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DTSTART;TZID=America/New_York:20260427T090000
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UID:10003757-1777280400-1777654800@cmsa.fas.harvard.edu
SUMMARY:Mathematics and Biology II: Mathematics and Science of Behavior
DESCRIPTION:Mathematics and Biology II: Mathematics and Science of Behavior \nDates: April 27 – May 1\, 2026 \nLocation: Harvard CMSA\, Room G10\, 20 Garden Street\, Cambridge MA \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) \nRegister to attend in-person \n  \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  \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 \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 \n3:15–4:30 pm: Discussion \n4:30–5:30 pm: CMSA Colloquium: Ofer Feinerman\, Weizmann Institute of Science \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: Towards fly-inspired legged robots\nAbstract: I will discuss our efforts to build biologically-inspired legged robots using behavioral measurements\, neuromechanical simulations\, and anatomical studies of Drosophila melanogaster. \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 \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. \n3:15–4:30 pm: Discussion \n  \nFriday\, May 1\, 2026 \n9:00–9:30 am: Breakfast \n9:30–10:15 am: 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. \n10:15–10:30 am: Discussion \n10:30–11:00 am: Tea Break \n11:00–11:45 am: Kirstin Petersen\, Cornell University\nTitle: Harnessing Embodied Intelligence in Robot Collectives\nAbstract: In the Collective Embodied Intelligence Lab\, we study embodied intelligence as a complement to artificial intelligence in robot collectives. Our work spans scales and mechanisms\, from behaviors encoded in robot morphology to collective behaviors that emerge through physical coupling and stigmergic coordination when many robots operate in shared environments. Many of these principles are inspired by biological systems\, including our studies of construction and aggregation in honeybees and subterranean and mound-building termites. In this talk\, I will present examples from our lab\, including soft robots that exploit viscous fluid–structure interactions for articulated control\, microrobots that leverage magnetic and hydrodynamic interactions to produce a range of collective behaviors\, and entangled robotic matter that achieves cohesive motion through transient physical entanglement. Together\, these systems illustrate how intelligence can be distributed across morphology\, interactions\, and shared substrates\, enabling scalable and robust robot collectives. \n11:45 am–12:00 pm: Discussion \n12:00–1:30 pm: Catered Lunch \n1:30–4:30 pm: Discussion \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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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260501T120000
DTEND;TZID=America/New_York:20260501T130000
DTSTAMP:20260416T101706
CREATED:20260212T190507Z
LAST-MODIFIED:20260212T190507Z
UID:10003908-1777636800-1777640400@cmsa.fas.harvard.edu
SUMMARY:Member Seminar
DESCRIPTION:Member Seminar \nSpeaker: tba
URL:https://cmsa.fas.harvard.edu/event/member-seminar-5126/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260504T150000
DTEND;TZID=America/New_York:20260504T160000
DTSTAMP:20260416T101706
CREATED:20260126T190454Z
LAST-MODIFIED:20260126T190454Z
UID:10003880-1777906800-1777910400@cmsa.fas.harvard.edu
SUMMARY:Quantum Field Theory and Physical Mathematics
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Surya Raghaven\, Yale University
URL:https://cmsa.fas.harvard.edu/event/qft_5426/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260504T163000
DTEND;TZID=America/New_York:20260504T173000
DTSTAMP:20260416T101706
CREATED:20260323T160718Z
LAST-MODIFIED:20260323T160748Z
UID:10003923-1777912200-1777915800@cmsa.fas.harvard.edu
SUMMARY:Colloquium
