 1:00pm Common Room\, CMSA Member seminar and lunch \n2:00 – 3:00 pm Room G-10\, Leonid Petrov\, University of Virginia: Random Fibonacci Words \nAbstract: Fibonacci words are words of 1’s and 2’s\, graded by the total sum of the digits. They form a differential poset YF which is an estranged cousin of the Young lattice powering irreducible representations of the symmetric group. We introduce families of “coherent” measures on YF depending on many parameters\, which come from the theory of clone Schur functions (Okada 1994). We characterize parameter sequences ensuring positivity of the measures\, and we describe the large-scale behavior of some ensembles of random Fibonacci words. The subject has connections to total positivity of tridiagonal matrices\, Stieltjes moment sequences\, orthogonal polynomials from the (q-)Askey scheme\, and residual allocation (stick-breaking) models. Based on a joint work with Jeanne Scott. \n3:30 – 4:00pm Common Room: Program tea \n\nWeek 7\n  \nMonday\, May 5 \n11:00am – 12:00pm Room G-10\, Jan De Gier\, University of Melbourne\, Lecture 1 of 3: Pfaffian point process for TASEP on the half line \n12:00 – 2:00pm Common Room: Program Lunch \n2:00 – 3:00 pm  Jiaoyang Huang\, University of Pennsylvania: Ramanujan Property and Edge Universality of Random Regular Graphs \nAbstract: Extremal eigenvalues of graphs are of particular interest in theoretical computer science and combinatorics. Specifically\, the spectral gap—the difference between the largest and second-largest eigenvalues—measures the expansion properties of a graph. In this talk\, I will focus on random d-regular graphs.I will begin by providing background on the eigenvalues of random d-regular graphs and their connections to random matrix theory. In the second part of the talk\, I will discuss our recent results on eigenvalue rigidity and edge universality for these graphs. Eigenvalue rigidity asserts that\, with high probability\, each eigenvalue concentrates around its classical location as predicted by the Kesten-McKay distribution. Edge universality states that the second-largest eigenvalue and the smallest eigenvalue of random d-regular graphs converge to the Tracy-Widom distribution from the Gaussian Orthogonal Ensemble. Consequently\, approximately 69% of d-regular graphs are Ramanujan graphs. This work is based on joint work with Theo McKenzie and Horng-Tzer Yau. \n  \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 –5:30pm Common Room\, CMSA colloquium: Ariel Procaccia\, Harvard University\, Thinking Outside the Ballot Box \n  \nTuesday\, May 6 \n11:00 am – 12:00pm Room G-10\, Jan De Gier\, University of Melbourne\, Lecture 2 of 3: Pfaffian point process for TASEP on the half line \n2:00 – 3:00 Richard Kenyon\, Yale University\, Multinomial dimers and 3d limit shapes \nAbstract: The “multinomial dimer model” on a graph G is the dimer model on the N-fold blow up of G (the graph obtained by replacing each vertex with N vertices and each edge with a complete bipartite graph K_{N\,N}). In the large N limit this model is tractable for general graphs: we find formulas for the partition function and limit shapes in some natural settings\, including a three-dimensional version of the Aztec Diamond. This is joint work with Catherine Wolfram (Yale). \n3:30 – 4:00pm Common Room: Program tea  \n  \nWednesday\, May 7 \n3:00 – 4pm Room G-10\, Jan De Gier\, University of Melbourne\, Lecture 3 of 3: Pfaffian point process for TASEP on the half line \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, May 8: \n2:00 – 3:00 pm Room G-10\, Andrea De Luca\, CNRS Cergy Paris University\, Monitored quantum systems\, product of random matrices and permutations \n3:30pm Common Room: Program tea  \n  \nFriday\, May 9: \n12:00 – 1:00pm Common Room: CMSA Member Seminar and lunch\, Sergiy Verstyuk\, Harvard CMSA\, Title TBD \n2:00 – 3:00 pm Room G-10\, Cesar Cuenca\, Ohio State University\, Random partitions at high temperature \nAbstract: By using Fourier transforms based on Jack symmetric polynomials\, we study discrete particle ensembles x_1>x_2>…>x_N with the inverse temperature beta in the regime where beta tends to zero\, as the number of particles tends to infinity. We prove the LLN and characterize the limiting measure in terms of a moment problem. For fixed-time distributions of special Markov chains\, the limiting measures can be expressed in terms of the eigenvalues of certain Jacobi operators. \n3:30 – 4:00pm Common Room: Program tea \n\nWeek 8\n  \nMonday\, May 12 \n11:00am – 12:00pm Room G-10\, Jimmy He\, Ohio State University\, Symmetries of periodic and free boundary measures on partitions \nAbstract: The periodic and free boundary q-Whittaker measures are probability measures on partitions defined in terms of q-Whittaker functions and an additional parameter $u$ controlling the behavior of the system at the boundary. I will explain a hidden distributional symmetry of this model which exchanges the $u$ and $q$ parameters\, as well as related results on Hall-Littlewood measures. As a special case\, we recover identities of Imamura–Mucciconi–Sasamoto. This is joint work with Michael Wheeler. \n12:00 – 2:00pm Common Room: Program Lunch \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 – 5:30pm Common Room\, CMSA colloquium: Anna Seigal\, Harvard University\, Factorizations for data analysis \n  \nTuesday\, May 13 \n3:30pm Common Room: Program tea  \n  \nWednesday\, May 14 \n12:00 – 1:00pm Common Room: CMSA Conference Reports seminar and lunch: Hugo Cui\, Harvard CMSA\, reporting on the Perimeter Institute Theory+AI Workshop \n3:00 – 4:00pm Room G-10\, Alexandre Krajenbrink\, Cambridge Quantum Computing and Quantinuum\, Unveiling the classical integrable structure of the weak noise theory of the KPZ class: example of the matrix Log–Gamma polymer and the q-TASEP \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, May 15 \n11:00am – 12:00pm Room G-10: Roger Van Peski\, Columbia University\, Integrability in discrete random matrix theory \n\nAbstract: Integrable structure has been well-used in classical random matrix theory\, and recently is also enjoying application in the parallel world of discrete random matrices (over integers\, p-adic integers\, and finite fields). In this talk I will try to cover—at least briefly—the following:\n\n\nSome favorite probabilistic results (convergence of discrete random matrix local limits to a new integrable interacting particle system\, the ‘reflecting Poisson sea’)\,\nSome exact formulas with Hall-Littlewood polynomials that make these results possible\, and \nSome intriguing newer formulas (joint with Jiahe Shen) for Hermitian and antisymmetric p-adic matrices\, which naturally feature ‘formal’ Hall-Littlewood processes with negative t parameter.\n\n\n\n2:00 – 3:00 pm Room G-10\, Matteo Mucciconi\, National University Singapore\, Orthogonality of spin q-Whittaker polynomials \nAbstract: Spin q-Whittaker polynomials are a family of symmetric polynomials that can be defined as partition functions of a solvable lattice model. Their study reveals that they possess mysterious properties such as additional “unorthodox” symmetries\, eigenrelations with respect to difference operators and a self orthogonality that I will prove in the talk. A particular case of these results include a novel orthogonality for the Grothendieck polynomials from K-theory of Grassmannian. I will also discuss applications to exact solutions of directed random polymer models with Beta weights. \n3:30pm Common Room: Program tea  \n  \nFriday\, May 16 \n12:00 – 1:00pm Common Room: CMSA Member Seminar  and lunch: Samy Jelassi\, Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining \n3:30 – 4:00pm Common Room: Program tea \n\nVideos are available on the Youtube Playlist. \n\n 
URL:https://cmsa.fas.harvard.edu/event/integrablesystems2025/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event,Programs
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240903T090000
DTEND;TZID=America/New_York:20241101T170000
DTSTAMP:20260613T181931
CREATED:20240105T033600Z
LAST-MODIFIED:20250305T175957Z
UID:10001112-1725354000-1730480400@cmsa.fas.harvard.edu
SUMMARY:Mathematics and Machine Learning Program
DESCRIPTION:Mathematics and Machine Learning Program \nDates: September 3 – November 1\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 0213 \nMachine learning and AI are increasingly important tools in all fields of research. Recent milestones in machine learning for mathematics include data-driven discovery of theorems in knot theory and representation theory\, the discovery and proof of new singular solutions of the Euler equations\, new counterexamples and lower bounds in graph theory\, and more. Rigorous numerical methods and interactive theorem proving are playing an important part in obtaining these results. Conversely\, much of the spectacular progress in AI has a surprising simplicity at its core. Surely there are remarkable mathematical structures behind this\, yet to be elucidated. \nThe program will begin and end with two week-long workshops\, and will feature focus weeks on number theory\, knot theory\, graph theory\, rigorous numerics in PDE\, and interactive theorem proving\, as well as a course on geometric aspects of deep learning.\n\n  \nSeptember 3–5\, 2024: Opening Workshop: AI for Mathematicians\, with Leon Bottou\, François Charton\, David McAllester\, Adam Wagner and Geordie Williamson.   A series of six lectures covering logic and theorem proving\, AI methods\, theory of machine learning\, two lectures on case studies in math-AI\, and a lecture and discussion on open problems and the ethics of AI in science.\nOpening Workshop Youtube Playlist \n\nSeptember 6–7\, 2024: Big Data Conference \n  \nSeptember 9–13\, 2024: Applying Machine Learning to Math\, with François Charton and Geordie Williamson\nPublic Lecture September 12\, 2024: Geordie Williamson\, University of Sydney: Can AI help with hard mathematics? (Youtube link)\nThe focus of this week will be on practical examples and techniques for the mathematics researcher keen to explore or deepen their use of AI techniques. We will have talks showcasing easily stated problems\, on which machine learning techniques can be employed profitably. These provide excellent toy examples for generating intuition. We will also have expert talks on some of the technical subtleties which arise. There are several instances where the accepted heuristics emerging from the study of large language models (LLM) and image recognition don’t appear to apply on mathematics problems\, and we will try to highlight these subtleties.\nApplying Machine Learning to Math Youtube Playlist \n  \nSeptember 16–20\, 2024: Number theory\, with Drew Sutherland\nThe focus of this week will be on the use of ML as a tool for finding and understanding statistical patterns in number-theoretic datasets\, using the recently discovered (and still largely unexplained) “murmurations” in the distribution of Frobenius traces in families of elliptic curves and other arithmetic L-functions as a motivating example.