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TZID:America/New_York
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TZOFFSETFROM:-0500
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DTSTART:20210314T070000
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220302T093000
DTEND;TZID=America/New_York:20220302T103000
DTSTAMP:20240222T171906Z
CREATED:20240214T040557Z
LAST-MODIFIED:20240222T171906Z
UID:10002521-1646213400-1646217000@cmsa.fas.harvard.edu
SUMMARY:Dimers and webs
DESCRIPTION:Speaker: Richard Kenyon (Yale) \nTitle: Dimers and webs \nAbstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”). \nThis is joint work with Dan Douglas and Haolin Shi.
URL:https://cmsa.fas.harvard.edu/event/dimers-and-webs/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.02.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220302T140000
DTEND;TZID=America/New_York:20220302T150000
DTSTAMP:20240517T193649Z
CREATED:20230808T182233Z
LAST-MODIFIED:20240517T193649Z
UID:10001206-1646229600-1646233200@cmsa.fas.harvard.edu
SUMMARY:Scaling Laws and Their Implications for Coding AI
DESCRIPTION:Speaker: Jared Kaplan\, Johns Hopkins Dept. of Physics & Astronomy \nTitle: Scaling Laws and Their Implications for Coding AI \nAbstract:  Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress.  I will briefly review scaling laws for generative models in a number of domains\, emphasizing language modeling.  Then I will discuss scaling results for transfer from natural language to code\, and results on python programming performance from “codex” and other models.  If there’s time I’ll discuss prospects for the future — limitations from dataset sizes\, and prospects for RL and other techniques.
URL:https://cmsa.fas.harvard.edu/event/3-2-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/03.2.2022-1553x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220304T093000
DTEND;TZID=America/New_York:20220304T103000
DTSTAMP:20240301T111217Z
CREATED:20240214T085309Z
LAST-MODIFIED:20240301T111217Z
UID:10002600-1646386200-1646389800@cmsa.fas.harvard.edu
SUMMARY:Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds
DESCRIPTION:Member Seminar \nSpeaker: Martin Lesourd \nTitle: Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds \nAbstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger\, Prof. S-T. Yau\, and two others are with R. Unger\, and Prof. D. A. Lee.
URL:https://cmsa.fas.harvard.edu/event/3-4-2022-member-seminar/
LOCATION:Hybrid – G10
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220309T093000
DTEND;TZID=America/New_York:20220309T103000
DTSTAMP:20240304T074318Z
CREATED:20240214T040341Z
LAST-MODIFIED:20240304T074318Z
UID:10002520-1646818200-1646821800@cmsa.fas.harvard.edu
SUMMARY:Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space
DESCRIPTION:Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications\, such as those involving natural images\, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting\, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However\, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function\, defined by a neural network\, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.
URL:https://cmsa.fas.harvard.edu/event/side-effects-of-learning-from-low-dimensional-data-embedded-in-an-euclidean-space/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.09.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220309T140000
DTEND;TZID=America/New_York:20220309T140000
DTSTAMP:20240813T160025Z
CREATED:20230808T182829Z
LAST-MODIFIED:20240813T160025Z
UID:10001207-1646834400-1646834400@cmsa.fas.harvard.edu
SUMMARY:Machine Learning 30 STEM Courses in 12 Departments
DESCRIPTION:Speaker: Iddo Drori\, MIT EE&CS and Columbia School of Engineering \nTitle: Machine Learning 30 STEM Courses in 12 Departments \nAbstract: We automatically solve\, explain\, and generate university-level course problems from thirty STEM courses (at MIT\, Harvard\, and Columbia) for the first time.\nWe curate a new dataset of course questions and answers across a dozen departments: Aeronautics and Astronautics\, Chemical Engineering\, Chemistry\, Computer Science\, Economics\, Electrical Engineering\, Materials Science\, Mathematics\, Mechanical Engineering\, Nuclear Science\, Physics\, and Statistics.\nWe generate new questions and use them in a Columbia University course\, and perform A/B tests demonstrating that these machine generated questions are indistinguishable from human-written questions and that machine generated explanations are as useful as human-written explanations\, again for the first time.\nOur approach consists of five steps:\n(i) Given course questions\, turn them into programming tasks;\n(ii) Automatically generate programs from the programming tasks using a Transformer model\, OpenAI Codex\, pre-trained on text and fine-tuned on code;\n(iii) Execute the programs to obtain and evaluate the answers;\n(iv) Automatically explain the correct solutions using Codex;\n(v) Automatically generate new questions that are qualitatively indistinguishable from human-written questions.\nThis work is a significant step forward in applying machine learning for education\, automating a considerable part of the work involved in teaching.\nOur approach allows personalization of questions based on difficulty level and student backgrounds\, and scales up to a broad range of courses across the schools of engineering and science. \nThis is joint work with students and colleagues at MIT\, Harvard University\, Columbia University\, Worcester Polytechnic Institute\, and the University of Waterloo.
