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DTSTART;TZID=America/New_York:20240826T090000
DTEND;TZID=America/New_York:20240828T170000
DTSTAMP:20260417T032042
CREATED:20240209T180835Z
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SUMMARY:Advances in Probability Theory and Interacting Particle Systems
DESCRIPTION:Advances in Probability Theory and Interacting Particle Systems\n\nA conference in honor of S. R. Srinivasa Varadhan.\n\nAugust 26 – August 28\, 2024\n\nHarvard Geological Lecture Hall\n\n\nConference Website: www.math.harvard.edu/event/math-conference-honoring-srinivasa-varadhan\n\nSpeakers\n\n\nInes Armendariz\, Universidad de Buenos Aires\nYuri Bakhtin\, Courant Institute\nGérard Ben Arous\, Courant Institute\nSourav Chatterjee\, Stanford University\nAmir Dembo\, Stanford University\nPeter K. Friz\, TU-Berlin\nNina Holden\, Courant Institute\nJiaoyang Huang\, University of Pennsylvania\nElena Kosygina\, City University of New York\nClaudio Landim\, IMPA\nEyal Lubetzky\, Courant Institute\nChiranjib Mukherjee\, Uni Münster\nStefano Olla\, Université Paris Dauphine\nJeremy Quastel\, University of Toronto\nKavita Ramanan\, Brown University\nAlejandro Ramirez\, NYU Shanghai\nFraydoun Rezakhanlou\, Berkeley\nSunder Sethuraman\, University of Arizona\nScott Sheffield\, MIT\nOfer Zeitouni\, Weizmann Institute\n\nOrganizers: Paul Bourgade (New York University\, Courant Institute) and Horng-Tzer Yau (Harvard University).\n\n\nSponsored by Harvard University Department of Mathematics and the Center of Mathematical Studies and Applications (CMSA).\n\nHarvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is\, on the basis of sex\, sexual orientation\, or gender identity\, excluded from participation in\, denied the benefits of\, or subjected to discrimination in any University program or activity. More information can be found here.
URL:https://cmsa.fas.harvard.edu/event/advances-in-probability-theory-and-interacting-particle-systems/
LOCATION:Harvard Geological Lecture Hall\, 24 Oxford St\, Cambridge\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/Varadhan-Poster.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240828T140000
DTEND;TZID=America/New_York:20240828T153000
DTSTAMP:20260417T032042
CREATED:20240822T161627Z
LAST-MODIFIED:20240826T155342Z
UID:10003416-1724853600-1724859000@cmsa.fas.harvard.edu
SUMMARY:Instanton in Lattice QCD from Higher Categories and Higher Anafunctors
DESCRIPTION:Speaker: Jing-Yuan Chen\, Tsinghua University \nTitle: Instanton in Lattice QCD from Higher Categories and Higher Anafunctors\n\n\nAbstract:  Putting continuum QFT (not just TQFT) on the lattice is important for both fundamental understandings and practical numerics. The traditional way of doing so\, based on simple intuitions\, however\, does not admit natural definitions for general topological operators of continuous-valued fields—one such example is the long standing problem in lattice QCD of lacking a natural definition for Yang-Mills instantons.\nIn this talk\, I will explain a more systematic way to relate continuum and lattice QFT\, based on higher categories and higher anafunctors\, so that the topological operators in the continuum can be naturally defined on the lattice. The idea\, though formulated formally\, is physically very intuitive—we want to effectively capture the different possibilities of how a lattice field may interpolate into the continuum\, so the higher categories that are employed to study higher homotopy theory should be naturally involved. Via this formalism\, we resolve the long-standing problem of defining instanton (as well as Chern-Simons term) in lattice Yang-Mills theory\, in terms of multiplicative bundle gerbes. Moreover\, when the fields become discrete\, our formalism can recover the Dijkgraaf-Witten and Turaev-Viro theory\, so we hope this formalism to be a good starting point towards (in the very long term) a comprehensive categorical understanding of QFT that encompass both continuous and discrete degrees of freedom\, applicable both to IR and to UV.