\nNumber Theory Youtube Playlist \n  \nSeptember 23–27\, 2024: Knot theory\, with Sergei Gukov\nKnot theory is a great source of labeled data that can be synthetically generated. Moreover\, many outstanding problems in knot theory and low-dimensional topology can be formulated as decision and classification tasks\, e.g. “Is the knot 123_45 slice?” or “Can two given Kirby diagrams be related by a sequence of Kirby moves?” During this focus week we will explore various ways in which AI can be applied to problems in knot theory and how\, based on these applications\, mathematical reasoning can advance development of AI algorithms. Another goal will be to develop formal knot theory libraries (e.g. contributions to mathlib) and to apply AI models to formal proof systems\, in particular in the context of knot theory.\nKnot Theory Youtube Playlist \n  \nSeptember 30: Teaching and Machine Learning Panel Discussion\, 3:30-5:30 pm ET \n  \nSeptember 30–October 4\, 2024: Graph theory and combinatorics\, with Adam Wagner\nThis week\, we will consider how machine learning can help us solve problems in combinatorics and graph theory\, broadly interpreted\, in practice. The advantage of these fields is that they deal with finite objects that are simple to set up using computers\, and programs that work for one problem can often be adapted to work for several other related problems as well. Many times\, the best constructions for a problem are easy to interpret\, making it simpler to judge how well a particular algorithm is performing. On the other hand\, there are lots of open conjectures that are simple to state\, for which the best-known constructions are counterintuitive\, making it perhaps more likely that machine learning methods can spot patterns that are difficult to understand otherwise.\nGraph Theory and Combinatorics Youtube Playlist \n  \nOctober 7–11\, 2024: More number theory\, with Drew Sutherland\nThe focus of this week will be on the use of AI as a tool to search for and/or construct interesting or extremal examples in number theory and arithmetic geometry\, using LLM-based genetic algorithms\, generative adversarial networks\, game-theoretic methods\, and heuristic tree pruning as alternatives to conventional local search strategies.\nMore Number Theory Youtube Playlist \n  \nOctober 14 –18\, 2024: Interactive theorem proving\nThis week we will discuss the use of interactive theorem proving systems such as Lean\, Coq and Isabelle in mathematical research\, and AI systems which prove theorems and translate between informal and formal mathematics.\nInteractive Theorem Proving Youtube Playlist \n  \nOctober 21–25\, 2024: Numerical Partial Differential Equations (PDE)\, with Tristan Buckmaster and Javier Gomez-Serrano\nThe focus of this week will be on constructing solutions to partial differential equations and dynamical systems (finite and infinite dimensional) more broadly defined. We will discuss several toy problems and comment on issues like sampling strategies\, optimization algorithms\, ill-posedness\, or convergence. We will also outline strategies about further developing machine-learning findings and turn them into mathematical theorems via computer-assisted approaches.\nNumerical PDEs Youtube Playlist \n  \nOctober 28–Nov. 1\, 2024: Closing Workshop: The closing workshop will provide a forum for discussing the most current research in these areas\, including work in progress and recent results from program participants.\nMath and Machine Learning Closing Workshop Youtube Playlist \n  \nSeptember 3–Nov. 1: Graduate topics in deep learning theory (Boston College) taught by Eli Grigsby\, held at the CMSA Tuesdays and Thursdays 2:30–3:45 pm Eastern Time. Course website (link).\nGraduate Topics in Deep Learning Youtube Playlist \nCourse description: This is a course on geometric aspects of deep learning theory. Broadly speaking\, we’ll investigate the question: How might human-interpretable concepts be expressed in the geometry of their data encodings\, and how does this geometry interact with the computational units and higher-level algebraic structures in various parameterized function classes\, especially neural network classes? During the portion of the course Sep. 3-Nov. 1\, the course will be presented as part of the Math and Machine Learning program at the CMSA in Cambridge. During that portion\, we will focus on the current state of research on mechanistic interpretability of transformers\, the architecture underlying large language models like Chat-GPT. \n\n\n\n\nPrerequisites: This course is targeted to graduate students and advanced undergraduates in mathematics and theoretical computer science. No prior background in machine learning or learning theory will be assumed\, but I will assume a degree of mathematical maturity (at the level of–say—the standard undergraduate math curriculum+ first-year graduate geometry/topology sequence)\n\n\n\n\n\nProgram Organizers \n\nFrancois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nMichael Freedman (Harvard CMSA)\nFabian Ruehle (Northeastern)\nGeordie Williamson (Univ. of Sydney)\n\n\nProgram Schedule  \nMonday\n10:30–noon\nOpen Discussion\nRoom G10 \n12:00–1:30 pm\nGroup lunch\nCMSA Common Room \nTuesday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \n4:00–5:00 pm\nOpen Discussion/Tea\nCMSA Common Room \nWednesday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n2:00–3:00 pm\nNew Technologies in Mathematics Seminar\nRoom G10 \nThursday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \nFriday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n\nHarvard CMSA thanks Mistral AI for a generous donation of computing credit.
URL:https://cmsa.fas.harvard.edu/event/mml2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240415T090000
DTEND;TZID=America/New_York:20240524T170000
DTSTAMP:20260613T181931
CREATED:20230904T173915Z
LAST-MODIFIED:20240624T181936Z
UID:10000003-1713171600-1716570000@cmsa.fas.harvard.edu
SUMMARY:Program on Mathematical Aspects of Scattering Amplitudes
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Program \nDates: April 15 – May 24\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 02138 \nThis program will bring together and foster interaction between theoretical physicists and mathematicians working on various topics connected to recent developments in our understanding of scattering amplitudes in quantum field theory. The field has advanced considerably since 2019 when the CMSA hosted the program “Spacetime and Quantum Mechanics\, Total Positivity and Motives.” Recent developments have primed this area for further significant advances\, which will be facilitated by bringing together many of the relevant experts for intensive discussion and collaboration. \nThe program will feature a weekly seminar series. \nTuesday\, April 16\, 2024\n4:15 pm\nSabrina Pasterski\, Perimeter Institute\nTitle: Radiation in Holography \n[Physics Talk]\nWednesday\, April 17\, 2024\n4:30 pm –  Cruft 309\nAna-Maria Raclariu\, King’s College London \nThursday\, April 18\, 2024\n4:15 pm\nLionel Mason\, University of Oxford\nTitle: Hidden symmetries of SD Poincare Einstein metrics in split signature \n[Physics Talk]\nTuesday\, April 23\, 2024\n4:30 pm – Jefferson 256\nJuan Maldacena\, Institute for Advanced Study \nThursday\, April 25\, 2024\n4:15 pm\nTomasz Taylor\, Northeastern University\nTitle: Progress in Yang-Mills-Liouville Theory \n[CMSA Colloquium]\nMonday\, April 29\, 2024\n4:30 – 5:30 pm\nLance Dixon\, Stanford\nTitle: The DNA of Particle Scattering \nTuesday\, April 30\, 2024\n9:00 am- Jefferson 453\nNima Arkani-Hamed\, IAS\nTitle: Surfaceology and the Real World Part 1 \n1:00 pm – Jefferson 453\nNima Arkani-Hamed\, IAS\nTitle: Surfaceology and the Real World Part 2 \n4:00 pm – Jefferson 453\nNima Arkani-Hamed\, IAS\nTitle: Surfaceology and the Real World Part 3 \nWednesday\, May 1\, 2024\n11:00 am – Science Center 507\nJaroslav Trnka\, UC Davis\nTitle: Loops of loops expansion in the Amplituhedron \n3:00 pm\nYu-tin Huang\, National Taiwan University\nTitle: Loop in trees: Chambers in amplitudes and correlation functions \n4:00 pm\nLivia Ferro\, University of Hertfordshire\nTitle: Scattering Amplitudes from Null-cone Geometry \n5:00 pm\nStephan Stieberger\, Max Planck Institute\nTitle: One-loop Double Copy Relation in String Theory and Twisted (Co)homology \nThursday\, May 2\, 2024\n11:00 am – Science Center 310\nDaniil Rudenko\, Chicago\nTitle: Introduction to Cluster Polylogarithms \nFriday\, May 3\, 2024\n11:00 am\nAndrew McLeod\, Edinburgh\nTitle: Genealogical Constraints on Feynman Integrals \nTuesday\, May 7\, 2024\n3:00 pm\nJacob Bourjaily\, Penn State\nTitle: The Algebraic and Transcendental Structure of Perturbative QFT \nWednesday\, May 8\, 2024\n3:00 pm\nRuth Britto\, Trinity\nTitle: Cuts and Symbols \nTuesday\, May 14\, 2024\n3:00 pm\nJames Drummond\, University of Southampton\nTitle: Multiple light-like Wilson loops in N=4 super Yang-Mills theory \nWednesday\, May 15\, 2024\n3:00 pm\nMatteo Parisi\, Harvard CMSA\nTitle: The amplituhedron and cluster algebras \nTuesday\, May 21\, 2024\n11:00 am\nMichael Borinsky\, ETH Zurich\nTitle: On the Euler characteristic of the commutative graph complex and the top-weight cohomology of the moduli space of curves \nWednesday\, May 22\, 2024\n11:00 am\nChaim Even-Zohar\, Technion\nTitle: Amplituhedron tiles and twistor polynomials \n  \nOrganizers: \n\nNima Arkani-Hamed (Institute for Advanced Study)\nMarcus Spradlin (Brown University)\nAndrew Strominger (Harvard University)\nAnastasia Volovich (Brown University)\nLauren Williams (Harvard University)\n\nParticipants: \n\n\nMichael Borinsky\, ETH Zurich\nJacob Bourjaily\, Pennsylvania State University\nRuth Britto\, Trinity College\nLance Dixon\, Stanford Linear Accelerator Center\nJames Drummond\, University of Southampton\nChaim Even-Zohar\, Technion\nLivia Ferro\, University of Hertfordshire\nCarolina Figueiredo\, Princeton University\nHadleigh Frost\, Oxford University\nBruno Gimenez\, University of Southampton\nOmer Gurdogan\, University of Southampton\nXuhua He\, Chinese University of Hong Kong\nPaul Heslop\, Durham University\nYu-Tin Huang\, National Taiwan University\nDani Kaufman\, University of Copenhagen\nJianrong Li\, University of Vienna\nTomasz Lukowski\, University of Hertfordshire\nYelena Mandelshtam\, University of California\, Berkeley\nLionel Mason\, University of Oxford\nAndrew McLeod\, University of Edinburgh\nNatalie Paquette\, University of Washington\nMatteo Parisi\, Harvard University\nSabrina Pasterski\, Perimeter Institute\nDmitri Pavlov\, Max Planck Institute for Mathematics in the Sciences\, Leipzig\nLizzie Pratt\, University of California\, Berkeley\nClaudia Rella\, University of Geneva\nDaniil Rudenko\, University of Chicago\nGiulio Salvatori\, Max Planck Institute for Physics\nMelissa Sherman-Bennett\, Massachusetts Institute of Technology\nJonah Stalknecht\, University of Hertfordshire\nStephan Stieberger\, Max Planck Institute\nTomasz Taylor\, Northeastern University\nRan Tessler\, Weizmann Institute of Science\nHugh Thomas\, Université du Québec à Montréal\nJaroslav Trnka\, University of California\, Davis\nCristian Vergu\, Pennsylvania State University