DESCRIPTION:Colloquium \nSpeaker: Nikita Nekrasov\, Simons Center \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium-5426/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260511T150000
DTEND;TZID=America/New_York:20260511T160000
DTSTAMP:20260416T101706
CREATED:20260409T140454Z
LAST-MODIFIED:20260409T140554Z
UID:10003931-1778511600-1778515200@cmsa.fas.harvard.edu
SUMMARY:Quantum Field Theory and Physical Mathematics
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \n 
URL:https://cmsa.fas.harvard.edu/event/qft_51126/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260511T163000
DTEND;TZID=America/New_York:20260511T173000
DTSTAMP:20260416T101706
CREATED:20251223T190403Z
LAST-MODIFIED:20260409T200727Z
UID:10003848-1778517000-1778520600@cmsa.fas.harvard.edu
SUMMARY:Statistical Shape Analysis of Complex Natural Structures
DESCRIPTION:Colloquium \nSpeaker: Anuj Srivastava\, Johns Hopkins University \nTitle: Statistical Shape Analysis of Complex Natural Structures \nAbstract: Statistical modeling and analysis of structured data is a fast-growing field in Statistics and Data Science. Rapid advances in imaging techniques have led to tremendous amounts of data for analyzing imaged objects across several scientific disciplines. Examples include shapes of cancer cells\, botanical trees\, human biometrics\, 3D genome\, brain anatomical structures\, crowd videos\, nano-manufacturing\, and so on. Shapes are relevant even in non-imaging data contexts\, e.g.\, the shapes of COVID rate curves or the shapes of activity cycles in lifestyle data. Imposing statistical models and inferences on shapes seems daunting because the shape is an abstract notion and one requires precise mathematical representations to quantify shapes. This talk has two parts. In the first part\, I will present some recent developments in “elastic representations” of structures such as functions\, curves\, surfaces\, and graphs. In the second part\, I will focus on statistical analyses: computing shape summaries\, estimation under shape constraints\, hypothesis testing\, time-series models\, and regression models involving shapes. \n 
URL:https://cmsa.fas.harvard.edu/event/colloquium-51126/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260514T160000
DTEND;TZID=America/New_York:20260514T170000
DTSTAMP:20260416T101706
CREATED:20260330T154547Z
LAST-MODIFIED:20260330T154547Z
UID:10003926-1778774400-1778778000@cmsa.fas.harvard.edu
SUMMARY:Algebra Seminar
DESCRIPTION:Algebra Seminar \nSpeaker: Aryaman Maithani\, University of Utah \nTitle/Abstract: TBA
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_51426/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260518T090000
DTEND;TZID=America/New_York:20260522T170000
DTSTAMP:20260416T101707
CREATED:20250623T220157Z
LAST-MODIFIED:20260413T141957Z
UID:10003754-1779094800-1779469200@cmsa.fas.harvard.edu
SUMMARY:Workshop on Calabi-Yau metrics and optimal transport
DESCRIPTION:Workshop on Calabi-Yau metrics and optimal transport \nDates: May 18–22\, 2026 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge MA \nRecent advances in the study of Calabi-Yau metrics have revealed an interesting connection with optimal transport\, and the regularity theory for optimal transport is expected to play an increasingly important role in the study of Kähler geometry. The goal of this workshop is to bring together the optimal transport and complex geometry communities to investigate problems arising from these exciting developments. \nLimited support may be available for approved postdocs and early career applicants. The application form can be found at: https://forms.gle/1zxTEKhZyz4TPfSY6 \n  \nRegister to attend in-person \nRegister for Zoom Webinar \n  \nMinicourse Speakers \n\nRobert McCann\, University of Toronto\nYang Li\, Cambridge University\n\nWorkshop Speakers \n\nRolf Andreasson\, Chalmers University\, Sweden\nBenjy Firester\, MIT\nJakob Hultgren\, Umea University\, Sweden\nYoung-Heon Kim\, University