URL:https://cmsa.fas.harvard.edu/event/3-9-2022-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.09.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220318T093000
DTEND;TZID=America/New_York:20220318T103000
DTSTAMP:20240301T111106Z
CREATED:20240214T084936Z
LAST-MODIFIED:20240301T111106Z
UID:10002599-1647595800-1647599400@cmsa.fas.harvard.edu
SUMMARY:Moduli Space of Metric SUSY Graphs
DESCRIPTION:Member Seminar \nSpeaker: Yingying Wu \nTitle: Moduli Space of Metric SUSY Graphs \nAbstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk\, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then\, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties\, followed by a discussion on the connection with the classical case.
URL:https://cmsa.fas.harvard.edu/event/3-18-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220323T093000
DTEND;TZID=America/New_York:20220323T103000
DTSTAMP:20240507T192932Z
CREATED:20240214T040105Z
LAST-MODIFIED:20240507T192932Z
UID:10002519-1648027800-1648031400@cmsa.fas.harvard.edu
SUMMARY:Fluctuation scaling or Taylor’s law of heavy-tailed data\, illustrated by U.S. COVID-19 cases and deaths
DESCRIPTION:Speaker: Joel E. Cohen (Rockefeller University and Columbia University) \nTitle: Fluctuation scaling or Taylor’s law of heavy-tailed data\, illustrated by U.S. COVID-19 cases and deaths \nAbstract: Over the last century\, ecologists\, statisticians\, physicists\, financial quants\, and other scientists discovered that\, in many examples\, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics\, as Taylor’s law in ecology\, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas\, motivations\, recent theoretical results\, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently\, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions\, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work\, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown\, Richard A. Davis\, Victor de la Peña\, Gennady Samorodnitsky\, Chuan-Fa Tang\, and Sheung Chi Phillip Yam.
URL:https://cmsa.fas.harvard.edu/event/colloquium_32223/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-03.23.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220323T140000
DTEND;TZID=America/New_York:20220323T150000
DTSTAMP:20240515T202339Z
CREATED:20230808T183247Z
LAST-MODIFIED:20240515T202339Z
UID:10001208-1648044000-1648047600@cmsa.fas.harvard.edu
SUMMARY:Formal Mathematics Statement Curriculum Learning
DESCRIPTION:Speaker: Stanislas Polu\, OpenAI \nTitle: Formal Mathematics Statement Curriculum Learning \nAbstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget\, expert iteration\, by which we mean proof search interleaved with learning\, dramatically outperforms proof search only.  We also observe that when applied to a collection of formal statements of sufficiently varied difficulty\, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems\,  without the need for associated ground-truth proofs. Finally\, by applying this expert iteration to a manually curated set of problem statements\, we achieve state-of-the-art on the miniF2F benchmark\,  automatically solving multiple challenging problems drawn from high school olympiads.
