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Speaker: Edward WittenTitle: CMSA Math-Science Literature Lecture: Knot Invariants From Gauge Theory in Three, Four, and Five DimensionsVenue: virtualEdward Witten (IAS) Title: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions Abstract: I will explain connections between a sequence of theories in two, three, four, and five dimensions and describe how these theories are related to the Jones polynomial of a knot and its categorification. Talk chair: Cliff Taubes Video |
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Speaker: Yujiro KawamataTitle: CMSA Math-Science Literature Lecture: Kunihiko Kodaira and complex manifoldsVenue: virtualYujiro Kawamata (University of Tokyo) Title: Kunihiko Kodaira and complex manifolds Abstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions. After quickly recalling the chronology of Kodaira, I will review some of Kodaira’s works in three sections on topics of harmonic analysis, deformation theory and compact complex surfaces. Each topic corresponds to a volume of Kodaira’s collected works in three volumes, of which I will cover only tiny parts. Talk chair: Baohua Fu Video |
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Speaker: Vyacheslav V. ShokurovTitle: CMSA Math-Science Literature Lecture: Birational geometryVenue: virtualVyacheslav V. Shokurov (Johns Hopkins University) Title: Birational geometry Abstract: About main achievements in birational geometry during the last fifty years. Talk chair: Caucher Birkar Video |
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Speaker: Claire VoisinTitle: CMSA Math-Science Literature Lecture: Hodge structures and the topology of algebraic varietiesVenue: virtualClaire Voisin (Collège de France) Title: Hodge structures and the topology of algebraic varieties Abstract: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of the results we will discuss rely on Hodge theory, which has some analytic aspects giving the Hodge and Lefschetz decompositions, and the Hodge-Riemann relations. We will see that a crucial ingredient, the existence of a polarization, is missing in the general Kaehler context. We will also discuss some results and problems related to algebraic cycles and motives. Talk chair: Joe Harris Video | Slides | Article |
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Speaker: Ralph CohenTitle: CMSA Math-Science Literature Lecture: Immersions of manifolds and homotopy theoryVenue: virtualRalph Cohen (Stanford University) Title: Immersions of manifolds and homotopy theory Abstract: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work in topology since the 1950’s. In this talk I will focus on one aspect of that interface: the problem of studying embeddings and immersions of manifolds using homotopy theoretic techniques. I will discuss the history of this problem, going back to the pioneering work of Whitney, Thom, Pontrjagin, Wu, Smale, Hirsch, and others. I will discuss the historical applications of this homotopy theoretic perspective, going back to Smale’s eversion of the 2-sphere in 3-space. I will then focus on the problems of finding the smallest… |
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Speaker: Harry ShumTitle: CMSA Math-Science Literature Lecture: From Deep Learning to Deep UnderstandingVenue: virtualHarry Shum (Tsinghua University) Title: From Deep Learning to Deep Understanding Abstract: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need to understand what we are learning, by shifting the focus from targeting effects to understanding causes. The second is the need for a hybrid neural/symbolic approach that leverages both commonsense knowledge and massive amount of data. Specifically, as an example, I will present some latest work at Microsoft Research on building a pre-trained grounded text generator for task-oriented dialog. It is a hybrid architecture that employs a large-scale Transformer-based deep learning model, and symbol manipulation modules such as business databases, knowledge graphs and commonsense rules. Unlike… |
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Speaker: Michael FreedmanTitle: CMSA Math-Science Literature Lecture: A personal story of the 4D Poincare conjectureVenue: virtualMichael Freedman (Microsoft – Station Q) Title: A personal story of the 4D Poincare conjecture Abstract: The proof of PC4 involved the convergence of several historical streams. To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: Casson towers come to life (in the sense of reproduction), a very intricate explicit shrinking argument (provided by Edwards), and the “blind fold” shrinking argument (which in retrospect is in the linage of Brown’s proof of the Schoenflies theorem). Beyond those mentioned: Kirby, Cannon, Ancel, Quinn, and Starbird helped me understand my proof. I will discuss the main points and how they fit… |