of British Columbia\nNam Le\, Indiana University\nJiakun Liu\, University of Sydney\nDuong H. Phong\, Columbia University\nArghya Rakshit\, University of Toronto\nGabor Szekelyhidi\, Northwestern University\nYueqiao Wu\, Johns Hopkins University\n\nOrganizers: \n\nTristan Collins\, University of Toronto\nMattias Jonsson\, University of Michigan\nConnor Mooney\, University of California\, Irvine\nFreid Tong\, University of Toronto\n\n  \n  \nSchedule (subject to change) \nMonday\, May 18\, 2026 \n9:00–9:30 am\nBreakfast \n9:30–10:45 am\nTutorial: Yang Li\, Cambridge University (via Zoom Webinar) \n10:45–11:15 am\nBreak \n11:15 am–12:30 pm\nTutorial: Robert McCann\, University of Toronto\nTitle: A geometric approach to apriori estimates for optimal transport maps\nAbstract: A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma-Trudinger-Wang condition is the Pogorelov second derivative bound. This translates to an a priori interior modulus of the differential estimate for smooth optimal maps. We describe a new derivation of this estimate with Brendle\, Leger and Rankin which relies in part on Kim\, McCann\, and Warren’s observation that the graph of an optimal map becomes a volume maximizing non-timelike submanifold when the product of the source and target domains is endowed with a suitable pseudo-Riemannian geometry that combines both the marginal densities and the cost. This unexpected links optimal transport to the plateau problem in geometry with split signature\, and shows the key difficulty is showing the maximizing non-timelike submanifold is in fact (uniformly) spacelike. J. Reine Angew. Math. 817 (2024) 251-266 doi.org/10.1515/crelle-2024-0071 arXiv 2311.10208 \n12:30–2:00 pm\nLunch (catered) \n2:00–3:15 pm\nTalk: Nam Le\, Indiana University\nTitle: Variational approach to degenerate Monge-Ampère equations with mixed measures and monotonicity\nAbstract: In this talk\, we will discuss the solvability and uniqueness for several degenerate Monge-Ampère equations including the Monge-Ampère eigenvalue problem in real Euclidean spaces that involve singular Borel measures. Our approach systematically analyzes the Monge-Ampère energy from the variational point of view and appropriately exploits monotonicity arguments. We will examine several essential tools: the mixed Monge-Ampère measure\, Aleksandrov-Blocki-Jerison type maximum principles\, convex envelope\, comparison principles for subcritical equations\, and integration by parts whose failure leads to symmetry breaking and nonuniqueness phenomena. \n3:15–3:45 pm\nBreak \n3:45–5:00 pm\nTalk: Yueqiao Wu\, Johns Hopkins University \n  \nTuesday\, May 19\, 2026 \n9:00–9:30 am\nBreakfast \n9:30–10:45 am\nTutorial: Robert McCann\, University of Toronto\nTitle: Trading linearity for ellipticity: A low regularity Lorentzian splitting theorem\nAbstract: While Einstein’s theory of gravity is formulated in a smooth setting\, the celebrated singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. It is thus of great interest to study the theory in low regularity settings. In the lecture\, we establish a low regularity splitting theorem by sacrificing linearity of the d’Alembertian to recover ellipticity. We exploit a negative homogeneity $p$-d’Alembert operator for this purpose. The same technique yields a simplified proof of Eschenberg (1988) Galloway (1989) and Newman’s (1990) confirmation of Yau’s (1982) conjecture\, bringing all three Lorentzian splitting results into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry. Based on joint work with Mathias Braun\, Nicola Gigli\, Argam Ohanyan\, and Clemens Saemann: 1) arXiv 2501.00702 2) arXiv 2408.15968 3) arXiv 2410.12632 4) arXiv 2507.06836 \n10:45–11:15 am\nBreak \n11:15 am–12:30 pm\nTutorial: Yang Li\, Cambridge University (via Zoom Webinar) \n12:30–2:00 pm\nLunch Break \n2:00–3:15 pm\nTalk: Young-Heon Kim\, University of British Columbia \n3:15–3:45 pm\nBreak \n3:45–5:00 