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DTSTART;TZID=America/New_York:20210915T093000
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UID:10002496-1631698200-1653474600@cmsa.fas.harvard.edu
SUMMARY:CMSA Colloquium 9/15/2021 - 5/25/2022
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a Colloquium\, organized by Du Pei\, Changji Xu\, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars\, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/26/2022\nSamir Mathur (Ohio State University)\nTitle: The black hole information paradox \nAbstract: In 1975\, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997\, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center\,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox\, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown\, using some theorems from quantum information theory\, that these extrapolations were incorrect\, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines\, with a postulate that information would leak out through wormholes. Recently\, it was shown that this wormhole idea had some basic flaws\, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle. \nVideo\n\n\n2/2/2022\nAdam Smith (Boston University)\nTitle: Learning and inference from sensitive data \nAbstract: Consider an agency holding a large database of sensitive personal information—say\,  medical records\, census survey answers\, web searches\, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records. \nI will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically\, why such models must sometimes memorize training data points nearly completely. On the more positive side\, I will present differential privacy\, a rigorous definition of privacy in statistical databases that is now widely studied\, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics\, and lay out directions for future investigation.\n\n\n2/8/2022\nWenbin Yan (Tsinghua University)\n(special time: 9:30 pm ET)\nTitle: Tetrahedron instantons and M-theory indices \nAbstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk\, we will review instanton moduli spaces\, explain the construction\, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory. \nVideo\n\n\n2/16/2022\nTakuro Mochizuki (Kyoto University)\nTitle: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles \nAbstract: In 1960’s\, Narasimhan and Seshadri discovered the equivalence\nbetween irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s\, Donaldson\, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles\nand stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then\, many interesting generalizations have been studied. \nIn this talk\, we would like to review a stream in the study of such correspondences for Higgs bundles\, integrable connections\, $D$-modules and periodic monopoles.\n\n\n2/23/2022\nBartek Czech (Tsinghua University)\nTitle: Holographic Cone of Average Entropies and Universality of Black Holes \nAbstract:  In the AdS/CFT correspondence\, the holographic entropy cone\, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual\, is currently known only up to n=5 regions. I explain that average\nentropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily\, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average\nEntropies” (HCAE). I conjecture the exact form of HCAE\, and find that it has the following properties: (1) HCAE is the simplest it could be\, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture\, the extremal rays of HCAE represent stages of unitary black hole evaporation\, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel\, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n\, namely its bounding inequalities are n-independent. (6) In a precise sense I describe\, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.\n\n\n3/2/2022\nRichard Kenyon (Yale University)\n\n\n\n3/9/2022\nRichard Tsai (UT Austin)\n\n\n\n3/23/2022\nJoel Cohen (University of Maryland)\n\n\n\n3/30/2022\nRob Leigh (UIUC)\n\n\n\n4/6/2022\nJohannes Kleiner (LMU München)\n\n\n\n4/13/2022\nYuri Manin (Max-Planck-Institut für Mathematik)\n\n\n\n4/20/2022\nTBA\n\n\n\n4/27/2022\nTBA\n\n\n\n5/4/2022\nMelody Chan (Brown University)\n\n\n\n5/11/2022\nTBA\n\n\n\n5/18/2022\nTBA\n\n\n\n5/25/2022\nHeeyeon Kim (Rutgers University)\n\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/15/2021\nTian Yang\, Texas A&M\nTitle: Hyperbolic Geometry and Quantum Invariants \nAbstract: There are two very different approaches to 3-dimensional topology\, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk\, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.\n\n\n9/29/2021\nDavid Jordan\, University of Edinburgh\nTitle: Langlands duality for 3 manifolds \nAbstract: Langlands duality began as a deep and still mysterious conjecture in number theory\, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds\, and hence the precise form of Langlands duality for them\, remains a mystery. \nIn this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi \, and I will explain a Langlands duality in this setting\, which we have conjectured with Ben-Zvi\, Gunningham and Safronov. \nIntriguingly\, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question\, beyond the scope of the talk.