URL:https://cmsa.fas.harvard.edu/event/3-23-2022-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.23.2022-1553x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220325T093000
DTEND;TZID=America/New_York:20220325T103000
DTSTAMP:20240301T110538Z
CREATED:20240214T084728Z
LAST-MODIFIED:20240301T110538Z
UID:10002597-1648200600-1648204200@cmsa.fas.harvard.edu
SUMMARY:Periods for singular CY families and Riemann–Hilbert correspondence
DESCRIPTION:Member Seminar \nSpeaker: Tsung-Ju Lee \nTitle: Periods for singular CY families and Riemann–Hilbert correspondence \nAbstract: A GKZ system\, introduced by Gelfand\, Kapranov\, and Zelevinsky\, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory\, algebraic geometry and mirror symmetry. In this talk\, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.
URL:https://cmsa.fas.harvard.edu/event/3-25-2022-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T093000
DTEND;TZID=America/New_York:20220330T103000
DTSTAMP:20240502T150948Z
CREATED:20240214T035843Z
LAST-MODIFIED:20240502T150948Z
UID:10002518-1648632600-1648636200@cmsa.fas.harvard.edu
SUMMARY:Edge Modes and Gravity
DESCRIPTION:Speaker: Rob Leigh\, UIUC \nTitle: Edge Modes and Gravity \nAbstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes\, paying attention to relevant symmetries\, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view\, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.
URL:https://cmsa.fas.harvard.edu/event/edge-modes-and-gravity/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.30.2022-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T140000
DTEND;TZID=America/New_York:20220330T150000
DTSTAMP:20240515T202223Z
CREATED:20230808T183529Z
LAST-MODIFIED:20240515T202223Z
UID:10001209-1648648800-1648652400@cmsa.fas.harvard.edu
SUMMARY:Memorizing Transformers
DESCRIPTION:Speaker: Yuhuai Wu\, Stanford and Google \nTitle: Memorizing Transformers \nAbstract: Language models typically need to be trained or fine-tuned in order to acquire new knowledge\, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time\, thus acquiring new knowledge immediately. In this talk\, I will discuss how we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate NN lookup into a non-differentiable memory of recent (key\, value) pairs improves language modeling across various benchmarks and tasks\, including generic webtext (C4)\, math papers (arXiv)\, books (PG-19)\, code (Github)\, as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. We also find that the model is capable of making use of newly defined functions and theorems during test time.
URL:https://cmsa.fas.harvard.edu/event/3-30-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.30.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220401T090000
DTEND;TZID=America/New_York:20220401T103000
DTSTAMP:20240301T110938Z
CREATED:20240214T084536Z
LAST-MODIFIED:20240301T110938Z
UID:10002596-1648803600-1648809000@cmsa.fas.harvard.edu
SUMMARY:Diffusive growth sourced by topological defects
DESCRIPTION:Member Seminar \nSpeaker: Farzan Vafa \nTitle: Diffusive growth sourced by topological defects \nAbstract: In this talk\, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time\, and predict that in the presence of a positive defect\, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature\, we exploit the fact that for axisymmetric surfaces\, the extrinsic geometry can be deduced entirely by the intrinsic geometry. We find that the resulting stationary geometry\, for polar order and small bending modulus\, is a deformed football.\nWe apply our framework to various biological systems. In an ex-vivo setting of cultured murine neural progenitor cells\, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting\, we show that the defect configuration consisting of a bound +1 defect state\, which is stabilized by activity\, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles\, consistent with observations of a basal marine invertebrate Hydra
URL:https://cmsa.fas.harvard.edu/event/4-1-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220406T093000
DTEND;TZID=America/New_York:20220406T103000
DTSTAMP:20240304T073658Z
CREATED:20240214T035619Z
LAST-MODIFIED:20240304T073658Z
UID:10002517-1649237400-1649241000@cmsa.fas.harvard.edu
SUMMARY:What is Mathematical Consciousness Science?
DESCRIPTION:Speaker: Johannes Kleiner\, LMU München \nTitle: What is Mathematical Consciousness Science? \nAbstract: In the last three decades\, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists\, psychologists\, and philosophers. Recently\, a decidedly mathematical perspective has emerged as well\, which is now called Mathematical Consciousness Science. In this talk\, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians\, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.