URL:https://cmsa.fas.harvard.edu/event/qm_82824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-08.28.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240903T090000
DTEND;TZID=America/New_York:20241101T170000
DTSTAMP:20260417T032042
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
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Machine-Learning-Program-poster-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240903T100000
DTEND;TZID=America/New_York:20240905T160000
DTSTAMP:20260417T032042
CREATED:20240105T031946Z
LAST-MODIFIED:20240918T190637Z
UID:10001110-1725357600-1725552000@cmsa.fas.harvard.edu
SUMMARY:Mathematics and Machine Learning Program Opening Workshop
DESCRIPTION:Mathematics and Machine Learning Program Opening Workshop \nDates: September 3 – 5\, 2024 \nLocation: Room G10\, CMSA\, 20 Garden Street\, Cambridge MA & via Zoom Webinar \nAI for Mathematicians\, with Leon Bottou\, François Charton\, David McAllester\, Adam Wagner\, Boris Hanin\, and Geordie Williamson.  A series of 6 tutorial lectures introducing concepts of AI and of theorem proving\, with many case studies of AI applied to mathematics\, and including lectures and discussion sessions on open questions\, future prospects\, and ethical questions.\n  \nSpeakers \n\nLeon Bottou (Meta AI)\nFrançois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nBoris Hanin (Princeton)\nDavid McAllester (TTIC)\nAdam Wagner (WPI)\nGeordie Williamson (University of Sydney)\n\nSchedule (link to downloadable pdf) \nVideos from the Opening Workshop (Youtube Link) \n\n\n\nTuesday Sep. 3\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nMike Douglas: Overview of AI for mathematics\nSlides (pdf)\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nDavid McAllester: Logic and formal methods\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n3:00–4:00 pm\nPanel Discussion: Automated mathematical discovery\n\n\n\n  \n\n\n\nWednesday Sep. 4\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nBoris Hanin: Theory of Machine Learning\nSlides (pdf)\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nAdam Wagner: Case studies I: Reinforcement learning and pattern finding\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n\n  \n\n\n\nThursday Sep. 5\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nFrançois Charton (slides-pdf)\nand Geordie Williamson: Case studies II\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nLeon Bottou: Open questions in AI\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n3:00–4:00 pm\nPanel Discussion: How might AI change mathematics?\n\n\n\n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mmlworkshop_924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/ML_Opening-workshop-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240905T160000
DTEND;TZID=America/New_York:20240905T170000
DTSTAMP:20260417T032042
CREATED:20240710T192944Z
LAST-MODIFIED:20241212T195515Z
UID:10003398-1725552000-1725555600@cmsa.fas.harvard.edu
SUMMARY:CMSA/Math Fall Gathering
DESCRIPTION:September 5\, 2024 \n4:00 pm \nCMSA Common Room\, 20 Garden Street\, Cambridge MA \nAll CMSA and Math affiliates are invited.
URL:https://cmsa.fas.harvard.edu/event/fallgathering2024/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event
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:20240906T090000
DTEND;TZID=America/New_York:20240907T170000
DTSTAMP:20260417T032042
CREATED:20240325T141950Z
LAST-MODIFIED:20250415T154033Z
UID:10003287-1725613200-1725728400@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2024
DESCRIPTION:  \n \nYoutube Playlist \nOn September 6-7\, 2024\, the CMSA hosted the tenth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nLocation: Harvard University CMSA\, 20 Garden Street\, Cambridge & via Zoom \n  \nSpeakers: \n\nTianxi Cai\, Harvard Chan School\nRaj Chetty\, Harvard\nBianca Dumitrascu\, Columbia\nBoris Hanin\, Princeton\nPeter Hull\, Brown\nJamie Morgenstern\, U Washington\nKavita Ramanan\, Brown\nNeil Thompson\, MIT\nMelanie Weber\, Harvard\nKun-Hsing Yu\, Harvard Medical School\n\nOrganizers: \n\nRediet Abebe\, Harvard Society of Fellows\nMorgane Austern\, Harvard University Statistics\nMichael R. Douglas\, Harvard CMSA\nYannai Gonczarowski\, Harvard University Economics and Computer Science\nSam Kou\, Harvard University Statistics\n\nSCHEDULE (downloadable pdf) \nFriday\, Sep. 6\, 2024 \n9:00 am: Breakfast \n9:30 am: Introductions \n9:45–10:45 am\nSpeaker: Peter Hull\, Brown University\nTitle: Measuring Discrimination in Multi-Phase Systems\, with an Application to Child Protection\nAbstract: Large racial disparities have been documented in many high-stakes settings—such as employment\, health care\, housing\, and criminal justice—raising concerns of discrimination by individual decision-makers. At the same time\, there is growing understanding that a focus on individual decisions can yield an incomplete view of discrimination; an extensive theoretical literature shows how discrimination can arise and compound across multiple decision-makers in interconnected systems. We develop new empirical tools for studying discrimination in such multi-phase systems and apply them to the setting of foster care placement by child protective services. Leveraging the quasi-random assignment of two sets of decision-makers—initial