news

Mike Hopkins Awarded Veblen Prize

Michael Hopkins--Department Chair and George Putnam Professor of Pure and Applied Mathematics--has been awarded the American Mathematical Society's Oscar Veblen Prize in Geometry for co-authorship...
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announcements

Current Developments in Mathematics 2021-22
March 18, 2022 - March 19, 2022     
Current Developments in Mathematics 2021-22 March 18-19, 2022 Harvard University Science Center Lecture Hall B   Speakers: Jessica Fintzen (Duke) Ryan O’Donnell (Carnegie Mellon) Jack...
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upcoming events

< 2021 >
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  • DIFFERENTIAL GEOMETRY SEMINAR
    3:00 AM-4:00 AM
    December 1, 2021

    will speak on:

    Lagrangians and mirror symmetry in the Higgs bundle moduli space


    The talk concerns recent work with Tamas Hausel in asking how SYZ mirror symmetry works for the moduli space of Higgs bundles. Focusing on C^*-invariant Lagrangian submanifolds, we use the notion of virtual multiplicity as a tool firstly to examine if the Lagrangian is closed, but  also to open up new features involving finite-dimensional algebras which are deformations of cohomology algebras. Answering some of the questions raised  requires revisiting basic constructions of stable bundles on curves.

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    For details visit:

    http://www.ims.cuhk.edu.hk/cgi-bin/SeminarAdmin/bin/Web

    http://www.ims.cuhk.edu.hk/activities/seminar/joint-dg-seminar/

     


    Zoom Link: https://cuhk.zoom.us/j/99285825827

    Meeting ID: 992 8582 5827
    Passcode: 20211201

  • CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The Principles of Deep Learning Theory
    2:00 PM-3:00 PM
    December 1, 2021

    Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data.

    In terms of their “microscopic” definition, deep neural networks are a flexible set of functions built out of many basic computational blocks called neurons, with many neurons in parallel organized into sequential layers. Borrowing from the effective theory framework, we will develop a perturbative 1/n expansion around the limit of an infinite number of neurons per layer and systematically integrate out the parameters of the network. We will explain how the network simplifies at large width and how the propagation of signals from layer to layer can be understood in terms of a Wilsonian renormalization group flow. This will make manifest that deep networks have a tuning problem, analogous to criticality, that needs to be solved in order to make them useful. Ultimately we will find a “macroscopic” description for wide and deep networks in terms of weakly-interacting statistical models, with the strength of the interactions between the neurons growing with depth-to-width aspect ratio of the network. Time permitting, we will explain how the interactions induce representation learning.

    This talk is based on a book, “The Principles of Deep Learning Theory,” co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.


    https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09

  • NUMBER THEORY SEMINAR

    NUMBER THEORY SEMINAR
    Mod p points on Shimura varieties

    3:00 PM-4:00 PM
    December 1, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    The study of mod p points on Shimura varieties was originally motivated by the study of the Hasse-Weil zeta function for Shimura varieties. It involves some rather subtle problems which test just how much we know about motives over finite fields. In this talk I will explain some recent results, and applications, and what still remains conjectural.
  • NUMBER THEORY SEMINAR

    NUMBER THEORY SEMINAR
    Mod p points on Shimura varieties

    3:00 PM-4:00 PM
    December 1, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    The study of mod p points on Shimura varieties was originally motivated by the study of the Hasse-Weil zeta function for Shimura varieties. It involves some rather subtle problems which test just how much we know about motives over finite fields. In this talk I will explain some recent results, and applications, and what still remains conjectural.
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  • 9:30 AM-10:30 AM
    December 7, 2021

    I will introduce a new brane engineering for 2d minimally supersymmetric, i.e. N=(0,1), gauge theories. Starting with 2d N=(0,2) gauge theories on D1-branes probing Calabi-Yau 4-folds, a brand new orientifold configuration named ’Spin(7) orientifold’ is constructed and the resultant 2d N=(0,1) theories on D1-branes are derived. Using this method, one can build an infinite family of 2d N=(0,1) gauge theories explicitly. Furthermore, the N=(0,1) triality, proposed by Gukov, Pei and Putrov, enjoys a geometric interpretation as the non-uniqueness of the map between gauge theories and Spin(7) orientifolds. The (0,1) triality can then be regarded as inherited from the N=(0,2) triality of gauge theories associated with Calabi-Yau 4-folds. Furthermore, there are theories with N=(0,1) sector coupled to (0,2) sector, where both sectors respectively enjoy (0,1) and (0,2) trialities.

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  • CMSA EVENT: CMSA Math-Science Literature Lecture Series
    9:30 AM-11:00 AM
    December 9, 2021

    will speak on:

    The Noether Theorems in Geometry: Then and Now


    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. In the second part of the talk, I describe why they are still relevant in geometric analysis: how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston. Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension. The talk finishes with an example or two from the literature.

    Register Online

  • COLLOQUIUMS
    4:30 PM-5:30 PM
    December 9, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    The dynamical degree of an invertible self-map of projective space is an asymptotic measure of the algebraic complexity of the iterates of the map. This numerical invariant controls many aspects of the dynamics of the map, and in this talk I will survey the significance of the dynamical degree and discuss some important examples. In these examples, the dynamical degree is an integer or an eigenvalue of an integer matrix, so an algebraic number, as was conjecturally the case for all such maps. I will discuss joint work with Bell, Diller, and Jonsson in which we refute this conjecture by constructing invertible maps of projective 3-space which have transcendental dynamical degree.

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