URL:https://cmsa.fas.harvard.edu/event/what-is-mathematical-consciousness-science/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-04.06.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220408T084500
DTEND;TZID=America/New_York:20220408T101500
DTSTAMP:20240301T105121Z
CREATED:20240214T084325Z
LAST-MODIFIED:20240301T105121Z
UID:10002595-1649407500-1649412900@cmsa.fas.harvard.edu
SUMMARY:Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning
DESCRIPTION:Speaker: Jörn Boehnke \nTitle: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning \nAbstract:  In the standard regression discontinuity setting\, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage\, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage\, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score\, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations\, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally\, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.
URL:https://cmsa.fas.harvard.edu/event/4-8-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220413T093000
DTEND;TZID=America/New_York:20220413T103000
DTSTAMP:20240304T073600Z
CREATED:20240214T035353Z
LAST-MODIFIED:20240304T073600Z
UID:10002516-1649842200-1649845800@cmsa.fas.harvard.edu
SUMMARY:Quantisation in monoidal categories and quantum operads
DESCRIPTION:Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S\, compatible with this structure. But in fact\, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops\, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics\, in a very definite sense\, going back at least to Archimedes. When quantum physics started to replace classical\, it turned out that classical symmetries must also be replaced by their quantum versions\, e.g. quantum groups. \nIn this talk we explain how to define and study quantum versions of symmetries\, relevant to information theory and other contexts.
URL:https://cmsa.fas.harvard.edu/event/quantisation-in-monoidal-categories-and-quantum-operads/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-04.13.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220427T093000
DTEND;TZID=America/New_York:20220427T103000
DTSTAMP:20240304T073208Z
CREATED:20240214T034934Z
LAST-MODIFIED:20240304T073208Z
UID:10002515-1651051800-1651055400@cmsa.fas.harvard.edu
SUMMARY:Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes
DESCRIPTION:Speaker: Venkatesan Guruswami\, UC Berkeley \nTitle: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes \nAbstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved\, or one could in fact correct deletion fractions approaching 1/2.\nWe show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2. \nOur techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools\, we find in any large code two strings with similar oscillation patterns\, which is exploited to find a long common subsequence. \nThis is joint work with Xiaoyu He and Ray Li.
URL:https://cmsa.fas.harvard.edu/event/long-common-subsequences-between-bit-strings-and-the-zero-rate-threshold-of-deletion-correcting-codes/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-04.27.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220429T093000
DTEND;TZID=America/New_York:20220429T110000
DTSTAMP:20240229T090935Z
CREATED:20240215T100221Z
LAST-MODIFIED:20240229T090935Z
UID:10002735-1651224600-1651230000@cmsa.fas.harvard.edu
SUMMARY:Machine Learning the Gravity Equation for International Trade
DESCRIPTION:Member Seminar \nSpeaker: Sergiy Verstyuk \nTitle: Machine Learning the Gravity Equation for International Trade \nAbstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next\, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally\, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]
URL:https://cmsa.fas.harvard.edu/event/4-29-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220513T093000
DTEND;TZID=America/New_York:20220513T110000
DTSTAMP:20240301T105004Z
CREATED:20240214T084053Z
LAST-MODIFIED:20240301T105004Z
UID:10002593-1652434200-1652439600@cmsa.fas.harvard.edu
SUMMARY:Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass
DESCRIPTION:Member Seminar \nSpeaker: Juven Wang \nTitle: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass \nAbstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G)\, whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged or gauged (SU(3)×SU(2)×U(1))/Zq Standard Model (SM) for q=1\,2\,3\,6 with a continuous or discrete (B−L) symmetry and with also a compatible discrete baryon plus lepton Z_{2Nf} B+L symmetry. (The Z_{2Nf} B+L is discrete due to the ABJ anomaly under the BPST instanton.) We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM\, including all these gauge and gravitational backgrounds\, via a cobordism theory\, which controls the SM’s deformation class. While many Grand Unified Theories violating the discrete B+L symmetry suffer from the proton decay\, the SM and some versions of Ultra Unification (constrained by Z_{16} class global anomaly that replaces sterile neutrinos with new exotic gapped/gapless topological or conformal sectors) can have a stable proton. Dictated by a Z_2 class global mixed gauge-gravitational anomaly\, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models — the Standard Model and beyond occur as neighbor phases. We will also comment on a new mechanism to give the neutrino mass via topological field theories and topological defects. Work based on arXiv:2112.14765\, arXiv:2204.08393\, arXiv:2202.13498 and references therein.