\n\n\n10/06/2021\nPiotr Sulkowski\, U Warsaw\nTitle: Strings\, knots and quivers \nAbstract: I will discuss a recently discovered relation between quivers and knots\, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence\, and it states that various invariants of a given knot are captured by characteristics of a certain quiver\, which can be associated to this knot. Among others\, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver\, it provides a new insight on knot categorification\, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.\n\n\n10/13/2021\nAlexei Oblomkov\, University of Massachusetts\nTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane. \nAbstract: The knot homology (defined by Khovavov\, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However\, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details\, using physics ideas of Kapustin-Rozansky-Saulina\, in the joint work with Rozansky\, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane\, the symmetry is the geometric counter-part of the mentioned Poincare duality.\n\n\n10/20/2021\nPeng Shan\, Tsinghua U\nTitle: Categorification and applications \nAbstract: I will give a survey of the program of categorification for quantum groups\, some of its recent development and applications to representation theory.\n\n\n10/27/2021\nKarim Adiprasito\, Hebrew University and University of Copenhagen\nTitle: Anisotropy\, biased pairing theory and applications \nAbstract: Not so long ago\, the relations between algebraic geometry and combinatorics were strictly governed by the former party\, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry\, specifically Hodge Theory. And so\, while we proved analogues for these results\, combinatorics felt subjugated to inspirations from outside of it.\nIn recent years\, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature\, we use intuitions from the Hall marriage theorem\, translated to algebra: once there\, they are statements about self-pairings\, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry\, which in turn established solutions to long-standing conjectures in combinatorics. \nI will survey this theory\, called biased pairing theory\, and new developments within it\, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki\, Vasiliki Petrotou and Johanna Steinmeyer.\n\n\n11/03/2021\nTamas Hausel\, IST Austria\nTitle: Hitchin map as spectrum of equivariant cohomology \nAbstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.\n\n\n11/10/2021\nPeter Keevash\, Oxford\nTitle: Hypergraph decompositions and their applications \nAbstract: Many combinatorial objects can be thought of as a hypergraph decomposition\, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example\, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general\, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs\, which I proved in 2014\, states that\, bar finitely many exceptions\, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting\, which implies an approximate formula for the number of designs; in particular\, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects\, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem)\, whist tournaments or generalised Sudoku squares. In this talk\, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.\n\n\n11/17/2021\nAndrea Brini\, U Sheffield\nTitle: Curve counting on surfaces and topological strings \nAbstract: Enumerative geometry is a venerable subfield of Mathematics\, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s\, in particular\, the interaction with String Theory has sent shockwaves through the subject\, giving both unexpected new perspectives and a remarkably powerful\, physics-motivated toolkit to tackle several traditionally hard questions in the field.\nI will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X\, D)\, with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X\, D)\, including the log Gromov-Witten invariants of the pair\, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety\, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds\, the Donaldson–Thomas theory of a class of symmetric quivers\, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.\n\n\n12/01/2021\nRichard Wentworth\, University of Maryland\nTitle: The Hitchin connection for parabolic G-bundles \nAbstract: For a simple and simply connected complex group G\, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks\, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.\n\n\n12/08/2021\nMaria Chudnovsky\, Princeton\nTitle: Induced subgraphs and tree decompositions \nAbstract: Tree decompositions are a powerful tool in both structural\ngraph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. \nTree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction\, exploring both the classical notion of bounded tree-width\, and concepts of more structural flavor. This talk will survey some of these ideas and results.\n\n\n12/15/21\nConstantin Teleman (UC Berkeley)\nTitle: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system \nAbstract: I will present a construction of the object in the title which\, applied to the classical Toda system\, controls the theory of categorical representations of compact Lie groups\, along with applications (some conjectural\, some rigorous) to gauged Gromov-Witten theory. Time permitting\, we will review applications to Coulomb branches and the categorified Weyl character formula.
URL:https://cmsa.fas.harvard.edu/event/cmsa-colloquium_2021-22/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
END:VEVENT
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
END:VCALENDAR