hotline call screeners and subsequent investigators—we study how unwarranted racial disparities arise and propagate through this system. Using a sample of over 200\,000 maltreatment allegations\, we find that calls involving Black children are 55% more likely to result in foster care placement than calls involving white children with the same potential for future maltreatment in the home. Call screeners account for up to 19% of this unwarranted disparity\, with the remainder due to investigators. Unwarranted disparity is concentrated in cases with potential for future maltreatment\, suggesting that white children may be harmed by “underplacement” in high-risk situations. \n10:45–11:00 am: Break \n11:00 am –12:00 pm\nSpeaker: Jamie Morgenstern\, U Washington\nTitle: What governs predictive disparity in modern machine learning applications?\nAbstract: The deployment of statistical models in impactful environments is far from new—simple correlations have been used to guide decisions throughout the sciences\, health care\, political campaigns\, and in pricing financial instruments and other products for decades. Many such models\, and the decisions they supported\, were known to have different degrees of predictive power for different demographic groups. These differences had numerous sources\, including: limited expressiveness of the statistical models; limited availability of data from marginalized populations; noisier measurements of both features and targets from certain populations; and features with less mutual information about the prediction target for some populations than others.\nModern decision systems which use machine learning are more ubiquitous than ever\, as are their differences in performance for different populations of people. In this talk\, I will discuss some similarities and differences in the sources of differing performance in contemporary ML systems including facial recognition systems and those incorporating generative AI. \n12:00–1:30 pm: Lunch Break \n1:30–2:30 pm\nSpeaker: Kavita Ramanan\, Brown University\nTitle: Understanding High-dimensional Stochastic Dynamics on Realistic Networks\nAbstract: Large collections of randomly evolving particles that interact locally with respect to an underlying network model a variety of phenomena ranging from magnetism\, the spread of diseases\, neural and neuronal networks\, opinion dynamics and load balancing on computer networks. Due to their high-dimensional nature\, these systems are typically intractable to analyze exactly. Classical work\, falling under the rubric of mean-field approximations\, has mostly focused on the case when this interaction graph is dense.  However\, most real-world networks are sparse and often random. We describe a new approach to develop principled approximations for dynamics on realistic networks that beats the curse of dimensionality\, and illustrate its efficacy on a class of epidemiological models. This is based on joint works with Michel Davydov\, Ankan Ganguly and Juniper Cocomello. \n2:30–2:45 pm: Break \n2:45–3:45 pm\nSpeaker: Raj Chetty\, Harvard University\nTitle: The Science of Economic Opportunity: New Insights from Big Data\nAbstract: How can we improve economic opportunities for children growing up in low-income families? This talk will present findings from a recent set of studies that use various sources of big data — ranging from anonymized tax records to social network data — to understand the science of economic opportunity. Among other topics\, the talk will discuss how and why children’s chances of climbing the income ladder vary across neighborhoods\, the drivers of racial disparities in economic mobility\, how highly selective colleges may amplify the persistence of privilege\, and the role of social capital as a driver of upward mobility. The talk will conclude by giving examples of how academic research using big data is informing policy decisions from the local to federal level to expand opportunities for all. \n3:45–4:00 pm: Break \n4:00–5:00 pm\nSpeaker: Neil Thompson\nTitle: How Algorithmic Progress is driving progress in Big Data and AI\nAbstract: Algorithm improvement is one of the purest forms of innovation: it allows the same computational task to be achieved with far fewer resources by proposing clever new ways to do that computation. In this talk\, I will discuss the work that my lab has done tracking and quantifying progress across decades of algorithm research and practice. As I will show\, this algorithmic progress has often outpaced hardware improvement as the most important driver of progress in Big Data and AI. \n  \nSaturday\, Sep. 7\, 2024 \n9:00 am: Breakfast \n9:30 am: Introductions \n9:45–10:45 am\nSpeaker: Tianxi Cai\, Harvard Chan School\nTitle: Crowdsourcing with Multi-institutional EHR to Improve Reliability of Real World Evidence – Opportunities and Challenges\nAbstract: The wide adoption of electronic health records (EHR) systems has led to the availability of large clinical datasets available for discovery research. EHR data\, linked with bio- repository\, is a valuable new source for deriving real-word\, data-driven prediction models of disease risk and progression. Yet\, they also bring analytical difficulties especially when aiming to leverage multi-institutional EHR data. Synthesizing