URL:https://cmsa.fas.harvard.edu/event/5-13-2022-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220518T093000
DTEND;TZID=America/New_York:20220518T103000
DTSTAMP:20240502T151226Z
CREATED:20240214T055948Z
LAST-MODIFIED:20240502T151226Z
UID:10002547-1652866200-1652869800@cmsa.fas.harvard.edu
SUMMARY:Statistical Mechanics of Mutilated Sheets and Shells
DESCRIPTION:Speaker: David Nelson\, Harvard University \nTitle: Statistical Mechanics of Mutilated Sheets and Shells \nAbstract:  Understanding deformations of macroscopic thin plates and shells has a long and rich history\, culminating with the Foeppl-von Karman equations in 1904\, a precursor of general relativity characterized by a dimensionless coupling constant (the “Foeppl-von Karman number”) that can easily reach  vK = 10^7 in an ordinary sheet of writing paper.  However\, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics\, as exemplified by experiments that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 10^13!)   A crumpling transition out of the flat phase for thermalized elastic membranes has been predicted when kT is large compared to the microscopic bending stiffness\, which could have interesting consequences for Dirac cones of electrons embedded in graphene.   It may be possible to lower the crumpling temperature for graphene to more readily accessible range by inserting a regular lattice of laser-cut perforations\, an expectation an confirmed by extensive molecular dynamics simulations.    We then move on to analyze the physics of sheets mutilated with puckers and stitches.   Puckers and stitches lead to Ising-like phase transitions riding on a background of flexural phonons\, as well as an anomalous coefficient of thermal expansion.  Finally\, we argue that thin membranes with a background curvature lead to thermalized spherical shells that must collapse beyond a critical size at room temperature\, even in the absence of an external pressure.
URL:https://cmsa.fas.harvard.edu/event/statistical-mechanics-of-mutilated-sheets-and-shells/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-05.18.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220722T093000
DTEND;TZID=America/New_York:20220722T110000
DTSTAMP:20240216T093333Z
CREATED:20240216T093333Z
LAST-MODIFIED:20240216T093333Z
UID:10002762-1658482200-1658487600@cmsa.fas.harvard.edu
SUMMARY:7/22/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/7-22-2020-quantum-matter-seminar/
LOCATION:MA
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220909T120000
DTEND;TZID=America/New_York:20220909T130000
DTSTAMP:20240301T084734Z
CREATED:20240301T084734Z
LAST-MODIFIED:20240301T084734Z
UID:10002889-1662724800-1662728400@cmsa.fas.harvard.edu
SUMMARY:Duality in Einstein’s Gravity
DESCRIPTION:Title: Duality in Einstein’s Gravity \nAbstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals\, in turn\, a wide range of new IR phenomena\, including aspects of the double copy for scattering amplitudes\, asymptotic symmetries and more.
URL:https://cmsa.fas.harvard.edu/event/duality-in-einsteins-gravity/
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:20220914T120000
DTEND;TZID=America/New_York:20220914T130000
DTSTAMP:20240229T110925Z
CREATED:20240214T114614Z
LAST-MODIFIED:20240229T110925Z
UID:10002707-1663156800-1663160400@cmsa.fas.harvard.edu
SUMMARY:Strategyproof-Exposing Mechanisms Descriptions
DESCRIPTION:Colloquium \nSpeaker: Yannai Gonczarowski (Harvard)\n\nTitle: Strategyproof-Exposing Mechanisms Descriptions \nAbstract: One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012\, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms\, it is “strategy-proof”: participants can never gain by misreporting their preferences (say\, over schools) to the algorithm. Alas\, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex\, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds\, but rather resort to an appeal to authority: Nobel laureates have proven this property\, so one should listen to them. Unsurprisingly perhaps\, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it\,” which results in a suboptimal match for themselves and for others. \nBy developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel\, starkly different\, yet equivalent\, description for the Deferred Acceptance algorithm\, which\, in a precise sense\, makes its strategyproofness far more apparent. Our description does have a downside\, though: some other of its most fundamental properties—for instance\, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop\, we mathematically address the question of whether and to what extent this downside is unavoidable\, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed\, it seems that in the design of all traditional descriptions of the algorithm\, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm\, at the expense of properties that are mostly of interest to policy makers\, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp\, which we also support with behavioral experiments in the lab. \nJoint work with Ori Heffetz and Clayton Thomas.
