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Current Developments in Mathematics 2023
April 7, 2023 - April 8, 2023     
Current Developments in Mathematics 2023 April 7-8, 2023 Harvard University Science Center Speakers: Amol Aggarwal - Columbia University Bhargav Bhatt - Institute for Advanced Study...
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< 2021 >
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  • CMSA EVENT: CMSA Interdisciplinary Science Seminar: Exploring Invertibility in Image Processing and Restoration

    Speaker: Qifeng Chen – The Hong Kong University of Science and Technology

    9:00 AM-10:00 AM
    November 4, 2021

    Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification, and we can share high-quality JPEG images easily on the internet, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g., retouching) and analysis. However, the huge size of raw data hinders its popularity in practice, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks, including image compression, reversible image conversion (e.g., image-to-video conversion), and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently non-invertible tasks.


    Zoom ID: 950 2372 5230 (Password: cmsa)

  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Fusion Category Symmetries in Quantum Field Theory

    Speaker: Yifan Wang – NYU

    10:30 AM-12:00 PM
    November 4, 2021

    Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.
    —–
    Subscribe to Harvard CMSA seminar videos (more to be uploaded):
    https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
    https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww
    —–
    Subscribe to Harvard CMSA seminar videos (more to be uploaded):
    https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
    https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww

    —–
    Subscribe to Harvard CMSA seminar videos (more to be uploaded):
    https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
    https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww

  • ALGEBRAIC DYNAMICS SEMINAR: A transcendental birational dynamical degree

    Speaker: Holly Krieger – University of Cambridge and Radcliffe Institute

    4:00 PM-6:00 PM
    November 4, 2021

    I will speak about recent joint work with Bell, Diller, and Jonsson in which we refute a conjecture of Bellon-Viallet by constructing (mostly) explicit examples of birational maps of projective 3-space with transcendental dynamical degree, also known as algebraic entropy.  The set of possible dynamical degrees for birational maps of projective space is known to be a countable set, with nearly all examples given by eigenvalues of integer matrices (and thus algebraic), yet we demonstrate the existence of infinitely many transcendental values in this set.  The proof builds on previous work of Bell-Diller-Jonsson, combining the study of monomial maps of toric varieties with classical techniques from Diophantine approximation.


    for more information, go to:

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  • CMSA EVENT: CMSA Colloquium: Curve counting on surfaces and topological strings

    Speaker: Andrea Brini – University of Sheffield

    9:30 AM-10:30 AM
    November 17, 2021

    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.
    I 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.

    https://harvard.zoom.us/j/95767170359

    (Password: cmsa)

  • NUMBER THEORY SEMINAR: Arithmetic volumes of unitary Shimura varieties

    Speaker: Benjamin Howard – Boston College

    3:00 PM-4:00 PM
    November 17, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    The integral model of a GU(n-1,1) Shimura variety carries a natural metrized line bundle of modular forms.  Viewing this metrized line bundle as a class in the codimension one arithmetic Chow group, one can define its arithmetic volume as an iterated self-intersection.  We will show that this volume can be expressed in terms of logarithmic derivatives of Dirichlet L-functions at integer points, and explain the connection with the arithmetic Siegel-Weil conjecture of Kudla-Rapoport.  This is joint work with Jan Bruinier.

  • NUMBER THEORY SEMINAR: Arithmetic volumes of unitary Shimura varieties

    Speaker: Benjamin Howard – Boston College

    3:00 PM-4:00 PM
    November 17, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    The integral model of a GU(n-1,1) Shimura variety carries a natural metrized line bundle of modular forms.  Viewing this metrized line bundle as a class in the codimension one arithmetic Chow group, one can define its arithmetic volume as an iterated self-intersection.  We will show that this volume can be expressed in terms of logarithmic derivatives of Dirichlet L-functions at integer points, and explain the connection with the arithmetic Siegel-Weil conjecture of Kudla-Rapoport.  This is joint work with Jan Bruinier.

  • SEMINARS: Joint Harvard-CUHK-YMSC Differential Geometry Seminar

    Speaker: Nick Sheridan – School of Mathematics, University of Edinburgh

    4:00 PM-5:00 PM
    November 17, 2021

    will speak on:

    Quantum cohomology as a deformation of symplectic cohomology


    Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.


    Zoom Link: https://cuhk.zoom.us/j/94377988344

    Meeting ID: 943 7798 8344
    Passcode: 20211117

  • OPEN NEIGHBORHOOD SEMINAR: Tales of random projections: where probability meets geometry

    Speaker: Kavita Ramanan – Brown University

    4:30 PM-5:30 PM
    November 17, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    In several areas of mathematics, including probability theory, asymptotic functional analysis, statistics and data science, one is interested in high-dimensional objects, such as measures, data or convex bodies. One common theme is to try to understand what lower-dimensional projections can say about the corresponding high-dimensional objects. I will describe several results that address this question, starting with classical results and moving on to more recent breakthroughs, my own research and some open questions. The talk will be self-contained and accessible to undergraduate students.

    Website: https://people.math.harvard.edu/~ana/ons/

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  • SEMINARS: Harvard-MIT-MSR Combinatorics Seminar

    Speaker: Grant Barkley – Harvard University

    3:30 PM-4:30 PM
    November 19, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    will speak on:

    Extended weak order in affine type


    The extended weak order is a partial order associated to a Coxeter system (W,S). It is the containment order on “biclosed” sets of positive roots in the (real) root system associated to W. When W is finite, this order coincides with the (right) weak order on W, but when W is infinite, the weak order on W is a proper order ideal in the extended weak order. It is well-known that the weak order on W is a lattice if and only if W is finite. In contrast, it is a longstanding conjecture of Matthew Dyer that the extended weak order is a lattice for any W, which is open in the case that W is infinite. I will present joint work with David Speyer where we prove this conjecture for the affine Coxeter groups.

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  • CMSA EVENT: CMSA Combinatorics, Probability and Physics Seminar: Resistance curvature – a new discrete curvature on graphs

    Speaker: Karel Devriendt – University of Oxford, Mathematical Institute

    9:30 AM-10:30 AM
    November 30, 2021

    The last few decades has seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings.
    In this talk, I will introduce a new notion of discrete curvature on graphs, which we call the resistance curvature, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.
    Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler.
    This work was done in collaboration with Renaud Lambiotte.
    Based on joint work with He Guo and Kalen Patton, see https://arxiv.org/abs/2011.09459   

     

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