information across healthcare systems is challenging due to heterogeneity and privacy. Statistical challenges also arise due to high dimensionality in the feature space. In this talk\, I’ll discuss analytical approaches for mining EHR data to improve the reliability and generalizability of real world evidence generated from the analyses. These methods will be illustrated using EHR data from Mass General Brigham and Veteran Health Administration. \n10:45–11:00 am: Break \n11:00 am–12:00 pm\nSpeaker: Bianca Dumitrascu\, Columbia Data Science Institute\nTitle: Statistical machine learning for learning representations of embryonic development\nAbstract: During embryonic development\, single cells read in local information from their environments and use this information to move\, divide and specialize. As a result\, the environments themselves change.  However\, it remains unclear how gene expression programs interact with cell morphology and mechanical forces to orchestrate organogenesis in early embryos. Recent advances in single cell techniques and in toto imaging enable unique venues in exploring this link between genomics and biophysics\, which dynamically maps cells to organisms.\nIn this talk\, I will describe statistical machine learning frameworks aimed at understanding how tissue level mechanical and morphometric information impact gene expression patterns in spatio-temporal contexts. We use these tools to understand boundary formation in the early development of mouse embryos and to align data from light sheet recordings of pre-gastrulation development. \n12:00–1:30 pm: Lunch Break \n1:30–2:30 pm\nSpeaker: Melanie Weber\, Harvard Mathematics\nTitle: Data and Model Geometry in Deep Learning\nAbstract: Data with geometric structure is ubiquitous in machine learning. Often such structure arises from fundamental symmetries in the domain\, such as permutation-invariance in graphs and sets\, and translation-invariance in images. In this talk we discuss implications of this structure on the design and complexity of neural networks. Equivariant architectures\, which encode symmetries as inductive bias\, have shown great success in applications with geometric data\, but can suffer from instabilities as their depths increases. We propose a new architecture based on unitary group convolutions\, which allows for deeper networks with less instability. In the second part of the talk we discuss the impact of data and model geometry on the learnability of neural networks. We discuss learnability in several geometric settings\, including equivariant neural networks\, as well as learnability with respect to the geometry of the input data manifold. \n2:30–2:45 pm: Break \n2:45–3:45 pm\nSpeaker: Boris Hanin\, Princeton University\nTitle: Scaling Limits of Neural Networks\nAbstract: Neural networks are often studied analytically through scaling limits: regimes in which taking some structural network parameters (e.g. depth\, width\, number of training datapoints\, and so on) to infinity results in simplified models of learning. I will motivative and discuss recent results using several such approaches. I will emphasize both new theoretical insights into how model\, training data\, and optimizer impact learning and their practical implications for hyperparameter transfer. \n3:45–4:00 pm: Break \n4:00–5:00 pm\nSpeaker: Kun-Hsing Yu\, Harvard Medical School\nTitle: Foundation Models for Real-Time Cancer Diagnosis\nAbstract: Artificial intelligence (AI) is transforming the landscape of medical research and practice. Recent advances in microscopic image digitization\, foundation models\, and scalable computing infrastructure have opened new avenues for AI-enhanced cancer diagnosis. In this talk\, I will highlight recent breakthroughs in multi-modal AI systems for cancer pathology evaluation\, discuss integrative biomedical informatics methods that link cell morphology with molecular profiles\, and outline critical challenges in developing robust medical AI systems. \n  \n\nInformation about the 2023 Big Data Conference can be found here.
URL:https://cmsa.fas.harvard.edu/event/bigdata_2024/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Big-Data-2024_8.5x11-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240909T163000
DTEND;TZID=America/New_York:20240909T173000
DTSTAMP:20260417T032042
CREATED:20240827T200454Z
LAST-MODIFIED:20240903T152309Z
UID:10003406-1725899400-1725903000@cmsa.fas.harvard.edu
SUMMARY:Combinatorics and geometry of the amplituhedron
DESCRIPTION:Colloquium \nSpeaker: Lauren Williams\, Harvard University \nTitle: Combinatorics and geometry of the amplituhedron \nAbstract: The amplituhedron is a geometric object introduced by Arkani-Hamed and Trnka to compute scattering amplitudes in N=4 super Yang Mills theory. It generalizes interesting objects such as cyclic polytopes and the positive Grassmannian. It has connections to tropical geometry\, cluster algebras\, and combinatorics (plane partitions\, Catalan numbers). I’ll give a gentle introduction to the amplituhedron\, then survey some recent progress on some of the main conjectures about the amplituhedron: the Magic Number Conjecture\, the BCFW tiling conjecture\, and the Cluster Adjacency conjecture.  Based on joint works withEvan-Zohar\, Lakrec\, Parisi\, Sherman-Bennett\, and Tessler.