URL:https://cmsa.fas.harvard.edu/event/scattering-amplitudes/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240205T090000
DTEND;TZID=America/New_York:20240329T170000
DTSTAMP:20260613T181931
CREATED:20240103T173754Z
LAST-MODIFIED:20240624T182151Z
UID:10001104-1707123600-1711731600@cmsa.fas.harvard.edu
SUMMARY:Arithmetic Quantum Field Theory Program
DESCRIPTION:Arithmetic Quantum Field Theory Program\nDates: Feb. 5–Mar. 29\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge MA 02138 \nArithmetic Quantum Field Theory Program Youtube Playlist \nOrganizers: \n\nDavid Ben-Zvi (University of Texas Austin)\nSolomon Friedberg (Boston College)\nNatalie Paquette (University of Washington Seattle)\nBrian Williams (Boston University)\n\nThis program features a weekly seminar series\, workshops\, and a conference. \nThe object of the program is to develop and disseminate exciting new connections emerging between quantum field theory and algebraic number theory\, and in particular between the fundamental invariants of each: partition functions and L-functions. \nOn one hand\, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds\, both on the level of states (via the Atiyah-Segal / Baez-Dolan / Lurie formalism of extended\, functorial field theory) and on the level of observables (via the Beilinson–Drinfeld / Costello–Gwilliam formalism of factorization algebras). On the other hand\, Weil’s Rosetta Stone and the Mazur–Morishita–Kapranov–Reznikov arithmetic topology (the “knots and primes” dictionary) provide a sturdy bridge between the topology of 2- and 3-manifolds and the arithmetic of number fields. Thus\, one can now port over quantum field theoretic ideas to number theory\, as first proposed by Minhyong Kim with his arithmetic counterpart of Chern-Simons theory. Most recently\, the work of Ben-Zvi–Sakellaridis–Venkatesh applies an understanding of the Langlands program as an arithmetic avatar of electric-magnetic duality in four-dimensional gauge theory to reveal a hidden quantum mechanical nature of the theory of $L$-functions. \nThe program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms\, harmonic analysis and L-functions. Conversely\, we will explore potential geometric and physical consequences of arithmetic ideas\, for example\, the Langlands correspondence theory of L-functions for 3-manifolds. \n\nSchedule \nThe first week of the program will feature several lecture series aimed at a broad local community of mathematicians and physicists\, aiming to introduce the main ideas underlying our program and help establish a common reference point. \nThe program will host a weekly seminar series on Fridays. \nThe speakers will be selected with the aim of covering a wide panorama of the subjects over the course of the program. \nThe program will conclude with a week-long Conference on Arithmetic Quantum Field Theory March 25–29\, 2024. \n\nAQFT Youtube Playlist \nLecture series \nAll lectures take place in Room G10\, Harvard CMSA\, 20 Garden Street Cambridge. \nWeek 1: Feb. 5–9\, 2024 \nAbstract: In this lecture series we will introduce some of the themes underlying the CMSA program on Arithmetic Quantum Field Theory taking place this winter and the upcoming conference March 25-29\, 2024. \nSome of the themes we plan to discuss include: \nStructures in QFT (like factorization for observables and functorial QFT for states and their relation to geometric / deformation quantization) that are sufficiently algebraic and formal to allow for arithmetic analogs. \nThe setup of arithmetic topology as a bridge between the background of QFT to that of arithmetic (both “global” and “local”)\, including the “middle realm” of positive characteristic function fields. \nQuestions and structures in arithmetic that have been / might be amenable to inspiration from QFT\, in particular the theory of L-functions and the Langlands program. \nSchedule \n\n\n\nMonday\, Feb. 5\, 2024\n \n \n\n\n11:00 am – 12:00 pm\n Minhyong Kim\nArithmetic topology and field theory\nVideo\n(Slides part 1 pdf)\n\n\n1:30 – 2:30 pm\nBrian Williams\nAlgebraic quantum field theory\nVideo\n(Lecture Notes)\n\n\n2:30 – 3:30 pm\nDavid Ben-Zvi\nThe Langlands program via arithmetic QFT\nVideo\n\n\nWednesday\, Feb. 7\, 2024\n \n \n\n\n11:00 am – 12:00 pm\nMinhyong Kim\nArithmetic topology and field theory\nVideo\n(Slides part 2 pdf)\n\n\n2:30 – 3:30 pm\nBrian Williams\nAlgebraic quantum field theory\nVideo\n(Lecture Notes)\n\n\nThursday\, Feb.8\, 2024\n \n \n\n\n2:30 – 3:30 pm\nMinhyong Kim\nArithmetic topology and field theory\nVideo\n(Slides part 3 pdf)\n\n\n4:00 – 5:00 pm\nDavid Ben-Zvi\nThe Langlands program via arithmetic QFT\nVideo\n\n\nFriday\, Feb. 9\, 2024\n \n \n\n\n1:00 – 2:00 pm\nBrian Williams\nAlgebraic quantum field theory\nVideo\n(Lecture Notes)\n\n\n2:00 – 3:00 pm\nDavid Ben-Zvi\nThe Langlands program via arithmetic QFT 1\nVideo\n\n\n3:30 – 4:30 pm\nDavid Ben-Zvi\nThe Langlands program via arithmetic QFT 2\nVideo\n\n\nMonday\, Feb. 26\, 2024\n\n\n\n\n1:00 – 2:00 pm\nOmer Offen (Brandeis)\nPeriod integrals of automorphic forms and the residue method\nVideo\n\n\nTuesday\, Feb. 27\, 2024\n\n\n\n\n2:00 – 3:00 pm\nWei Zhang (MIT)\nShtuka special cycles and their generating series\nVideo\n\n\nFriday\, March 1\, 2024\n\n\n\n\n11:00 am – 12:00 pm\nChen Wan (Rutgers Newark)\nSome examples of the relative Langlands duality\nVideo\n\n\n2:00 – 3:00 pm\nPeng Shan (Tsinghua)\nSkein algebras and quantized Coulomb branches\nVideo\n\n\nThursday\, March 7\, 2024\n\n\n\n\n1:30 – 2:30 pm\nAn Huang (Brandeis)\nTate’s thesis and p-adic strings\nVideo\n\n\n3:00 – 4:00 pm\nJohn Francis (Northwestern)\nIntegrating braided categories over 3-manifolds\nVideo\n\n\nFriday\, March 8\, 2024\n\n\n\n\n1:00 – 2:00 pm\nDihua Jiang (U Minnesota)\nShalika Periods: Functoriality and Arithmetic\nVideo\n\n\nFriday\, March 15\, 2024\n\n\n\n\n11:45 – 1:00 pm\nBaiying Liu (Purdue)\nRecent progress on certain problems related to local Arthur packets of classical groups\nVideo\n\n\n2:15 – 3:30 pm\nTasho Kaletha (Michigan)\nCovers of reductive groups and functoriality\nVideo\n\n\nMonday\, March 18\, 2024\n\n\n\n\n1:00 – 3:00 pm\nXinwen Zhu (Stanford)\nThe tame categorical local Langlands correspondence\nVideo\n\n\n4:30 – 5:30 pm\nNatalie Paquette (U Washington)\nKoszul duality & twisted holography for asymptotically flat spacetimes\n\n\nWednesday\, March 20\, 2024\n\n\n\n\n11:00 – 12:15 pm\nStephen D. Miller (Rutgers)\nWhat 4-graviton scattering amplitudes had to say about the unitary dual\n\n\nFriday\, March 22\, 2024\n\n\n\n\n1:45 – 3:00 pm\nJayce Getz (Duke)\nThe Poisson summation conjecture and the fiber bundle method\nVideo\n\n\n\n\n\n\n\n\n\nProgram Visitors \n\nMina Aganagic\, University of California\, Berkeley\nAnne-Marie Aubert\, Institut de Mathématiques de Jussieu-Paris Rive Gauche\, March 15-29\nClark Barwick\, University of Edinburgh\, February 19-March 15\nAlexander Braverman\, Perimeter Institute\nAlejandra Castro\, Cambridge University\, March 25-29\nYoungJu Choie\, Pohang University of Science and Technology\, February 12-16; March 22-28\nJohn Francis\, Northwestern University\, March 1-14\nDavid Gaiotto\, Perimeter Institute\, March 25-29\nJayce Getz\, Duke University\, March 18-22\nEzra Getzler\, Northwestern University\, March 11-22\nSam Gunningham\, Montana State University\, February 9-12\nSarah Harrison\, Northeastern University\nDihua Jiang\, University of Minnesota\, February 29-March 9\nTasho Kaletha\, University of Michigan\, March 12-20\nMinhyong Kim\, University of Edinburgh\, February 1-29\nAxel Kleinschmidt\, Max Planck Institute for Gravitational Physics\, Potsdam\, March 18-28\nKim Klinger-Logan\, Kansas State University\, March 25-29\nKobi Kremnitzer\, Oxford University\, March 25-29\n\nBaiying Liu\, Purdue University\, March 13-16\n\n\nSteven Miller\, Rutgers University\n\nGreg Moore\, Rutgers University\, February 5-9\nDavid Nadler\, University of California\, Berkeley\, March 17-30\nBảo Châu Ngô\, University of Chicago\, March 25-29\nGeorge Pappas\, Michigan State University\, March 25-29\nDaniel Persson\, Chalmers Institute of Technology\, March 25-29\nSam Raskin\, Yale University\, March 26-29\nYiannis Sakellaridis\, Johns Hopkins University\, March 18-22\nPeng Shan\, Tsinghua University\, February 12-April 14\nAkshay Venkatesh\, Institute for Advanced Study\nRoberto Volpato\, University of Padova\, February 4-10\nChen Wan\, Rutgers University\, February 29-March 9\nFei Yan\, Brookhaven National Laboratory\, March 18-29\nXinwen Zhu\, Stanford University\n\n  \n 
URL:https://cmsa.fas.harvard.edu/event/aqft2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Poster_AQFT-Program_letter-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220521T090000
DTEND;TZID=America/New_York:20220612T170000
DTSTAMP:20260613T181931
CREATED:20230706T182609Z
LAST-MODIFIED:20240229T094452Z
UID:10000147-1653123600-1655053200@cmsa.fas.harvard.edu
SUMMARY:2022 Summer Introduction to Mathematical Research
DESCRIPTION:The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description: \nSummer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department) \nIn this course\, we will start with an introduction to computer programming\, algorithms\, and scientific computing. Then we will discuss topics in topology\, classical geometry\, projective geometry\, and differential geometry\, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning\, different deep neural network models\, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography\, introducing some of the iconic topics: Yao’s Millionaires’ problem\, zero-knowledge proof\, the multi-party computation algorithm\, and its proof. \nThe program hopes to provide several research mentors from various disciplines who will give some of the course lectures. Students will have the opportunity to work with one of the research mentors offered by the program. \nPrerequisites: Basic coding ability in some programming language (C/Python/Matlab or CS50 experience). Some background in calculus and linear algebra is needed too. If you wish to work with a research mentor on differential geometry\, more background in geometry such as from Math 132 or 136 will be useful. If you wish to work with a research mentor on computer science\, coding experience mentioned above will be very useful. If you wish to work with a medical scientist\, some background in life science or basic organic chemistry is recommended. \nThe course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events. \nThis program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials\, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard-related perks (such as a place to live if you are in Boston over the summer.) \nHowever: As with the summer tutorials\, those enrolled are eligible* to receive a stipend of $700\, and if you are a Mathematics concentrator\, any written paper for the course can be submitted to fulfill the Math Concentration third-year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program\, nor is it available for PRISE participants or participants in the Herchel Smith program.) \nIf you wish to join this program\, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited\, so don’t wait too long to apply.