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Speaker: Camillo De LellisTitle: CMSA Math-Science Literature Lecture: Area-minimizing integral currents and their regularityVenue: virtualCamillo De Lellis (IAS) Title: Area-minimizing integral currents and their regularity Abstract: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has had tremendous impacts in several areas of mathematics: superficially through direct applications of the main theorems, but more deeply because of the techniques which have been invented to deal with related analytical and geometrical challenges. In this lecture I will review the basic concepts, the related existence theory of solutions of the Plateau problem, and what is known about their regularity. I will… |
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Speaker:Title: Existence of Canonical Metrics on Non-Kähler GeometryVenue: VirtualOn Wednesday September 9, CMSA director Prof. Shing-Tung Yau gave a lecture for the Simons foundation on “Existence of Canonical Metrics on Non-Kähler Geometry.“ In this lecture, Prof. Yau surveys the existence of canonical balanced metrics on non-Kähler complex manifolds through the Hull-Strominger system, which was motivated by string theory on compactifications. He discusses works by Jun Li of Fudan University in Shanghai, Ji-Xiang Fu of Fudan University, Ivan Smith of the University of Cambridge, Richard P. Thomas of Imperial College London, Tristan C. Collins of the Massachusetts Institute of Technology, French mathematician Émile Picard, Teng Fei of Rutgers University in Newark, New Jersey, Adam Jacob of the University of California, Davis, and Duong H. Phong of Columbia… |
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Speaker: Sanjeev Arora (Princeton), Juan Camilo Castillo (U Penn), Joseph Dexter (Dartmouth), Nicole Immorlica (Microsoft), Amin Saberi (Stanford), Vira Semenova (UC Berkeley), Varda Shalev (Tel Aviv University)Title: 2020 Big Data Conference (Virtual)Venue: VirtualOn August 24-25, 2020 the CMSA hosted our sixth annual Conference on Big Data. The Conference featured many 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. The 2020 Big Data Conference took place virtually. Videos of the talks are available in this youtube playlist. Organizers: Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business Horng-Tzer Yau, Professor of Mathematics, Harvard University Sergiy Verstyuk, CMSA, Harvard University Speakers: Sanjeev Arora, Princeton University Juan Camilo Castillo, University of Pennsylvania Joseph Dexter, Dartmouth College Nicole Immorlica, Microsoft Amin Saberi, Stanford University Vira Semenova,… |
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Speaker: Ciprian ManolescuTitle: CMSA Math-Science Literature Lecture: Four-dimensional topologyVenue: virtualCiprian Manolescu (Stanford) Title: Four-dimensional topology Abstract: I will outline the history of four-dimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the Seiberg-Witten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the focus shifted to four-manifolds with boundary and cobordisms. Floer homology has led to numerous applications, and recently there have also been a few novel results (and proofs of old results) using Khovanov homology. The talk will be accessible to a general mathematical audience. Video |
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Speaker: Bong LianTitle: CMSA Math-Science Literature Lecture: From string theory and Moonshine to vertex algebrasVenue: virtualBong Lian (Brandeis) Title: From string theory and Moonshine to vertex algebras Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as well as some of the subsequent and recent developments. The lecture is aimed at a general audience. Slides | Video |
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Speaker: Robert GriessTitle: CMSA Math-Science Literature Lecture: My life and times with the sporadic simple groupsVenue: virtualRobert Griess (University of Michigan) Title: My life and times with the sporadic simple groups Abstract: Five sporadic simple groups were proposed in 19th century and 21 additional ones arose during the period 1965-1975. There were many discussions about the nature of finite simple groups and how sporadic groups are placed in mathematics. While in mathematics grad school at University of Chicago, I became fascinated with the unfolding story of sporadic simple groups. It involved theory, detective work and experiments. During this lecture, I will describe some of the people, important ideas and evolution of thinking about sporadic simple groups. Most should be accessible to a general mathematical audience. Video | Slides |