URL:https://cmsa.fas.harvard.edu/event/colloquium_9924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-09.09.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240910T143000
DTEND;TZID=America/New_York:20240910T154500
DTSTAMP:20260417T032042
CREATED:20240905T173435Z
LAST-MODIFIED:20240905T173435Z
UID:10003403-1725978600-1725983100@cmsa.fas.harvard.edu
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://cmsa.fas.harvard.edu/event/deeplearning_91024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240910T160000
DTEND;TZID=America/New_York:20240910T170000
DTSTAMP:20260417T032042
CREATED:20240909T154001Z
LAST-MODIFIED:20240911T195555Z
UID:10003475-1725984000-1725987600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Open Discussion/Tea
DESCRIPTION:Open Discussion/Tea
URL:https://cmsa.fas.harvard.edu/event/mml_tea_91024/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240910T160000
DTEND;TZID=America/New_York:20240910T180000
DTSTAMP:20260417T032042
CREATED:20240905T130004Z
LAST-MODIFIED:20240910T150123Z
UID:10003443-1725984000-1725991200@cmsa.fas.harvard.edu
SUMMARY:BPS Algebras in Landau-Ginzburg Models
DESCRIPTION:Speaker: Ahsan Khan (CMSA) \nTitle: BPS Algebras in Landau-Ginzburg Models \nAbstract: The study of BPS states in supersymmetric quantum field theory has been a fruitful source of both mathematical and physical insights. In particular their study often leads to rich algebraic structures – from the “Algebra of the Infrared” of Gaiotto-Moore-Witten to the “Cohomological Hall Algebras” of Kontsevich-Soibelman. In this talk\, I will provide an overview of some of these algebraic constructions\, with a particular emphasis on BPS states in two-dimensional Landau-Ginzburg models. In the second half of the talk\, I will discuss how these algebraic structures can be extended to more general Landau-Ginzburg models defined by closed holomorphic one-forms.
URL:https://cmsa.fas.harvard.edu/event/geometry-and-quantum-theory-seminar_91024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-09.10.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240911T103000
DTEND;TZID=America/New_York:20240911T120000
DTSTAMP:20260417T032042
CREATED:20240907T155038Z
LAST-MODIFIED:20240911T210751Z
UID:10003444-1726050600-1726056000@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_91124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240912T100000
DTEND;TZID=America/New_York:20240912T110000
DTSTAMP:20260417T032042
CREATED:20240907T170232Z
LAST-MODIFIED:20240917T140551Z
UID:10003412-1726135200-1726138800@cmsa.fas.harvard.edu
SUMMARY:Twisted Tools for (Untwisted) Quantum Field Theory
DESCRIPTION:Mathematical Physics and Algebraic Geometry \nSpeaker: Justin Kulp (Simons Center for Geometry and Physics) \nTitle: Twisted Tools for (Untwisted) Quantum Field Theory \nAbstract: One of the most important properties of QFTs is that they can be deformed by “turning on interactions.” Essentially every observable can be viewed as coupling the theory to some external system. Famously\, adding interactions (generically) breaks scale invariance\, leading to familiar ideas of EFTs and RG flows in the space of QFTs. An underappreciated fact is that one can actually consider flows generated by any transformation\, not just the usual scale transformations. \nIn my talk\, I will discuss a flow in the space of QFTs coming from (an analogue of) BRST symmetry. The beta-function for this “BRST-flow” controls deformations of the QFT and is highly mathematically constrained\, endowing the space of interactions with an L∞ algebra structure. The structure constants/brackets of the L∞ algebra are highly computable (requiring only a first course in QFT to compute) and contain familiar information such as anomalies and Operator Product Expansion coefficients. I will prove a non-renormalization theorem for holomorphic-topological QFTs with more than one topological direction\, which can be thought of as a generalization of a formality theorem of Kontsevich. Time permitting\, I will discuss how this formalism enables the systematic computation of minimal BPS operators in supersymmetric QFTs and describe the “holomorphic confinement” of N=1 SYM.  Based on arXiv:2403.13049.
URL:https://cmsa.fas.harvard.edu/event/mathphys_91224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematica-Physics-and-Algebraic-Geometry-09.12.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240912T143000
DTEND;TZID=America/New_York:20240912T154500
DTSTAMP:20260417T032042
CREATED:20240907T152919Z
LAST-MODIFIED:20240907T154504Z
UID:10003408-1726151400-1726155900@cmsa.fas.harvard.edu
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://cmsa.fas.harvard.edu/event/deeplearning_91224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240912T160000
DTEND;TZID=America/New_York:20240912T170000
DTSTAMP:20260417T032042
CREATED:20240718T152520Z
LAST-MODIFIED:20240919T192322Z
UID:10003400-1726156800-1726160400@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Lecture: Can AI help with hard mathematics?