URL:https://cmsa.fas.harvard.edu/event/2022-summer-introduction-to-mathematical-research/
LOCATION:Virtual
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-2-600x338-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220124T090000
DTEND;TZID=America/New_York:20220521T170000
DTSTAMP:20260613T181931
CREATED:20230904T083438Z
LAST-MODIFIED:20240215T103430Z
UID:10000055-1643014800-1653152400@cmsa.fas.harvard.edu
SUMMARY:General Relativity Program
DESCRIPTION:During the Spring 2022 semester\, the CMSA hosted a program on General Relativity. \nThis semester-long program included four minicourses\,  a conference\, and a workshop. \nGeneral Relativity Mincourses: March–May\, 2022 \nGeneral Relativity Conference: April 4–8\, 2022 \nGeneral Relativity Workshop: May 2–5\, 2022 \n  \nProgram Visitors \n\nDan Lee\, CMSA/CUNY\, 1/24/22 – 5/20/22\nStefan Czimek\, Brown\, 2/27/22 – 3/3/22\nLan-Hsuan Huang\, University of Connecticut\, 3/13/22 – 3/19/222\, 3/21/22 – 3/25/22\, 4/17 /22– 4/23/22\nMu-Tao Wang\, Columbia\, 3/21/22 – 3/25/22\, 5/7/22 – 5/9/22\nPo-Ning Chen\, University of California\, Riverside\, 3/21/22 – 3/25/22\,  5/7/22–5/9/22\nMarnie Smith\, Imperial College London\, 3/27/22 – 4/11/22\nChristopher Stith\, University of Michigan\, 3/27/22 – 4/23/22\nMartin Taylor\, Imperial College London\,  3/27/22 – 4/11/22\nMarcelo Disconzi\, Vanderbilt\, 5/9/22 – 5/21/22\nLydia Bieri\, University of Michigan\, 5/5/22 – 5/9/22\n\n 
URL:https://cmsa.fas.harvard.edu/event/general-relativity-program/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GR-Program-Banner_800x450-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211218T090000
DTEND;TZID=America/New_York:20211231T170000
DTSTAMP:20260613T181931
CREATED:20230904T080332Z
LAST-MODIFIED:20250303T193414Z
UID:10000049-1639818000-1640970000@cmsa.fas.harvard.edu
SUMMARY:CONDENSED MATTER PROGRAM
DESCRIPTION:The methods of topology have been applied to condensed matter physics in the study of topological phases of matter. Topological states of matter are new quantum states that can be characterized by their topological properties. For example\, the first topological states of matter discovered were the integer quantum Hall states. The two dimensional integer quantum Hall effect was characterized by an integral number which can be understood as a Chern number of the Berry phase. Chern numbers are topological invariants that play an important role in different areas of mathematics. More recently\, new topological states of matter known as topological insulators and topological superconductors have been realized theoretically and experimentally. The characterization of new phases of matter using topological invariants has allowed for a better understanding and even predictions of new phases of matter. The use of topology could lead to the discovery of new electronic\, photonic\, and ultracold atomic states of matter previously unknown. The concrete problems in the physical phenomena could inspire new developments in the study of topological invariants in mathematics. \nHere is a list of the scholars participating in this program. \n\n\n\n\nName\n\n\n\n\nShing-Tung Yau\n\n\nHai Lin\n\n\nJuven Wang\n\n\nPeng Gao
URL:https://cmsa.fas.harvard.edu/event/condensed-matter-program/
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210913T090000
DTEND;TZID=America/New_York:20220513T170000
DTSTAMP:20260613T181931
CREATED:20230904T083009Z
LAST-MODIFIED:20240213T113945Z
UID:10000053-1631523600-1652461200@cmsa.fas.harvard.edu
SUMMARY:Swampland Program
DESCRIPTION:During the 2021–2022 academic year\, the CMSA will host a program on the so-called “Swampland.” \nThe Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory\, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology\,  which has led to a great deal of activity in the field in the last years. \nThe Swampland is intrinsically interdisciplinary\, with ramifications in string compactifications\, holography\, black hole physics\, cosmology\, particle physics\, and even mathematics. \nThis program will include an extensive group of visitors and a slate of seminars. Additionally\, the CMSA will host a school oriented toward graduate students. \nMore information will be posted here. \nSeminars\nSwampland Seminar Series & Group Meetings \nProgram Visitors\n\nPieter Bomans\, Princeton\, 10/30/21 – 11/02/21\nIrene Valenzuela\, Instituto de Física Teórica\, 02/14/22 – 02/21/22\nMariana Grana\, CEA/Saclay\, 03/21/22 – 03/25/22\nHector Parra De Freitas\, IPHT Saclay\, 03/21/22 – 04/01/22\nTimo Weigand\, 03/21/22 – 03/28/22\nGary Shiu\, University of Wisconsin-Madison\, 04/03/22 – 04/10/22\nThomas van Riet\, Leuven University\, 04/03/22 – 04/09/22\nLars Aalsma\, University of Wisconsin-Madison\, 04/11/22 – 04/15/22\nSergio Cecotti\, 05/08/22 – 05/21/22\nTom Rudelius\, 05/09/22 – 05/13/22
URL:https://cmsa.fas.harvard.edu/event/swampland-program/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210521T090000
DTEND;TZID=America/New_York:20210612T170000
DTSTAMP:20260613T181931
CREATED:20230831T034826Z
LAST-MODIFIED:20250304T172540Z
UID:10000047-1621587600-1623517200@cmsa.fas.harvard.edu
SUMMARY:2021 Summer Introduction to Mathematical Research
DESCRIPTION:The Math Department and Harvard’s Center of Mathematical Sciences and Applications (CMSA) will be running a math program/course for mathematically minded undergraduates this summer. The course will be run by Dr. Yingying Wu from CMSA. Here is a description: \nSummer Introduction to Mathematical Research (sponsored by CMSA and the Harvard Math Department) \nIn this course\, we will start with an introduction to computer programming\, algorithm\, and scientific computing. Then we will discuss topics in topology\, classical geometry\, projective geometry\, differential geometry\, and see how they can be applied to machine learning. We will go on to discuss fundamental concepts of deep learning\, different deep neural network models\, and mathematical interpretations of why deep neural networks are effective from a calculus viewpoint. We will conclude the course with a gentle introduction to cryptography\, introducing some of the iconic topics: Yao’s Millionaires’ problem\, zero-knowledge proof\, the multi-party computation algorithm\, and its proof. \nThe course will meet 3 hours per week for 7 weeks via Zoom on days and times that will be scheduled for the convenience of the participants. There may be other times to be arranged for special events. \nThis program is only open to current Harvard undergraduates; both Mathematics concentrators and non-math concentrators are invited to apply. People already enrolled in a Math Department summer tutorial are welcome to partake in this program also. As with the summer tutorials\, there is no association with the Harvard Summer School; and neither Math concentration credit nor Harvard College credit will be given for completing this course. This course has no official Harvard status and enrollment does not qualify you for any Harvard related perks (such as a place to live if you are in Boston over the summer.) \nHowever: As with the summer tutorials\, those enrolled are eligible* to receive a stipend of $700\, and if you are a Mathematics concentrator\, any written paper for the course can be submitted to fulfill the Math Concentration third year paper requirement. (*The stipend is not available for people already receiving a stipend via the Math Department’s summer tutorial program\, nor is it available for PRISE participants or participants in the Herchel Smith program.) \nIf you wish to join this program\, please email Cliff Taubes (chtaubes@math.harvard.edu). The enrollment is limited to 10 people\, so don’t wait too long to apply.
