|
Speaker: Scott KominersTitle: CMSA/Tsinghua Math-Science Literature Lecture: Scott KominersVenue: virtualCMSA/Tsinghua Math-Science Literature Lecture Prof. Scott Kominers will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series. Date: Monday, November 20, 2023 Time: 9:00 – 10:30 am ET Location: Via Zoom Webinar Registration is required. Register here to attend virtually: Zoom Webinar Registration Title: 60 Years of Matching: From Gale and Shapley to Trading Networks Abstract: Gale and Shapley’s 1962 American Mathematical Monthly paper, “College Admissions and the Stability of Marriage,” is by now one of the most cited articles in the journal’s history, having served as the foundation for an entire branch of the field of market design. This success owes in large part to the beautiful, applicable, and surprisingly general theory of matching mechanisms uncovered in Gale and Shapley’s… |
|
Speaker: Hugh WoodinTitle: CMSA/Tsinghua Math-Science Literature Lecture: Large cardinals and small sets: The AD+ Duality ProgramVenue: CMSA Room G10CMSA/Tsinghua Math-Science Literature Lecture Prof. Hugh Woodin will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series. Date: Wednesday, November 9, 2022 Time: 9:30 – 11:00 am ET Location: Via Zoom Webinar and Room G10, CMSA, 20 Garden Street, Cambridge MA 02138 Directions and Recommended Lodging Registration is required. Register here to attend virtually: Zoom Webinar Registration Register here to attend in-person: In-Person Registration Title: Large cardinals and small sets: The AD+ Duality Program Abstract: The determinacy axiom, AD, was introduced by Mycielski and Steinhaus over 60 years ago as an alternative to the Axiom of Choice for the study of arbitrary sets of real numbers. The modern view is that determinacy axioms concern generalizations of the… |
|
Speaker: Eric MaskinTitle: CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Auction TheoryVenue: virtualEric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians April 22, 2022 | 9:30 – 11:00 am ET Title: Auction Theory Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher). Talk chairs: Scott Kominers, Sergiy Verstyuk SLIDES | VIDEO Answers to Questions from Talks 2 and 3 |
|
Speaker: Eric MaskinTitle: CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Mechanism DesignVenue: virtualEric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians April 20, 2022 | 9:30 – 11:00 am ET Title: Mechanism Design Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal? Talk chairs: Scott Kominers, Sergiy Verstyuk SLIDES | VIDEO |
|
Speaker: Eric MaskinTitle: CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Game Theory Basics and Classical Existence TheoremsVenue: virtualEric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians April 18, 2022 | 9:30 – 11:00 am ET Title: Game Theory Basics and Classical Existence Theorems Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo Talk chairs: Scott Kominers, Sergiy Verstyuk SLIDES | VIDEO |
|
Speaker: Karen UhlenbeckTitle: CMSA Math-Science Literature Lecture – Karen UhlenbeckVenue: virtualKaren Uhlenbeck (Institute for Advanced Study) Title: The Noether Theorems in Geometry: Then and Now Abstract: The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk, I outline a brief history of the theorems, explain a bit of the language, translate the first theorem into coordinate invariant language and give a few examples. I will mention only briefly their importance in physics and integrable systems…. |
|
Speaker: Sergiu KlainermanTitle: CMSA Math-Science Literature Lecture: Nonlinear stability of Kerr black holes for small angular momentumVenue: virtualSergiu Klainerman (Princeton University) Title: Nonlinear stability of Kerr black holes for small angular momentum Abstract: According to a well-known conjecture, initial data sets, for the Einstein vacuum equations, sufficiently close to a Kerr solution with parameters $a, m$, $|a|/m <1$, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of a future event horizon) which approaches (globally) a nearby Kerr solution. I will describe the main ideas in my recent joint work with Jeremie Szeftel concerning the resolution of the conjecture for small angular momentum, i.e. $, $|a|/m $ sufficiently small. The work, ArXiv:2104.11857v1, also depends on forthcoming work on solutions of nonlinear wave equations in realistic perturbations of Kerr, with Szeftel and Elena Giorgi, which I will also… |
|