DESCRIPTION:Math and Machine Learning Lecture \nDate: Thursday\, Sep. 12\, 2024 \nTime: 4:00 – 5:00 pm \nLocation: Science Center & via Zoom Webinar \n  \n \nSpeaker: Geordie Williamson\, University of Sydney \nTitle: Can AI help with hard mathematics? \nAbstract: The last years have seen remarkable advances in what AI can do. It is perhaps surprising that its impact on research in pure mathematics has been modest. Reasoning\, which is so quintessential to the mathematical process\, remains a major challenge for current AI systems. I will survey some exciting recent applications of AI in mathematics research\, trying to highlight what AI can do and the challenges that remain.
URL:https://cmsa.fas.harvard.edu/event/aimath_91224/
LOCATION:Hybrid
CATEGORIES:Event,MML Lecture
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/ML_public-lecture.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240913T103000
DTEND;TZID=America/New_York:20240913T120000
DTSTAMP:20260417T032042
CREATED:20240911T210525Z
LAST-MODIFIED:20240911T210525Z
UID:10003497-1726223400-1726228800@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_91324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240913T120000
DTEND;TZID=America/New_York:20240913T130000
DTSTAMP:20260417T032042
CREATED:20240907T183113Z
LAST-MODIFIED:20240911T193907Z
UID:10003414-1726228800-1726232400@cmsa.fas.harvard.edu
SUMMARY:Abundance for mixed characteristic threefolds
DESCRIPTION:Member Seminar \nSpeaker: Iacopo Brivio (CMSA) \nTitle: Abundance for mixed characteristic threefolds \nAbstract: The Minimal Model Program (MMP) predicts that every algebraic variety X is birational to either a fibration in Fano varieties\, or it admits a “minimal model” X’\, that is a birational model with nef canonical bundle K_X’. The Abundance conjecture predicts then that K_X’ is actually semiample\, in particular it endows X’ with the structure of a Calabi-Yau fibration. These conjectures were initially phrased for complex varieties\, but more recently there has been a lot of interest in working over positive characteristic fields\, or even mixed characteristic rings. In this talk I will give a broad overview of the subject\, starting from the case of complex surfaces. In the last part I will outline a proof of the Abundance conjecture for mixed characteristic threefolds (based on joint work with F. Bernasconi and L. Stigant).
URL:https://cmsa.fas.harvard.edu/event/member-seminar_91324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-09.13.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240913T143000
DTEND;TZID=America/New_York:20240913T170000
DTSTAMP:20260417T032042
CREATED:20240723T202450Z
LAST-MODIFIED:20240911T134726Z
UID:10003401-1726237800-1726246800@cmsa.fas.harvard.edu
SUMMARY:Freedman CMSA Seminar
DESCRIPTION:Freedman CMSA Seminar \n  \n2:00-3:30 pm ET \nSpeaker: Mike Freedman\, Harvard CMSA \nTitle: Detecting hidden structures in linear maps \nAbstract: I’ll consider the problem of detecting spectral features and tensor structures within linear maps both in a quantum and classical contexts. In the quantum context there is the question of whether a Hamiltonian is local\, and if so\, local in distinct coordinate systems (a “duality”). Also\, in the case of a unitary described by a quantum circuit\, does it possess unusual spectral features or tensor structure? In ML one optimizes many linear maps. How would we know – and would we care – if the resulting maps (approximately) tensor factored? \n  \n3:30-4:00 pm ET \nBreak/Discussion \n  \n4:00-5:30 pm ET \nSpeaker: Ryan O’Donnell\, Carnegie Mellon University \nTitle: Quartic quantum speedups for planted inference \nAbstract: Consider the following task (“noisy 4XOR”)\, arising in CSPs\, optimization\, and cryptography. There is a ‘secret’ Boolean vector x in {-1\,+1}^n. One gets m randomly chosen pairs (S\, b)\, where S is a set of 4 coordinates from [n] and b is x^S := prod_{i in S} x_i with probability 1-eps\, and -x^S with probability eps. Can you tell the difference between the cases eps = 0.1 and eps = 0.5? \nIt depends on m. The best known algorithms use the “Kikuchi method” and run in time ~n^L when m ~ n^2/L. We will review this method\, and also show that the running time can be improved to roughly n^{L/4} with a quantum algorithm. \nJoint work with Alexander Schmidhuber (MIT)\, Robin Kothari (Google)\, and Ryan Babbush (Google).
URL:https://cmsa.fas.harvard.edu/event/freedman_91324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-09.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240916T093000
DTEND;TZID=America/New_York:20240916T103000
DTSTAMP:20260417T032042
CREATED:20240907T170536Z
LAST-MODIFIED:20240912T174105Z
UID:10003445-1726479000-1726482600@cmsa.fas.harvard.edu
SUMMARY:Ringdown in the SYK model
DESCRIPTION:Joint BHI/CMSA Foundation Seminar \nSpeaker: Matthew Dodelson (Harvard) \nTitle: Ringdown in the SYK model \nAbstract: Thermal correlators in large N systems equilibrate at late times\, but the precise late-time behavior is unknown away from holographic and free field limits. In this talk I will analyze this problem in the case of the SYK model away from the low-temperature limit. The basic technique is a resummation of perturbation theory which is reminiscent of the double cone construction. We will also discuss the interpretation of the result in terms of a dual stringy black hole.