URL:https://cmsa.fas.harvard.edu/event/2021-summer-introduction-to-mathematical-research/
CATEGORIES:Programs
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-2-600x338-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190901T090000
DTEND;TZID=America/New_York:20191220T170000
DTSTAMP:20260613T181931
CREATED:20230904T082838Z
LAST-MODIFIED:20250327T185837Z
UID:10000007-1567328400-1576861200@cmsa.fas.harvard.edu
SUMMARY:Spacetime and quantum mechanics\, total positivity and motives
DESCRIPTION:Recent developments have poised this area to make serious advances in 2019\, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end\, the organizers will host a small workshop during Fall 2019\, with between 20-30 participants. They will also invite 10-20 longer-term visitors throughout the semester. Additionally\, there will be a seminar held weekly on Thursdays at 2:30pm in CMSA G10. \nOrganizers: \n\nNima Arkani-Hamed (IAS)\nLauren Williams (Harvard)\nAlexander Postnikov (MIT)\nThomas Lam (Michigan)\n\n. \nWorkshops: \n \n  \nSpacetime and Quantum Mechanics Workshop\, October 28-30\, 2019\n\n\nHere is a partial list of the mathematicians and physicists who have indicated that they will attend part or all of this special program as a visitor: \n\nPaolo Benincasa\, 11/17/2019 – 11/29/2019\nJacob Bourjaily\, 9/1/2019 – 12/15/2019\nFrancis Brown\, 9/15/2019 – 9/20/2019\nSimon Caron-Huot\, 9/30/2019 – 10/04/2019\nLance Dixon\, 9/9/2019 – 9/20/2019\nCharles Doran\, 10/19/2019 – 11/1/2019\nJames Drummond\, 10/14/2019 – 10/18/2019\nNick Early\, 11/18/2019 – 11/22/2019\nLivia Ferro\, 10/27/2019 – 11/9/2019\nSergey Fomin\, 10/6/2019 – 10/16/2019\nSebastian Franco\, 10/9/2019 – 10/19/2019\nHadleigh Frost\, 9/15/2019 – 12/20/2019\nMichael Green\, 10/05/2019 – 10/13/2019\nAlexander Goncharov\, 12/05/2019 – 12/20/2019\nSong He\, 9/29/2019 – 11/10/2019\nXuhua He\, 10/30/2019-11/03/2019\nEnrico Herrmann\, 10/27/2019 – 11/9/2019\nYutin Huang\, 9/30/2019 – 10/12/2019\nSteven Karp\, 10/11/2019 – 11/03/2019\nTomasz Lukowski\, 10/27/2019 – 11/11/2019\nAndrew McLeod\, 10/6/2019 – 10/19/2019 & 11/3/2019 – 11/16/2019\nSebastian Mizera\, 10/28/2019 – 11/1/2019\nErik Panzer\, 9/15/2019 – 9/25/2019\nMatteo Parisi\, 10/26/2019 – 11/10/2019\nJulio Parra-Martinez\, 10/10/2019 – 05/12/2019\n Pierpaolo Mastrolia\, 11/8/2019 – 11/16/2019\nPasha Pylyavskyy\, 9/8/2019 – 9/22/2019 & 10/14/2019 – 11/1/2019\nJunjie Rao\, 10/25/2019 – 11/04/2019\nGiulio Salvatori\, 9/3/2019 – 12/15/2019\nMichael Shapiro\, 10/27/2019 – 11/2/2019\nDavid Speyer\, 10/14/2019 – 10/18/2019\nHugh Thomas\, 10/27/2019 – 11/22/2019\nJaroslav Trnka\, 9/30/2019 – 10/04/2019\, 10/28/2019 – 11/01/2019\, 11/18/2019 – 11/22/2019\nCristian Vergu\, 11/10/2019 – 11/30/2019\nMatthias Volk\, 10/14/2019 – 10/25/2019\nMatthew von Hippel\, 11/11/2019 – 11/22/2019\nPierre Vanhove\, 10/22/2019 – 10/31/2019\nMatthias Wilhelm\, 10/14/2019 – 10/25/2019
URL:https://cmsa.fas.harvard.edu/event/spacetime-and-quantum-mechanics-total-positivity-and-motives/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181203T083000
DTEND;TZID=America/New_York:20181205T143000
DTSTAMP:20260613T181931
CREATED:20230715T090021Z
LAST-MODIFIED:20250305T212541Z
UID:10000103-1543825800-1544020200@cmsa.fas.harvard.edu
SUMMARY:Morphogenesis: Geometry and Physics
DESCRIPTION:Just over a century ago\, the biologist\, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book – a literary masterpiece – is a visionary synthesis of the geometric biology of form. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. In the century since its publication\, we have seen a revolution in biology following the discovery of the genetic code\, which has uncovered the molecular and cellular basis for life\, combined with the ability to probe the chemical\, structural\, and dynamical nature of molecules\, cells\, tissues and organs across scales. In parallel\, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems\, and a gradual unveiling of the complexity of physical form. So\, how far are we from realizing the century-old vision that “Cell and tissue\, shell and bone\, leaf and flower\, are so many portions of matter\, and it is in obedience to the laws of physics that their particles have been moved\, moulded and conformed ?” \nTo address this requires an appreciation of the enormous ‘morphospace’ in terms of the potential shapes and sizes that living forms take\, using the language of mathematics. In parallel\, we need to consider the biological processes that determine form in mathematical terms is based on understanding how instabilities and patterns in physical systems might be harnessed by evolution. \nIn Fall 2018\, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context\, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems.\nThe first workshop will focus on the interface between Morphometrics and Mathematics\, while the second will focus on the interface between Morphogenesis and Physics.The workshop is organized by L. Mahadevan (Harvard)\, O. Pourquie (Harvard)\, A. Srivastava (Florida). \nAs part of the program on Mathematical Biology a workshop on Morphogenesis: Geometry and Physics will take place on December 3-5\, 2018.  The workshop will be held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA. \nVideos\nSpeakers:\n\nArkhat Abzhanov\, Imperial College\nYohanns Bellaiche\, Paris\nCheng Ming Chuong\, USC\nZev Gartner\, UCSF\nThomas Gregor\, Princeton\nDagmar Iber\, Zurich\nIan Jermyn\, Durham University\nRaymond Keller\, UVA\nAllon Klein\, HMS\nLisa Manning\, Syracuse\nCristina Marchetti\, UCSB\nSean Megason\, HMS\nElliot Meyerowitz\, Caltech\nMichel Milinkovitch\, Geneva\nLeonardo Morsut\, USC\nOlivier Pourquié\, HMS\nEric Siggia\, Rockefeller University\nBen Simons\, Cambridge\nSebastian Streichan\, UCSB\nAryeh Warmflash\, Rice
URL:https://cmsa.fas.harvard.edu/event/morphogenesis-geometry-and-physics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181022T090000
DTEND;TZID=America/New_York:20190417T170000
DTSTAMP:20260613T181931
CREATED:20230904T082647Z
LAST-MODIFIED:20240105T154957Z
UID:10000009-1540198800-1555520400@cmsa.fas.harvard.edu
SUMMARY:Mathematical Biology
DESCRIPTION:During Academic year 2018-19\, the CMSA will be hosting a Program on Mathematical Biology. \nJust over a century ago\, the biologist\, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call for mathematical and physical approaches to understanding the evolution and development of shape. \nIn the century since its publication\, we have seen a revolution in biology following the discovery of the genetic code\, which has uncovered the molecular and cellular basis for life\, combined with the ability to probe the chemical\, structural\, and dynamical nature of molecules\, cells\, tissues and organs across scales. In parallel\, we have seen a blossoming of our understanding of spatiotemporal patterning in physical systems\, and a gradual unveiling of the complexity of physical form. And in mathematics and computation\, there has been a revolution in terms of posing and solving problems at the intersection of computational geometry\, statistics and inference.  So\, how far are we from realizing a descriptive\, predictive and controllable theory of biological shape? \nIn Fall 2018\, CMSA will focus on a program that aims at recent mathematical advances in describing shape using geometry and statistics in a biological context\, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems \nThe CMSA will be hosting three workshops as part of this program. The Workshop on Morphometrics\, Morphogenesis and Mathematics will take place on October 22-26.  \nA workshop on Morphogenesis: Geometry and Physics will take place on December 3-6\, 2018. \nA workshop on Invariance and Geometry in Sensation\, Action and Cognition will take place on April 15-17\, 2019.
URL:https://cmsa.fas.harvard.edu/event/mathematical-biology/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181022T083000
DTEND;TZID=America/New_York:20181024T140000
DTSTAMP:20260613T181931
CREATED:20230715T084844Z
LAST-MODIFIED:20250305T212456Z
UID:10000099-1540197000-1540389600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Morphometrics\, Morphogenesis and Mathematics
DESCRIPTION:In Fall 2018\, the CMSA will host a Program on Mathematical Biology\, which aims to describe recent mathematical advances in using geometry and statistics in a biological context\, while also considering a range of physical theories that can predict biological shape at scales ranging from macromolecular assemblies to whole organ systems. \nThe plethora of natural shapes that surround us at every scale is both bewildering and astounding – from the electron micrograph of a polyhedral virus\, to the branching pattern of a gnarled tree to the convolutions in the brain. Even at the human scale\, the   shapes seen in a garden at the scale of a pollen grain\, a seed\, a sapling\, a root\, a flower or leaf are so numerous that “it is enough to drive the sanest man mad\,” wrote Darwin. Can we classify these shapes and understand their origins quantitatively? \nIn biology\, there is growing interest in and ability to quantify growth and form in the context of the size and shape of bacteria and other protists\, to understand how polymeric assemblies grow and shrink (in the cytoskeleton)\, and how cells divide\, change size and shape\, and move to organize tissues\, change their topology and geometry\, and link multiple scales and connect biochemical to mechanical aspects of these problems\, all in a self-regulated setting. \nTo understand these questions\, we need to describe shape (biomathematics)\, predict shape (biophysics)\, and design shape (bioengineering). \nFor example\, in mathematics there are some beautiful links to Nash’s embedding theorem\,  connections to quasi-conformal geometry\, Ricci flows and geometric PDE\, to Gromov’s h principle\, to geometrical singularities and singular geometries\, discrete and computational differential geometry\, to stochastic geometry and shape characterization (a la Grenander\, Mumford etc.). A nice question here is to use the large datasets (in 4D) and analyze them using ideas from statistical geometry (a la Taylor\, Adler) to look for similarities and differences across species during development\, and across evolution. \nIn physics\, there are questions of generalizing classical theories to include activity\, break the usual Galilean invariance\, as well as isotropy\, frame indifference\, homogeneity\, and create both agent (cell)-based and continuum theories for ordered\, active machines\, linking statistical to continuum mechanics\, and understanding the instabilities and patterns that arise. Active generalizations of liquid crystals\, polar materials\, polymers etc. are only just beginning to be explored and there are some nice physical analogs of biological growth/form that are yet to be studied. \nThe CMSA will be hosting a Workshop on Morphometrics\, Morphogenesis and Mathematics from October 22-24\, 2018 at the Center of Mathematical Sciences and Applications\, located at 20 Garden Street\, Cambridge\, MA. \nThe workshop is organized by L. Mahadevan (Harvard)\, O. Pourquie (Harvard)\, A. Srivastava (Florida). \nVideos of the talks\nConfirmed Speakers:\n\nArkhat Abzhanov\, Imperial College\nSiobhan Braybrook\, UCLA\nCassandra Extavour\, Harvard\nAnjali Goswami\, University College London\nDavid Gu\, Stony Brook\nJukka Jernvall\, Helsinki\nEric Klassen\, Florida State\nSayan Mukherjee\, Duke\nPeter Olver\, U Minnesota\nNipam Patel\, Berkeley\nStephanie Pierce\, Harvard\nKaren Sears\, UCLA\nAlain Trouve\, ENS-Cachan\, France\nLaurent Younes\, Johns Hopkins