URL:https://cmsa.fas.harvard.edu/event/collquium-title-tba/
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-09.14.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220914T140000
DTEND;TZID=America/New_York:20220914T150000
DTSTAMP:20240301T091205Z
CREATED:20230808T183823Z
LAST-MODIFIED:20240301T091205Z
UID:10001210-1663164000-1663167600@cmsa.fas.harvard.edu
SUMMARY:Breaking the one-mind-barrier in mathematics using formal verification
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Johan Commelin\, Mathematisches Institut\, Albert-Ludwigs-Universität Freiburg \nTitle: Breaking the one-mind-barrier in mathematics using formal verification \nAbstract: In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed\, formal verification allows a team of mathematicians to collaborate on a project\, without one person understanding all parts of the project. At the same time\, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier. \nI will use the Liquid Tensor Experiment as an example\, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces\, following up on a challenge by Peter Scholze. \nVideo
URL:https://cmsa.fas.harvard.edu/event/breaking-the-one-mind-barrier-in-mathematics-using-formal-verification/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220916T110000
DTEND;TZID=America/New_York:20220916T120000
DTSTAMP:20240301T084243Z
CREATED:20240214T105636Z
LAST-MODIFIED:20240301T084243Z
UID:10002686-1663326000-1663329600@cmsa.fas.harvard.edu
SUMMARY:Derivation of AdS/CFT for Vector Models
DESCRIPTION:Member Seminar\n\nSpeaker: Shai Chester\n\nTitle: Derivation of AdS/CFT for Vector Models\nAbstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two\, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory\, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping\, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk\, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. We also discuss generalizations of the map to gauge theories\, and at finite temperature.
URL:https://cmsa.fas.harvard.edu/event/derivation-of-ads-cft-for-vector-models/
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:20220921T123000
DTEND;TZID=America/New_York:20220921T133000
DTSTAMP:20240502T145616Z
CREATED:20240214T114047Z
LAST-MODIFIED:20240502T145616Z
UID:10002705-1663763400-1663767000@cmsa.fas.harvard.edu
SUMMARY:Moduli spaces of graphs
DESCRIPTION:Colloquium\n\nSpeaker: Melody Chan\, Brown\n\nTitle: Moduli spaces of graphs\n\nAbstract: A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs” to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs\, but roughly\, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while\, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.