Speaker: Frances KirwanTitle: CMSA Math-Science Literature Lecture: Moment maps and the Yang-Mills functionalVenue: virtualFrances Kirwan (University of Oxford) Title: Moment maps and the Yang-Mills functional Abstract: In the early 1980s Michael Atiyah and Raoul Bott wrote two influential papers, ‘The Yang-Mills equations over Riemann surfaces’ and ‘The moment map and equivariant cohomology’, bringing together ideas ranging from algebraic and symplectic geometry through algebraic topology to mathematical physics and number theory. The aim of this talk is to explain their key insights and some of the new directions towards which these papers led. This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Talk chair: Peter Kronheimer Video |
|
Speaker: Amit SahaiTitle: CMSA Math-Science Literature Lecture: Indistinguishability Obfuscation: How to Hide Secrets within SoftwareVenue: virtualAmit Sahai (UCLA) Title: Indistinguishability Obfuscation: How to Hide Secrets within Software Abstract: At least since the initial public proposal of public-key cryptography based on computational hardness conjectures (Diffie and Hellman, 1976), cryptographers have contemplated the possibility of a “one-way compiler” that translates computer programs into “incomprehensible” but equivalent forms. And yet, the search for such a “one-way compiler” remained elusive for decades. In this talk, we look back at our community’s attempts to formalize the notion of such a compiler, culminating in our 2001 work with Barak, Goldreich, Impagliazzo, Rudich, Vadhan, and Yang, which proposed the notion of indistinguishability obfuscation (iO). Roughly speaking, iO requires that the compiled versions of any two equivalent programs (with the same size and running… |
|
Speaker: Dan FreedTitle: CMSA Math-Science Literature Lecture: The Atiyah-Singer Index TheoremVenue: virtualDan Freed (The University of Texas at Austin) Title: The Atiyah-Singer Index Theorem Abstract: The story of the index theorem ties together the Gang of Four—Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator. This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Talk chair: Cumrun Vafa Video |
|
Speaker: Yi MaTitle: CMSA Math-Science Literature Lecture: Deep Networks from First PrinciplesVenue: virtualYi MaPhoto Copyright Noah Berger / 2019 Yi Ma (University of California, Berkeley) Title: Deep Networks from First Principles Abstract: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of so-obtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises… |
|
Speaker: Peter ShorTitle: CMSA Math-Science Literature Lecture: Quantum error correcting codes and fault toleranceVenue: virtualPeter Shor (MIT) Title: Quantum error correcting codes and fault tolerance Abstract: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field. Talk chair: Zhengwei Liu Video |
|
Speaker:Title: Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch, and SingerVenue: virtualIn 2021, the CMSA hosted a lecture series on the literature of the mathematical sciences. This series highlights significant accomplishments in the intersection between mathematics and the sciences. Speakers include Edward Witten, Lydia Bieri, Simon Donaldson, Michael Freedman, Dan Freed, and many more. Videos of these talks can be found in this Youtube playlist. https://youtu.be/vb_JEhUW9t4 In the Spring 2021 semester, the CMSA hosted a sub-program on this series titled A Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch and Singer. Below is the schedule for talks in that subprogram April 6, 2021 | 9:00 – 10:30am ET Edward Witten (IAS) Title: Isadore Singer’s Work on Analytic Torsion April 13, 2021 | 9:00 – 10:30am ET Claire Voisin (College… |
|
Speaker: Edward WittenTitle: CMSA Math-Science Literature Lecture: Isadore Singer’s Work on Analytic TorsionVenue: virtualEdward Witten (IAS) Title: Isadore Singer’s Work on Analytic Torsion Abstract: I will review two famous papers of Ray and Singer on analytic torsion written approximately half a century ago. Then I will sketch the influence of analytic torsion in a variety of areas of physics including anomalies, topological field theory, and string theory. This talk is part of a subprogram of the Mathematical Science Literature Lecture series, a Memorial Conference for the founders of index theory: Atiyah, Bott, Hirzebruch, and Singer. Talk chair: Cumrun Vafa Slides | Video |
|