URL:https://cmsa.fas.harvard.edu/event/workshop-on-morphometrics-morphogenesis-and-mathematics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180827T090000
DTEND;TZID=America/New_York:20190505T170000
DTSTAMP:20260613T181931
CREATED:20230904T082011Z
LAST-MODIFIED:20250303T193339Z
UID:10000010-1535360400-1557075600@cmsa.fas.harvard.edu
SUMMARY:PROGRAM ON TOPOLOGICAL ASPECTS OF CONDENSED MATTER
DESCRIPTION:During Academic year 2018-19\, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics\, and have highlighted new connections with high energy physics\, mathematics and quantum information theory. Additionally\, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines. \nAs part of the Program\, the CMSA will be hosting two workshops: \n\nWorkshop on Topology and Quantum Phases of Matter (August 27-28\, 2018)\nWorkshop on Topological Aspects of Condensed Matter (September 10-11\, 2019)\n\n. \nAdditionally\, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10. \n\nHere is a partial list of the mathematicians who have indicated that they will attend part or all of this special program\n\n\n\n\n\nName\nTentative Visiting Dates\n\n\n\n\n\nJason Alicea \n\n11/12/2018-11/16/2018\n\n\nMaissam Barkeshli\n4/22/2019 – 4/26/2019\n\n\nXie Chen\n4/15-17/2019 4/19-21/2019 4/24-30/2019\n\n\n\nLukasz Fidkowski \n\n1/7/2019-1/11/2019\n\n\n\nZhengcheng Gu \n\n8/15/2018-8/30/2018 & 5/9/2019-5/19/2019\n\n\n\nYin Chen He \n\n10/14/2018-10/27/2018\n\n\nAnton Kapustin\n8/26/2018-8/30/2018 & 3/28/2019-4/5/2019\n\n\n\nMichael Levin \n\n3/11/2019-3/15/2019\n\n\nYuan-Ming Lu\n4/29/2019-6/01/2019\n\n\n\nAdam Nahum \n\n4/2/2019- 4/19/2019\n\n\n\nMasaki Oshikawa \n\n4/22/2019-5/22/2019\n\n\nChong Wang\n 10/22/2018-11/16/2018\n\n\n\nJuven Wang \n\n4/1/2019-4/16/2019\n\n\nCenke Xu\n 8/26/2018-10/1/2018\n\n\n\nYi-Zhuang You \n\n4/1/2019-4/19/2019\n\n\n\nMike Zaletel \n\n5/1/2019-5/10/2019
URL:https://cmsa.fas.harvard.edu/event/topological-aspects-of-condensed-matter/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180102T090000
DTEND;TZID=America/New_York:20180518T170000
DTSTAMP:20260613T181931
CREATED:20230904T080137Z
LAST-MODIFIED:20250304T172359Z
UID:10000048-1514883600-1526662800@cmsa.fas.harvard.edu
SUMMARY:Simons Collaboration on Homological Mirror Symmetry
DESCRIPTION:The Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving Homological Mirror Symmetry (HMS) in full generality\, and fully exploring its applications. This program is funded by the Simons Foundation. \nMirror symmetry\, which emerged in the late 1980s as an unexpected physical duality between quantum field theories\, has been a major source of progress in mathematics. At the 1994 ICM\, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). \nWe envision that our goal of proving HMS in full generality can be accomplished by combining three main viewpoints: \n\ncategorical algebraic geometry and non-commutative (nc) spaces: in this language\, homological mirror symmetry is the statement that the same nc-spaces can arise either from algebraic geometry or from symplectic geometry.\nthe Strominger-Yau-Zaslow (SYZ) approach\, which provides a global geometric prescription for the construction of mirror pairs.\nLagrangian Floer theory and family Floer cohomology\, which provide a concrete path from symplectic geometry near a given Lagrangian submanifold to an open domain in a mirror analytic space.\n\nThe Center of Mathematical Sciences and Applications is hosting the following short-term visitors for an HMS focused semester: \n\nJacob Bourjaily (Neils Bohr Institute)  4/1/2018 – 4/14/2018\nColin Diemer (IHES)  2/25/2018 – 3/10/2018\nCharles Doran (University of Alberta) 5/13/2018 – 5/25/2018\nBaohua Fu (Chinese Academy of Sciences)  4/15/2018 – 4/28/2018\nAndrew Harder (University of Miami)  4/15/2018 – 4/28/2018\nShinobu Hosono (Gakushuin University) 2/25/2018 – 3/10/2018\nAdam Jacob (UC Davis) 3/5/2018 – 3/16/2018\nTsung-Ju Lee (National Taiwan University) 4/18/2018 – 5/13/2018\nIvan Loseu (Northeastern University) 1/21/2018 – 2/3/2018\nCheuk-Yu Mak (Cambridge University) 4/1/2018 – 4/15/2018\nDaniel Pomerleano (Imperial College) 3/19/2018 – 3/23/2018\nMauricio Romo (Tsinghua University) 4/1/2018 – 4/18/ 2018\nEmanuel Scheidegger (Albert Ludwigs University of Freiburg) 2/22/2018 – 3/22/2018\nDmytro Shklyarov (Technische Universität Chemnitz) 3/4/2018 – 3/17/2018\nAlan Thompson (University of Cambridge) 4/15/2018 – 4/21/2018\nWeiwei Wu (University of Georgia) 4/27/2018 – 5/6/2018\nMatt Young (Chinese University of Hong Kong) 1/15/2018 – 2/9/2018\nJeng-Daw Yu (National Taiwan University) 4/2/2018 – 4/6/2018\nMinxian Zhu (Yau Mathematical Sciences Center\, Tsinghua University) 1/ 22/2018 – 2/25/2018\n\nAs part of their CMSA visitation\, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester.  Click here for information. \n\n\nThe Collaboration will include two workshops hosted by The Center. The workshops will take place January 10-13\, 2018  and April 5-7\, 2018 at CMSA. Click here for more information.
URL:https://cmsa.fas.harvard.edu/event/simons-collaboration-on-homological-mirror-symmetry-2/
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160506T090000
DTEND;TZID=America/New_York:20160508T170000
DTSTAMP:20260613T181931
CREATED:20230831T035136Z
LAST-MODIFIED:20250304T171749Z
UID:10000008-1462525200-1462726800@cmsa.fas.harvard.edu
SUMMARY:The Simons Collaboration Program in Homological Mirror Symmetry
DESCRIPTION:The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry\, Symplectic geometry\, Arithmetic geometry\, Quantum topology and mathematical aspects of high energy physics\, specially string theory with the goal of proving the homological mirror symmetry conjecture (HMS) in full generality and explore its applications. Mirror symmetry\, which emerged in the late 1980s as an unexpected physical duality between quantum field theories\, has been a major source of progress in mathematics. At the 1994 ICM\, Kontsevich reinterpreted mirror symmetry as a deep categorical duality: the HMS conjecture states that the derived category of coherent sheaves of a smooth projective variety is equivalent to the Fukaya category of a mirror symplectic manifold (or Landau-Ginzburg model). We are happy to announce that the Simons Foundation has agreed to renew funding for the HMS collaboration program for three additional years. \nA brief induction of the Brandeis-Harvard CMSA HMS/SYZ research agenda and team members are as follows: \n\nDirectors: \n\nShing-Tung Yau (Harvard University) \nBorn in Canton\, China\, in 1949\, S.-T. Yau grew up in Hong Kong\, and studied in the Chinese University of Hong Kong from 1966 to 1969. He did his PhD at UC Berkeley from 1969 to 1971\, as a student of S.S. Chern. He spent a year as a postdoc at the Institute for Advanced Study in Princeton\, and a year as assistant professor at SUNY at Stony Brook. He joined the faculty at Stanford in 1973. On a Sloan Fellowship\, he spent a semester at the Courant Institute in 1975. He visited UCLA the following year\, and was offered a professorship at UC Berkeley in 1977. He was there for a year\, before returning to Stanford. He was a plenary speaker at the 1978 ICM in Helsinki. The following year\, he became a faculty member at the IAS in Princeton. He moved to UCSD in 1984. Yau came to Harvard in 1987\, and was appointed the Higgins Professor of Mathematics in 1997. He has been at Harvard ever since. Yau has received numerous prestigious awards and honors throughout his career. He was named a California Scientist of the Year in 1979. In 1981\, he received a Oswald Veblen Prize in Geometry and a John J. Carty Award for the Advancement of Science\, and was elected a member of the US National Academy of Sciences. In 1982\, he received a Fields Medal for “his contributions to partial differential equations\, to the Calabi conjecture in algebraic geometry\, to the positive mass conjecture of general relativity theory\, and to real and complex MongeAmpre equations”. He was named Science Digest\, America’s 100 Brightest Scientists under 40\, in 1984. In 1991\, he received a Humboldt Research Award from the Alexander von Humboldt Foundation in Germany. He was awarded a Crafoord Prize in 1994\, a US National Medal of Science in 1997\, and a China International Scientific and Technological Cooperation Award\, for “his outstanding contribution to PRC in aspects of making progress in sciences and technology\, training researchers” in 2003. In 2010\, he received a Wolf Prize in Mathematics\, for “his work in geometric analysis and mathematical physics”. Yau has also received a number of research fellowships\, which include a Sloan Fellowship in 1975-1976\, a Guggenheim Fellowship in 1982\, and a MacArthur Fellowship in 1984-1985. Yau’s research interests include differential and algebraic geometry\, topology\, and mathematical physics. As a graduate student\, he started to work on geometry of manifolds with negative curvature. He later became interested in developing the subject of geometric analysis\, and applying the theory of nonlinear partial differential equations to solve problems in geometry\, topology\, and physics. His work in this direction include constructions of minimal submanifolds\, harmonic maps\, and canonical metrics on manifolds. The most notable\, and probably the most influential of this\, was his solution of the Calabi conjecture on Ricci flat metrics\, and the existence of Kahler-Einstein metrics. He has also succeeded in applying his theory to solve a number of outstanding conjectures in algebraic geometry\, including Chern number inequalities\, and the rigidity of complex structures of complex projective spaces. Yau’s solution to the Calabi conjecture has been remarkably influential in mathematical physics over the last 30 years\, through the creation of the theory of Calabi-Yau manifolds\, a theory central to mirror symmetry. He and a team of outstanding mathematicians trained by him\, have developed many important tools and concepts in CY geometry and mirror symmetry\, which have led to significant progress in deformation theory\, and on outstanding problems in enumerative geometry. Lian\, Yau and his postdocs have developed a systematic approach to study and compute period integrals of CY and general type manifolds. Lian\, Liu and Yau (independently by Givental) gave a proof of the counting formula of Candelas et al for worldsheet instantons on the quintic threefold. In the course of understanding mirror symmetry\, Strominger\, Yau\, and Zaslow proposed a new geometric construction of mirror symmetry\, now known as the SYZ construction. This has inspired a rapid development in CY geometry over the last two decades. In addition to CY geometry and mirror symmetry\, Yau has done influential work on nonlinear partial differential equations\, generalized geometry\, Kahler geometry\, and general relativity. His proof of positive mass