URL:https://cmsa.fas.harvard.edu/event/collquium-92122/
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-09.21.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220923T110000
DTEND;TZID=America/New_York:20220923T120000
DTSTAMP:20240301T083553Z
CREATED:20240214T105452Z
LAST-MODIFIED:20240301T083553Z
UID:10002685-1663930800-1663934400@cmsa.fas.harvard.edu
SUMMARY:Random determinants\, the elastic manifold\, and landscape complexity beyond invariance
DESCRIPTION:Member Seminar \nSpeaker: Ben McKenna \nTitle: Random determinants\, the elastic manifold\, and landscape complexity beyond invariance \nAbstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices\, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold\, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting\, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba/
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:20220928T123000
DTEND;TZID=America/New_York:20220928T133000
DTSTAMP:20240229T110654Z
CREATED:20230817T172722Z
LAST-MODIFIED:20240229T110654Z
UID:10001265-1664368200-1664371800@cmsa.fas.harvard.edu
SUMMARY:The Tree Property and uncountable cardinals
DESCRIPTION:Colloquium \nSpeaker: Dima Sinapova (Rutgers University) \nTitle: The Tree Property and uncountable cardinals \nAbstract: In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers\, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes. \nWe will focus on one such key combinatorial property\, the tree property. A classical result from graph theory (König’s infinity lemma) shows the existence of this property for countable trees. We will discuss what happens in the case of uncountable trees.\n\n 
URL:https://cmsa.fas.harvard.edu/event/collquium-title-tba-2-2/
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-09.28.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220928T140000
DTEND;TZID=America/New_York:20220928T150000
DTSTAMP:20240214T110335Z
CREATED:20230808T184138Z
LAST-MODIFIED:20240214T110335Z
UID:10001211-1664373600-1664377200@cmsa.fas.harvard.edu
SUMMARY:Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling
DESCRIPTION:New Technologies in Mathematics \nSpeaker: Surya Ganguli\, Stanford University \n\nTitle: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling\n\n\n\n\nAbstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  In particular\, we will be able to use the Kac-Rice formula and the replica method to calculate the number\, location\, energy levels\, and Hessian eigenspectra of all critical points of any index.  Second we will review recent work on neural power laws\, which reveal that the error of many neural networks falls off as a power law with network size or dataset size.  Such power laws have motivated significant societal investments in large scale model training and data collection efforts.  Inspired by statistical mechanics calculations\, we show both in theory and in practice how we can beat neural power law scaling with respect to dataset size\, sometimes achieving exponential scaling\, by collecting small carefully curated datasets rather than large random ones.\n\n\n\nReferences: Y. Bahri\, J. Kadmon\, J. Pennington\, S. Schoenholz\, J. Sohl-Dickstein\, and S. Ganguli\, Statistical mechanics of deep learning\, Annual Reviews of Condensed Matter Physics\, 2020.\n\nSorscher\, Ben\, Robert Geirhos\, Shashank Shekhar\, Surya Ganguli\, and Ari S. Morcos. 2022. Beyond Neural Scaling Laws: Beating Power Law Scaling via Data Pruning https://arxiv.org/abs/2206.14486 (NeurIPS 2022).
URL:https://cmsa.fas.harvard.edu/event/8303/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-09.28.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220930T110000
DTEND;TZID=America/New_York:20220930T120000
DTSTAMP:20240301T081921Z
CREATED:20240214T105247Z
LAST-MODIFIED:20240301T081921Z
UID:10002683-1664535600-1664539200@cmsa.fas.harvard.edu
SUMMARY:Kahler geometry in twisted materials
DESCRIPTION:Member Seminar \nSpeaker: Jie Wang \nTitle: Kahler geometry in twisted materials \nAbstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong\, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction\, exact parent Hamiltonian\, conformal field theory analogous and other exact aspects. In generic flatbands\, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries\, in particular the Berry curvature and the Fubini-Study metric\, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics\, making many-body states less stable in flatbands. \nIn this talk\, I will disprove this common belief by showing a large family of flatbands (ideal flatbands) where quantum geometries can be highly non-uniform\, but still exhibit exact properties such as model wavefunctions\, density algebra\, exact parent Hamiltonians. I will discuss both the theory of ideal flatband\, its experimental realization in Dirac materials as well as implications.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-93022/
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:20221005T140000
DTEND;TZID=America/New_York:20221005T160000
DTSTAMP:20240214T110102Z
CREATED:20230808T184616Z
LAST-MODIFIED:20240214T110102Z
UID:10001212-1664978400-1664985600@cmsa.fas.harvard.edu
SUMMARY:Minerva: Solving Quantitative Reasoning Problems with Language Models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Guy Gur-Ari\, Google Research \nTitle: Minerva: Solving Quantitative Reasoning Problems with Language Models \nAbstract: Quantitative reasoning tasks which can involve mathematics\, science\, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large\, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva\, a model that combines these techniques\, achieves SOTA on several math and science benchmarks. I will describe the model\, its capabilities and limitations.
URL:https://cmsa.fas.harvard.edu/event/minerva-solving-quantitative-reasoning-problems-with-language-models/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/10.05.2022.png
END:VEVENT
END:VCALENDAR