pm\nTalk: Duong Phong\, Columbia University \n6:30 pm\nDinner \n  \nWednesday\, May 20\, 2026 \n9:00–9:30 am\nBreakfast \n9:30–10:45 am\nTutorial: Yang Li\, Cambridge University (via Zoom Webinar) \n10:45–11:15 am\nBreak \n11:15 am–12:30 pm\nTutorial: Robert McCann\, University of Toronto\nTitle: The monopolist’s free boundary problem in the plane: an excursion into the economic value of private information\nAbstract: The principal-agent problem is an important paradigm in economic theory for studying the value of private information: the nonlinear pricing problem faced by a monopolist is one example; others include optimal taxation and auction design. For multidimensional spaces of consumers (i.e. agents) and products\, Rochet and Chone (1998) reformulated this problem as a concave maximization over the set of convex functions\, by assuming agent preferences are bilinear in the product and agent parameters. This optimization corresponds mathematically to a convexity-constrained obstacle problem. The solution is divided into multiple regions\, according to the rank of the Hessian of the optimizer.\nIf the monopolists costs grow quadratically with the product type we show that a partially smooth free boundary delineates the region where it becomes efficient to customize products for individual buyers. We give the first complete solution of the problem on square domains\, and discover new transitions from unbunched to targeted and from targeted to blunt bunching as market conditions become more and more favorable to the seller.\nBased on works with Kelvin Shuangjian Zhang\, Cale Rankin\, and Lucas O’Brien in various combinations:\n1) Math. Models Methods Appl. Sci. 34 (2024) 2351-2394; 2) J. Convex Anal. (Rockafellar 90 Issue)\, 32 (2) (2025) 579-584; 3) arXiv 2303.04937; 4) arxiv 2412.15505; 5) arXiv 2603.14100. \n  \nThursday\, May 21\, 2026 \n9:00–9:30 am\nBreakfast \n9:30–10:45 am\nTalk: Gabor Szekelyhidi\, Northwestern University \n10:45–11:15 am\nBreak \n11:15 am–12:30 pm\nTalk: Rolf Andreasson\, Chalmers University\, Sweden \n12:30–2:00 pm\nLunch Break \n2:00–3:15 pm\nTalk: Jakob Hultgren\, Umea University\, Sweden \n3:15–3:45 pm\nBreak \n3:45–5:00 pm\nTalk: Benjy Firester\, MIT \n  \nFriday\, May 22\, 2026 \n9:00–9:30 am\nBreakfast \n9:30–10:45 am\nTalk: Jiakun Liu\, University of Sydney\nTitle: Free boundary problems in optimal transportation\nAbstract: In this talk\, I will present some recent results on the regularity of free boundaries in optimal transportation\, including higher-order regularity\, global regularity\, and a model case involving multiple targets. These results are based on a series of joint works with Shibing Chen\, Xianduo Wang\, and Xu-Jia Wang. \n10:45–11:15 am\nBreak \n11:15 am–12:30 pm\nTalk: Arghya Rakshit\, University of Toronto\nTitle: Solutions to the Monge–Ampère equation with singular structures\nAbstract: We construct examples of solutions to the Monge–Ampère equation with point masses exhibiting polyhedral singular structures. We further analyze the stability of these singular sets under small perturbations of the data. In addition\, we construct solutions whose Monge–Ampère measure contains a singular component supported on lower-dimensional sets and we study the regularity of such solutions. \n 
URL:https://cmsa.fas.harvard.edu/event/cymetrics/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CY-Workshop_2.jpg
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20260518T150000
DTEND;TZID=America/New_York:20260518T160000
DTSTAMP:20260416T101707
CREATED:20260413T151244Z
LAST-MODIFIED:20260413T151244Z
UID:10003933-1779116400-1779120000@cmsa.fas.harvard.edu
SUMMARY:Quantum Field Theory and Physical Mathematics
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \n 
URL:https://cmsa.fas.harvard.edu/event/qft_51826/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
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END:VCALENDAR