Speaker: Maxim KontsevichTitle: CMSA Math-Science Literature Lecture: On the History of quantum cohomology and homological mirror symmetryVenue: virtualMaxim Kontsevich (IHÉS) Title: On the History of quantum cohomology and homological mirror symmetry Abstract: About 30 years ago, string theorists made remarkable discoveries of hidden structures in algebraic geometry. First, the usual cup-product on the cohomology of a complex projective variety admits a canonical multi-parameter deformation to so-called quantum product, satisfying a nice system of differential equations (WDVV equations). The second discovery, even more striking, is Mirror Symmetry, a duality between families of Calabi-Yau varieties acting as a mirror reflection on the Hodge diamond. Later it was realized that the quantum product belongs to the realm of symplectic geometry, and a half of mirror symmetry (called Homological Mirror Symmetry) is a duality between complex algebraic and symplectic varieties. The… |
|
Speaker: Kenji FukayaTitle: CMSA Math-Science Literature Lecture: Homological (homotopical) algebra and moduli spaces in Topological Field theoriesVenue: virtualKenji Fukaya (Simons Center for Geometry and Physics) Title: Homological (homotopical) algebra and moduli spaces in Topological Field theories Abstract: Moduli spaces of various gauge theory equations and of various versions of (pseudo) holomorphic curve equations have played important role in geometry in these 40 years. Started with Floer’s work people start to obtain more sophisticated object such as groups, rings, or categories from (system of) moduli spaces. I would like to survey some of those works and the methods to study family of moduli spaces systematically. Talk chair: Peter Kronheimer Slides | Video |
|
Speaker: Dan SpielmanTitle: CMSA Math-Science Literature Lecture: Discrepancy Theory and Randomized Controlled TrialsVenue: virtualDan Spielman (Yale University) Title: Discrepancy Theory and Randomized Controlled Trials Abstract: Discrepancy theory tells us that it is possible to partition vectors into sets so that each set looks surprisingly similar to every other. By “surprisingly similar” we mean much more similar than a random partition. I will begin by surveying fundamental results in discrepancy theory, including Spencer’s famous existence proofs and Bansal’s recent algorithmic realizations of them. Randomized Controlled Trials are used to test the effectiveness of interventions, like medical treatments. Randomization is used to ensure that the test and control groups are probably similar. When we know nothing about the experimental subjects, uniform random assignment is the best we can do. When we know information about… |
|
Speaker: Don ZagierTitle: CMSA Math-Science Literature Lecture: Quantum topology and new types of modularityVenue: virtualDon Zagier (Max Planck Institute for Mathematics and International Centre for Theoretical Physics) Title: Quantum topology and new types of modularity Abstract: The talk concerns two fundamental themes of modern 3-dimensional topology and their unexpected connection with a theme coming from number theory. A deep insight of William Thurston in the mid-1970s is that the vast majority of complements of knots in the 3-sphere, or more generally of 3-manifolds, have a unique metric structure as hyperbolic manifolds of constant curvature -1, so that 3-dimensional topology is in some sense not really a branch of topology at all, but of differential geometry. In a different direction, the work of Vaughan Jones and Ed Witten in the late 1980s gave… |
|
Speaker: Nigel HitchinTitle: CMSA Math-Science Literature Lecture: Michael Atiyah: Geometry and PhysicsVenue: virtualNigel Hitchin (University of Oxford) Title: Michael Atiyah: Geometry and Physics Abstract: In mid-career, as an internationally renowned mathematician, Michael Atiyah discovered that some problems in physics responded to current work in algebraic geometry and this set him on a path to develop an active interface between mathematics and physics which was formative in the links which are so active today. The talk will focus, in a fairly basic fashion, on some examples of this interaction, which involved both applying physical ideas to solve mathematical problems and introducing mathematical ideas to physicists. Talk chair: Peter Kronheimer Video |
|
Speaker: Arthur JaffeTitle: CMSA Math-Science Literature Lecture: Is relativity compatible with quantum theory?Venue: virtualArthur Jaffe (Harvard University) Title: Is relativity compatible with quantum theory? Abstract: We review the background, mathematical progress, and open questions in the effort to determine whether one can combine quantum mechanics, special relativity, and interaction together into one mathematical theory. This field of mathematics is known as “constructive quantum field theory.” Physicists believe that such a theory describes experimental measurements made over a 70 year period and now refined to 13-decimal-point precision—the most accurate experiments ever performed. Talk chair: Zhengwei Liu Video |