conjecture is a widely regarded as a cornerstone in the classical theory of general relativity. In addition to publishing well over 350 research papers\, Yau has trained more than 60 PhD students in a broad range of fields\, and mentored dozens of postdoctoral fellows over the last 40 years. \n\nProfessor Bong Lian (Brandeis University) \nBorn in Malaysia in 1962\, Bong Lian completed his PhD in physics at Yale University under the direction of G. Zuckerman in 1991. He joined the permanent faculty at Brandeis University in 1995\, and has remained there since. Between 1995 and 2013\, he had had visiting research positions at numerous places\, including the National University of Taiwan\, Harvard University\, and Tsinghua University. Lian received a J.S. Guggenheim Fellowship in 2003. He was awarded a Chern Prize at the ICCM in Taipei in 2013\, for his “influential and fundamental contributions in mathematical physics\, in particular in the theory of vertex algebras and mirror symmetry.” He has also been co-Director\, since 2014\, of the Tsinghua Mathcamp\, a summer outreach program launched by him and Yau for mathematically talented teenagers in China. Since 2008\, Lian has been the President of the International Science Foundation of Cambridge\, a non-profit whose stated mission is “to provide financial and logistical support to scholars and universities\, to promote basic research and education in mathematical sciences\, especially in the Far East.” Over the last 20 years\, he has mentored a number of postdocs and PhD students. His research has been supported by an NSF Focused Research Grant since 2009. Published in well over 60 papers over 25 years\, Lian’s mathematical work lies in the interface between representation theory\, Calabi-Yau geometry\, and string theory. Beginning in the late 80’s\, Lian\, jointly with Zuckerman\, developed the theory of semi-infinite cohomology and applied it to problems in string theory. In 1994\, he constructed a new invariant (now known as the Lian- Zuckerman algebra) of a topological vertex algebra\, and conjectured the first example of a G algebra in vertex algebra theory. The invariant has later inspired a new construction of quantum groups by I. Frenkel and A. Zeitlin\, as semi-infinite cohomology of braided vertex algebras\, and led to a more recent discovery of new relationships between Courant algebroids\, A-algebras\, operads\, and deformation theory of BV algebras. In 2010\, he and his students Linshaw and Song developed important applications of vertex algebras in equivariant topology. Lian’s work in CY geometry and mirror symmetry began in early 90’s. Using a characteristic p version of higher order Schwarzian equations\, Lian and Yau gave an elementary proof that the instanton formula of Candelas et al implies Clemens’s divisibility conjecture for the quintic threefold\, for infinitely many degrees. In 1996\, Lian (jointly with Hosono and Yau) answered the so-called Large Complex Structure Limit problem in the affirmative in many important cases. Around the same year\, they announced their hyperplane conjecture\, which gives a general formula for period integrals for a large class of CY manifolds\, extending the formula of Candelas et al. Soon after\, Lian\, Liu and Yau (independently by Givental) gave a proof of the counting formula. In 2003\, inspired by mirror symmetry\, Lian (jointly with Hosono\, Oguiso and Yau) discovered an explicit counting formula for Fourier-Mukai partners\, and settled an old problem of Shioda on abelian and K3 surfaces. Between 2009 and 2014\, Lian (jointly with Bloch\, Chen\, Huang\, Song\, Srinivas\, Yau\, and Zhu) developed an entirely new approach to study the so-called Riemann-Hilbert problem for period integrals of CY manifolds\, and extended it to general type manifolds. The approach leads to an explicit description of differential systems for period integrals with many applications. In particular\, he answered an old question in physics on the completeness of Picard-Fuchs systems\, and constructed new differential zeros of hypergeometric functions. \n\nDenis Auroux (Harvard University) \nDenis Auroux’s research concerns symplectic geometry and its applications to mirror symmetry. While his early work primarily concerned the topology of symplectic 4-manifolds\, over the past decade Auroux has obtained pioneering results on homological mirror symmetry outside of the Calabi-Yau setting (for Fano varieties\, open Riemann surfaces\, etc.)\, and developed an extension of the SYZ approach to non-Calabi-Yau spaces.After obtaining his PhD in 1999 from Ecole Polytechnique (France)\, Auroux was employed as Chargé de Recherche at CNRS and CLE Moore Instructor at MIT\, before joining the faculty at MIT in 2002 (as Assistant Professor from 2002 to 2004\, and as Associate Professor from 2004 to 2009\, with tenure starting in 2006). He then moved to UC Berkeley as a Full Professor in 2009.\nAuroux has published over 30 peer-reviewed articles\, including several in top journals\, and given 260 invited presentations about his work. He received an Alfred P. Sloan Research Fellowship in 2005\, was an invited speaker at the 2010 International Congress of Mathematicians\, and in 2014 he was one of the two inaugural recipients of the Poincaré Chair at IHP. He has supervised 10 PhD dissertations\, won teaching awards at MIT and Berkeley\, and participated in the organization of over 20 workshops and conferences in symplectic geometry and mirror symmetry.\n\n \n\n\n\nSenior Personnel: \n\nArtan Sheshmani (Harvard CMSA) \nArtan Sheshmani’s research is focused on enumerative algebraic geometry and mathematical aspects of string theory. He is interested in applying techniques in algebraic geometry\, such as\, intersection theory\, derived category theory\, and derived algebraic geometry to construct and compute the deformation invariants of algebraic varieties\, in particular Gromov-Witten (GW) or Donaldson-Thomas (DT) invariants. In the past Professor Sheshmani has worked on proving modularity property of certain DT invariants of K3-fibered threefolds (as well as their closely related Pandharipande-Thomas (PT) invariants)\, local surface threefolds\, and general complete intersection Calabi-Yau threefolds. The modularity of DT/PT invariants in this context is predicted in a famous conjecture of  string theory called S-duality modularity conjecture\, and his joint work has provided the proof to some cases of it\, using degenerations\, virtual localizations\, as well as wallcrossing techniques. Recently\, Sheshmani has focused on proving a series of dualities relating the various enumerative invariants over threefolds\, notably the GW invariants and invariants that arise in topological gauge theory. In particular in his joint work with Gholampour\, Gukov\, Liu\, Yau he studied DT gauge theory and its reductions to D=4 and D=2 which are equivalent to local theory of surfaces in Calabi-Yau threefolds. Moreover\, in a recent joint work with Yau and Diaconescu\, he has studied the construction and computation of DT invariants of Calabi-Yau fourfolds via a suitable derived categorical reduction of the theory to the DT theory of threefolds. Currently Sheshmani is interested in a wide range of problems in enumerative geometry of CY varieties in dimensions 3\,4\,5. \nArtan has received his PhD and Master’s degrees in pure mathematics under Sheldon Katz and Thomas Nevins from the University of Illinois at Urbana Champaign (USA) in 2011 and 2008 respectively. He holds a Master’s degree in Solid Mechanics (2004) and two Bachelor’s degrees\, in Mechanical Engineering and Civil Engineering from the Sharif University of Technology\, Tehran\, Iran.  Artan has been a tenured Associate Professor of Mathematics with joint affiliation at Harvard CMSA and center for Quantum Geometry of Moduli Spaces (QGM)\, since 2016. Before that he has held visiting Associate Professor and visiting Assistant Professor positions at MIT. \nAn Huang (Brandeis University) \nThe research of An Huang since 2011 has been focused on the interplay between algebraic geometry\, the theory of special functions and mirror symmetry. With S. Bloch\, B. Lian\, V. Srinivas\, S.-T. Yau\, X. Zhu\, he has developed the theory of tautological systems\, and has applied it to settle several important problems concerning period integrals in relation to mirror symmetry. With B. Lian and X. Zhu\, he has given a precise geometric interpretation of all solutions to GKZ systems associated to Calabi-Yau hypersurfaces in smooth Fano toric varieties. With B. Lian\, S.-T. Yau\, and C.-L. Yu\, he has proved a conjecture of Vlasenko concerning an explicit formula for unit roots of the zeta functions of hypersurfaces\, and has further related these roots to p-adic interpolations of complex period integrals. Beginning in 2018\, with B. Stoica and S.-T. Yau\, he has initiated the study of p-adic strings in curved spacetime\, and showed that general relativity is a consequence of the self-consistency of quantum p-adic strings. One of the goals of this study is to understand p-adic A and B models. \nAn Huang received his PhD in Mathematics from the University of California at Berkeley in 2011. He was a postdoctoral fellow at the Harvard University Mathematics Department\, and joined Brandeis University as an Assistant Professor in Mathematics in 2016.\n\n\n\nSiu Cheong Lau (Boston University) \nThe research interest of Siu Cheong Lau lies in SYZ mirror symmetry\, symplectic and algebraic geometry.  His thesis work has successfully constructed the SYZ mirrors for all toric Calabi-Yau manifolds based on quantum corrections by open Gromov-Witten invariants and their wall-crossing phenomenon.  In collaboration with N.C. Leung\, H.H. Tseng and K. Chan\, he derived explicit formulas for the open Gromov-Witten invariants for semi-Fano toric manifolds which have an obstructed moduli theory.  It has a beautiful relation with mirror maps and Seidel representations.   Recently he works on a local-to-global approach to SYZ mirror symmetry.  In joint works with C.H. Cho and H. Hong\, he developed a noncommutative local mirror construction for immersed Lagrangians\, and a natural gluing method to construct global mirrors.  The construction has been realized in various types of geometries including orbifolds\, focus-focus singularities and pair-of-pants decompositions of Riemann surfaces. \nSiu-Cheong Lau has received the Doctoral Thesis Gold Award (2012) and the Best Paper Silver Award (2017) at the International Congress of Chinese Mathematicians.  He was awarded the Simons Collaboration Grant in 2018.  He received a Certificate of Teaching Excellence from Harvard University in 2014. \n\nAffiliates: \n\nNetanel Rubin-Blaier (Cambridge)\nKwokwai Chan (Chinese University of Hong Kong)\nMandy Cheung (Harvard University\, BP)\nChuck Doran (University of Alberta)\nHansol Hong (Yonsei University)\nShinobu Hosono (Gakushuin University\, Japan)\nConan Leung (Chinese University of Hong Kong)\nYu-Shen Lin (Boston University)\nHossein Movassati (IMPA Brazil)\nArnav Tripathhy (Harvard University\, BP)\n\n  \nPostdocs: \n\nDennis Borisov\nTsung-Ju Lee\nDingxin Zhang\nJingyu Zhao\nYang Zhou\n\n  \nTo learn about previous programming as part of the Simons Collaboration\, click here.