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Speaker: Lydia BieriTitle: CMSA Math-Science Literature Lecture: Black Hole FormationVenue: virtualLydia Bieri (University of Michigan) Title: Black Hole Formation Abstract: Can black holes form through the focusing of gravitational waves? This was an outstanding question since the early days of general relativity. In his breakthrough result of 2008, Demetrios Chrstodoulou answered this question with “Yes!” In order to investigate this result, we will delve deeper into the dynamical mathematical structures of the Einstein equations. Black holes are related to the presence of trapped surfaces in the spacetime manifold. Christodoulou proved that in the regime of pure general relativity and for arbitrarily dispersed initial data, trapped surfaces form through the focusing of gravitational waves provided the incoming energy is large enough in a precisely defined way. The proof combines new ideas from… |
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Speaker: Joe HarrisTitle: CMSA Math-Science Literature Lecture: Rationality questions in algebraic geometryVenue: virtualJoe Harris (Harvard) Title: Rationality questions in algebraic geometry Abstract: Over the course of the history of algebraic geometry, rationality questions — motivated by both geometric and arithmetic problems — have often driven the subject forward. The rationality or irrationality of cubic hypersurfaces in particular have led to the development of abelian integrals (dimension one), birational geometry (dimension two) and Hodge theory (dimension 3). But there remained much we didn’t understand about the condition of rationality, such as how it behaves in families. However, there has been recent progress: work of Hassett, Tschinkel, Pirutka and others, working with examples in dimension 4, showed that it is in general neither an open condition nor a closed one, but does behave well with respect… |
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Speaker: Donald RubinTitle: CMSA Math-Science Literature Lecture: Why do some universities have separate departments of statistics?Venue: virtualDonald Rubin (Harvard) Title: Why do some universities have separate departments of statistics? And are they all anachronisms, destined to follow the path of other dinosaurs? Video | Slides |
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Speaker: Pavel EtingofTitle: CMSA Math-Science Literature Lecture: Quantum GroupsVenue: virtualPavel Etingof (MIT) Title: Quantum Groups Abstract: The theory of quantum groups developed in mid 1980s from attempts to construct and understand solutions of the quantum Yang-Baxter equation, an important equation arising in quantum field theory and statistical mechanics. Since then, it has grown into a vast subject with profound connections to many areas of mathematics, such as representation theory, the Langlands program, low-dimensional topology, category theory, enumerative geometry, quantum computation, algebraic combinatorics, conformal field theory, integrable systems, integrable probability, and others. I will review some of the main ideas and examples of quantum groups and try to briefly describe some of the applications. Video | Slides |
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Speaker: Simon DonaldsonTitle: CMSA Math-Science Literature Lecture: The ADHM construction of Yang-Mills instantonsVenue: virtualSimon Donaldson (Stony Brook) Title: The ADHM construction of Yang-Mills instantons Abstract: In 1978 (Physics Letters 65A) Atiyah, Hitchin, Drinfeld and Manin (ADHM) described a construction of the general solution of the Yang-Mills instanton equations over the 4-sphere using linear algebra. This was a major landmark in the modern interaction between geometry and physics, and the construction has been the scene for much research activity up to the present day. In this lecture we will review the background and the original ADHM proof, using Penrose’s twistor theory and results on algebraic vector bundles over projective 3-space. As time permits, we will also discuss some further developments, for example, the work of Nahm on monopoles and connections to Mukai duality… |
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Speaker:Title: Frontiers in Applied Mathematics and ComputationVenue: VirtualTogether with the School of Engineering and Applied Sciences, the CMSA will be hosting a lecture series on the Frontiers in Applied Mathematics and Computation. Talks in this series will aim to highlight current research trends at the interface of applied math and computation and will explore the application of these trends to challenging scientific, engineering, and societal problems. Lectures will take place on March 25, April 1, and April 29, 2021. Speakers: George Biros (U.T. Austin) Laura Grigori (INRIA Paris) Samory K. Kpotufe (Columbia) Jonas Martin Peters (University of Copenhagen) Joseph M. Teran (UCLA) The schedule below will be updated as talks are confirmed. Date/Time Speaker Title/Abstract 3/25/2021 10:00 – 11:00am ET Joseph M. Teran Title: Affine-Particle-In-Cell with Conservative… |
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Speaker: Shing-Tung YauTitle: CMSA Math-Science Literature Lecture: Shiing-Shen Chern as a Great Geometer of 20th CenturyVenue: virtualShing-Tung Yau (Harvard) Title: Shiing-Shen Chern as a Great Geometer of 20th Century Video | Slides | Article |