URL:https://cmsa.fas.harvard.edu/event/foundation_91624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Foundation Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-BHI-Joint-Foundations-Seminar-09.16.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240916T103000
DTEND;TZID=America/New_York:20240916T120000
DTSTAMP:20260417T032042
CREATED:20240911T153307Z
LAST-MODIFIED:20240911T165549Z
UID:10003477-1726482600-1726488000@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_91624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240916T163000
DTEND;TZID=America/New_York:20240916T173000
DTSTAMP:20260417T032042
CREATED:20240903T193540Z
LAST-MODIFIED:20240916T163127Z
UID:10003430-1726504200-1726507800@cmsa.fas.harvard.edu
SUMMARY:Periodic pencils of flat connections and their p-curvature
DESCRIPTION:Colloquium \nSpeaker: Pavel Etingof (MIT) \nTitle: Periodic pencils of flat connections and their p-curvature \n A periodic pencil of flat connections on a smooth algebraic variety  is a linear family of flat connections  \, where  are local coordinates on  and  are matrix-valued regular functions. A pencil is periodic if it is generically invariant under the shifts  up to isomorphism. I will explain that periodic pencils have many remarkable properties\, and there are many interesting examples of them\, e.g. Knizhnik-Zamolodchikov\, Dunkl\, Casimir connections and equivariant quantum connections for conical symplectic resolutions with finitely many torus fixed points. I will also explain that in characteristic \, the -curvature operators  of a periodic pencil  are isospectral to the commuting endomorphisms \, where  is the Frobenius twist of . This allows us to compute the eigenvalues of the -curvature for the above examples\, and also to show that a periodic pencil of connections always has regular singularites. This is joint work with Alexander Varchenko. \n(Abstract link (pdf)
URL:https://cmsa.fas.harvard.edu/event/colloquium_91624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-09.16.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240917T143000
DTEND;TZID=America/New_York:20240917T154500
DTSTAMP:20260417T032042
CREATED:20240907T181351Z
LAST-MODIFIED:20240907T181351Z
UID:10003456-1726583400-1726587900@cmsa.fas.harvard.edu
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://cmsa.fas.harvard.edu/event/deeplearning_91724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240917T160000
DTEND;TZID=America/New_York:20240917T170000
DTSTAMP:20260417T032042
CREATED:20240911T201656Z
LAST-MODIFIED:20240911T201656Z
UID:10003484-1726588800-1726592400@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Open Discussion/Tea
DESCRIPTION:Open Discussion/Tea
URL:https://cmsa.fas.harvard.edu/event/mml_tea_91724/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240917T160000
DTEND;TZID=America/New_York:20240917T180000
DTSTAMP:20260417T032042
CREATED:20240907T170124Z
LAST-MODIFIED:20240916T162843Z
UID:10003411-1726588800-1726596000@cmsa.fas.harvard.edu
SUMMARY:Mathematics around Twisted Holography
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Keyou Zeng (CMSA) \nTitle: Mathematics around Twisted Holography \nAbstract: The holography principle is an important idea in physics and has been widely studied since the 90s. Twisted holography offers a way to simplify physical holography models through the procedure called twisting. In the first part of the talk\, I’ll introduce some of the mathematical structures underlying this twisted version of holography\, such as Koszul duality. \nIn the second part\, I’ll discuss the concept of vertex algebras in symmetric monoidal categories\, specifically in Deligne category. This framework will serve as a tool to rigorously define the “large N” algebra that emerges from twisted holography. \n 
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_91724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-09.17.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240918T090000
DTEND;TZID=America/New_York:20240918T103000
DTSTAMP:20260417T032042
CREATED:20240904T181255Z
LAST-MODIFIED:20250328T150446Z
UID:10003442-1726650000-1726655400@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Marc Lackenby
DESCRIPTION:CMSA/Tsinghua Math-Science Literature Lecture \nDate: Wednesday\, September 18\, 2024 \nTime: 9:00 – 10:30 am ET \nLocation: Via Zoom Webinar \nSpeaker: Marc Lackenby\, University of Oxford \nTitle: The complexity of knots \nAbstract: In his final paper in 1954\, Alan Turing wrote `No systematic method is yet known by which one can tell whether two knots are the same.’ Within the next 20 years\, Wolfgang Haken and Geoffrey Hemion had discovered such a method. However\, the computational complexity of this problem remains unknown. In my talk\, I will give a survey on this area\, that draws on the work of many low-dimensional topologists and geometers. Unfortunately\, the current upper bounds on the computational complexity of the knot equivalence problem remain quite poor. However\, there are some recent results indicating that\, perhaps\, knots are more tractable than they first seem. Specifically\, I will explain a theorem that provides\, for each knot type K\, a polynomial p_K with the property that any two diagrams of K with n_1 and n_2 crossings differ by at most p_K(n_1) + p_K(n_2) Reidemeister moves. \n\nBeginning in Spring 2020\, the CMSA began hosting a lecture series on literature in the mathematical sciences\, with a focus on significant developments in mathematics that have influenced the discipline\, and the lifetime accomplishments of significant scholars.