URL:https://cmsa.fas.harvard.edu/event/the-simons-collaboration-in-homological-mirror-symmetry/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20160201
DTEND;VALUE=DATE:20161231
DTSTAMP:20260613T181931
CREATED:20230904T081643Z
LAST-MODIFIED:20250328T145717Z
UID:10000052-1454284800-1483142399@cmsa.fas.harvard.edu
SUMMARY:Nonlinear Equations Program
DESCRIPTION:  \nMost physical phenomena\, from the gravitating universe to fluid dynamics\, are modeled on nonlinear differential equations. The subject also makes close connections with other branches of mathematics. In particular\, some of the deepest results in complex geometry and topology were obtained through solutions of nonlinear equations. \nThe subject underwent rapid developments in the last century and foundational results were established. Compared to linear equations\, the difficulty of solving nonlinear equations is of a different order of magnitude and the methods employed in solving them are also much more diversified. To this date\, it is an active field with recent exciting discoveries and renewed interests\, and several long standing problems seem to be within reach. The special year aims to spur activity in this subject\, to provide a natural setting for the most cutting edge results to be communicated\, and to facilitate interaction among researchers of different backgrounds. \nDuring the year\, there will be two weekly seminar programs.  Each program participants will be asked to give a talk on geometric analysis\, or the evolution of equations\, hyperbolic equations\, and fluid dynamics.    \nSeminar on Geometric Analysis \nSeminar on Evolution Equations \nSeminar on General Relativity \nConcluding Conference on Nonlinear Equations Program \nMini-School on Nonlinear Equations\, Dec. 2016 \nHere is a partial list of the mathematicians who have indicated that they will attend part or all of this special program \n\n\n\n\n\n\nName\nHome Institution\nTentative Visiting Dates\n\n\n\n\nStefano Bianchini\nSISSA\n04/01/2016 – 05/31/2016\n\n\nLydia Bieri\nUniversity of Michigan\n02/01/2016 – 04/30/2016\n\n\nAlbert Chau\nUniversity of British Columbia\n02/26/2016 – 05/26/2016\n\n\nBinglong Chen\nSun Yat-sen University\n09/01/2015 – 11/30/2015\n\n\nQingtao Chen\nETHZ (Swiss Federal Institute of Technology in Zurich)\n03/17/2016 – 04/04/2016\n\n\nPiotr Chrusciel\nUniversity of Vienna\n03/01/2016 – 05/30/2016\n\n\nFernando Coda Marques\nPrinceton University\n04/25/2016 – 04/29/2016 05/23/2016 – 05/27/2016\n\n\nMihalis Dafermos\nPrinceton University\n04/01/2016 – 04/30/2016\n\n\nCamillo De Lellis\nUniversity of Zurich\n02/01/2016 – 4/30/2016\n\n\nMichael Eichmair\nUniversity of Vienna\n03/21/2016 – 04/01/2016\n\n\nFelix Finster\nUniversitat Regensburg\n09/20/2015 – 10/20/2015 03/20/2016 – 04/20/2016\n\n\nXianfeng David Gu\nSUNY at Stony Brook\n04/01/2016 – 04/30/2016\n\n\nZheng-Cheng Gu\nPerimeter Institute for Theoretical Physics\n08/15/2015 – 09/15/2015\n\n\nPengfei Guan\nMcGill University\n10/10/2015 – 10/17/2015\n\n\nXiaoli Han\nTsinghua University\n01/20/2016 – 04/19/2016\n\n\nThomas Hou\nCalifornia Institute of Technology\n11/01/2016 – 11/30/2016\n\n\nFeimin Huang\nChinese Academy of Sciences\n02/15/2016 – 04/15/2016\n\n\nXiangdi Huang\nChinese Academy of Sciences\n09/10/2015 – 12/10/2015\n\n\nTom Ilmanen\nETH Zurich\n10/19/2015 – 12/18/2015\n\n\nNiky Kamran\nMcGill Univeristy\n04/04/2016 – 04/08/2016\n\n\nNicolai Krylov\nUniversity of Minnesota\n11/01/2015 – 11/30/2015\n\n\nJunbin Li\nSun Yat-sen University\n02/01/2016 – 04/30/2016\n\n\nYong Lin\nRenmin University of China\n02/01/2016 – 03/31/2016\n\n\nAndre Neves\nImperial College London\n4/25/2016 – 4/29/2016; 5/23/2016 – 5/27/2016\n\n\nDuong H. Phong\nColumbia University\n04/08/2016 – 04/10/2016\n\n\nOvidiu Savin\nColumbia University\n10/15/2015 – 12/14/2015\n\n\nRichard Schoen\nStanford University\n03/21/2016 – 03/25/2016\n\n\nMao Sheng\nUniversity of Science and Technology of China\n01/15/2016 – 01/28/2016\n\n\nValentino Tosatti\nNorthwestern University\n02/01/2016 – 04/15/2016\n\n\nJohn Toth\nMcGill University\n04/04/2016 – 04/08/2016\n\n\nChung-Jun Tsai\nNational Taiwan University\n05/01/2016 – 05/08/2016\n\n\nTai-Peng Tsai\nUniversity of British Columbia\n03/20/2016 – 05/31/2016\n\n\nLi-Sheng Tseng\nUC Irvine\n02/08/2016 – 02/19/2016; 04/27/2016 – 05/11/2016\n\n\nChun Peng Wang\nJilin University\n02/01/2016 – 04/30/2016\n\n\nXu-Jia Wang\nAustralian National University\n04/01/2016 – 05/31/2016\n\n\nBen Weinkove\nNorthwestern University\n02/28/2016 – 03/18/2016\n\n\nSijue Wu\nUniversity of Michigan\n04/01/2016 – 04/30/2016\n\n\nChunjing Xie\nShanghai Jiao Tong University\n09/08/2015 – 12/07/2015\n\n\nZhou Ping Xin\nThe Chinese University of Hong Kong\n10/01/2015 – 11/30/2015\n\n\nHongwei Xu\nZhejiang University\n09/01/2015 – 11/30/2015\n\n\nPeng Ye\nUniversity of Illinois at Urbana-Champaign\n11/15/2015 – 11/22/2015\n\n\nPin Yu\nTshinghua University\n09/07/2015 – 12/10/2015\n\n\nYi Zhang\nFudan University\n01/18/2016 – 05/31/2016
URL:https://cmsa.fas.harvard.edu/event/nonlinear-equations-program/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Event,Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150817T140000
DTEND;TZID=America/New_York:20150817T170000
DTSTAMP:20260613T181931
CREATED:20230904T081317Z
LAST-MODIFIED:20250305T171843Z
UID:10000050-1439820000-1439830800@cmsa.fas.harvard.edu
SUMMARY:GAMES ON HETEROGENEOUS GRAPHS
DESCRIPTION:A major challenge in evolutionary biology is to understand how spatial population structure affects the evolution of social behaviors such as\ncooperation. This question can be investigated mathematically by studying evolutionary processes on graphs. Individuals occupy vertices and interact with neighbors according to a matrix game. Births and deaths occur stochastically according to an update rule. Previously\, full mathematical results have only been obtained for graphs with strong symmetry properties. Our group is working to extend these results to certain classes of asymmetric graphs\, using tools such as random walk theory and harmonic analysis. \n \n\n\n  \nHere is a list of the scholars participating in this program. \n\n\n\n\nName\n\n\n\n\nShing-Tung Yau\n\n\nMartin Nowak\n\n\nBen Adlam\n\n\nBen Allen\n\n\nYu-Ting Chen\n\n\nAn Huang\n\n\nGabor Lippner
URL:https://cmsa.fas.harvard.edu/event/games-on-heterogeneous-graphs/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Programs,Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150102T090000
DTEND;TZID=America/New_York:20151231T170000
DTSTAMP:20260613T181931
CREATED:20230904T081503Z
LAST-MODIFIED:20250228T180655Z
UID:10000051-1420189200-1451581200@cmsa.fas.harvard.edu
SUMMARY:MATH-PHYSICS PROGRAM
DESCRIPTION:In the past thirty years there have been deep interactions between mathematics and theoretical physics which have tremendously enhanced both subjects. The focal points of these interactions include string theory\, general relativity\, and quantum many-body theory. \nString theory has been at the center of the ongoing effort to uncover the fundamental principles of nature and in particular to unify Einstein’s geometric theory of gravity with quantum theory. The development of this field has sparked a historically unprecedented synergy between mathematics and physics. Progress at the forefront of theoretical physics has relied crucially on very recent developments in pure mathematics. At the same time insights from physics have led to both new branches of pure mathematics as well as dramatic progress in old branches. \nSeveral examples from the recent past exemplifying this synergy include the prediction from string theory of mirror symmetry\, a highly unexpected mathematical equivalence between distinct pairs of Calabi-Yau manifolds. This fueled exciting developments in algebraic\, enumerative and symplectic geometry. At the same time the realization of string theory as a phenomenologically viable physical theory depends crucially on detailed mathematical properties of these manifolds. In Einstein’s theory of general relativity the proofs of the positive energy theorem and the stability of flat spacetime were accompanied by fundamental new results in functional analysis\, differential geometry and minimal surface theory. In the coming decades we expect many more important discoveries to arise from the interface of mathematics and physics. The Cheng Fund will foster these efforts. \n\n\nHere is a partial list of the mathematicians who have indicated that they will attend part or all of this special program \n\n\n\n\nName\nTentative Visiting Dates\n\n\n\n\nPo-Ning Chen\n2/1/15-4/30/15\n\n\nHong-Jian He\n3/5/15-5/5/15\n\n\nMonica Guica\n12/1/14-3/15/15\n\n\nAmer Iqbal\n1/8/15-4/8/15\n\n\nSuvrat Raju\n2/25/15-5/25/15\n\n\nMithat Ünsal\n9/1/15-12/31/15
URL:https://cmsa.fas.harvard.edu/event/math-physics-program/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141117T090000
DTEND;TZID=America/New_York:20141218T170000
DTSTAMP:20260613T181931
CREATED:20230904T081818Z
LAST-MODIFIED:20250402T182846Z
UID:10000012-1416214800-1418922000@cmsa.fas.harvard.edu
SUMMARY:Random Matrix Program
DESCRIPTION:Large random matrices provide some of the simplest models for large\, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality\, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a rigorous understanding of universality in the case of orthogonal\, Hermitian\, or symplectic matrices with independent entries\, resolving a conjecture of Wigner-Dyson-Mehta dating back 50 years. These new developments have exploited techniques from a wide range of mathematical areas in addition to probability\, including combinatorics\, partial differential equations\, and hydrodynamic limits. It is hoped that these new techniques will be useful in the analysis of universal behaviour in matrix ensembles with more complicated structure such as random regular graph models\, or 2D matrix ensembles\, as well as more physically relevant systems such as band matrices and random Schroedinger-type Hamiltonians. For some of these models\, results in the direction of universality have already been obtained. \n\n\nHere is a partial list of the mathematicians who are participating in this program. \n\n\n\n\nName\n\n\n\n\nHorng-Tzer Yau\n\n\nQian Lin\n\n\nRoland Bauerschmidt\n\n\nMiika Nikula\n\n\nYu-Ting Chen\n\n\nBen Landon\n\n\nYuchen Pei\n\n\nPhilippe Sosoe
URL:https://cmsa.fas.harvard.edu/event/random-matrix-program/
CATEGORIES:Programs
END:VEVENT
END:VCALENDAR