URL:https://cmsa.fas.harvard.edu/event/mathscilit2024_ml/
LOCATION:Virtual
CATEGORIES:Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Mathlit_Lackenby_8.5x11.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240918T103000
DTEND;TZID=America/New_York:20240918T120000
DTSTAMP:20260417T032042
CREATED:20240910T135135Z
LAST-MODIFIED:20240911T203928Z
UID:10003476-1726655400-1726660800@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_91824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240918T120000
DTEND;TZID=America/New_York:20240918T130000
DTSTAMP:20260417T032042
CREATED:20240907T160427Z
LAST-MODIFIED:20240924T195406Z
UID:10003409-1726660800-1726664400@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Noam Elkies
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Noam Elkies\, Harvard Math \nTopic: How to show E8 and Leech lattices have optimal sphere packings?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_91824/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240919T100000
DTEND;TZID=America/New_York:20240919T110000
DTSTAMP:20260417T032043
CREATED:20240917T135258Z
LAST-MODIFIED:20240917T155533Z
UID:10003507-1726740000-1726743600@cmsa.fas.harvard.edu
SUMMARY:Feynman graph integrals from topological holomorphic theories 
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Minghao Wang (Boston University) \nTitle: Feynman graph integrals from topological holomorphic theories \nAbstract: Feynman graph integrals from topological theories were developed by M. Kontsevich\, S. Axelrod and I. M. Singer in 1990s. These integrals have many mathematical applications\, such as knot invariants\, operad theory and formality theorems. In this talk\, I will talk about Feynman graph integrals from topological-holomorphic theories. In particular\, I will prove the finiteness of Feynman graph integrals when spacetime is flat spaces and a vanishing result of graph integrals. Combining the vanishing result with Batalin-Vilkovisky(BV) formalism\, we can show the absence of anomalies of topological-holomorphic theories on flat spaces with at least two topological dimensions. As a consequence\, we can construct factorization algebras of quantum observables. This is a joint with Brian Williams.
URL:https://cmsa.fas.harvard.edu/event/mathphys_91924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-09.19.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240919T143000
DTEND;TZID=America/New_York:20240919T154500
DTSTAMP:20260417T032043
CREATED:20240907T181700Z
LAST-MODIFIED:20240907T182411Z
UID:10003459-1726756200-1726760700@cmsa.fas.harvard.edu
SUMMARY:Topics in Deep Learning Theory
DESCRIPTION:Topics in Deep Learning Theory \nEli Grigsby
URL:https://cmsa.fas.harvard.edu/event/deeplearning_91924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topics in Deep Learning Theory
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240920T103000
DTEND;TZID=America/New_York:20240920T120000
DTSTAMP:20260417T032043
CREATED:20240912T144302Z
LAST-MODIFIED:20240912T144302Z
UID:10003498-1726828200-1726833600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240920T120000
DTEND;TZID=America/New_York:20240920T130000
DTSTAMP:20260417T032043
CREATED:20240907T183145Z
LAST-MODIFIED:20240916T164559Z
UID:10003462-1726833600-1726837200@cmsa.fas.harvard.edu
SUMMARY:Communication Complexity of Combinatorial Auctions
DESCRIPTION:Member Seminar \nSpeaker: Tomer Ezra (CMSA) \nTitle: Communication Complexity of Combinatorial Auctions \nAbstract: We study the communication complexity of welfare maximization in combinatorial auctions with m items and two subadditive bidders. A 2-approximation can be guaranteed by a trivial randomized protocol with zero communication\, or a trivial deterministic protocol with O(1) communication. We show that outperforming these trivial protocols requires exponential communication\, settling an open question of [DobzinskiNS10\, Feige09]. \nSpecifically\, we show that any (randomized) protocol guaranteeing a o(logm)-approximation requires communication exponential in m. We complement it by presenting an O(logm)-approximation in poly(m) communication.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-92024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
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