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  • CMSA EVENT: **CANCELED** CMSA Colloquium: Errors and Correction in Cumulative Knowledge **CANCELED**

    Speaker: Madhu Sudan – Harvard University

    4:30 PM-5:30 PM
    April 1, 2024
    20 Garden Street, Cambridge, MA 02138

    **CANCELED**

    Societal accumulation of knowledge is a complex, and arguably error-prone, process. The correctness of new units of knowledge depends not only on the correctness of the new reasoning, but also on the correctness of old units that the new one builds on. If left unchecked, errors could completely ruin the validity of most of this knowledge so there must some error-correcting going on. What are the error-corrections processes employed in nature and how effective are they? In this talk, we describe our attempts to model such phenomena using probablistic models – we describe models for growth of cumulative knowledge, emergence of errors and methods to check for errors and eliminate them. We then analyze in this compound model, when effects of errors may survive, and when they are totally eliminated.

    The central discovery in our work is the following optimistic statement: If we do checking correctly (most of the time) investing just a constant factor (<1) of our effort in checking (and saving the remaining constant factor towards deriving new units of knowledge), then effects of errors can be kept in check. Notably the amount of effort expended on checking does not scale with the volume of total knowledge or the depth of dependencies in the new units of knowledge, either of which would be overwhelming.

    Based on the papers:

    Is this correct? Let’s check!
    Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel, Madhu Sudan
    arXiv:2211.12301

    Errors are Robustly Tamed in Cumulative Knowledge Processes
    Anna Brandenberger, Cassandra Marcussen, Elchanan Mossel, Madhu Sudan
    arXiv:2309.05638

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  • CONFERENCE: Current Developments in Mathematics 2024
    All day
    April 6, 2024-April 6, 2024
    1 Oxford Street, Cambridge, MA 02138 USA
    A poster detailing the time and place of the 2024 Current Developments in Mathematics conference.

    Current Developments in Mathematics 2024

    April 5-6, 2024
    Harvard University Science Center
    Friday—Lecture Hall C
    Saturday—Lecture Hall A
    Register Here

     

     

    Funding application is closed as of March 12.

    Download PDF for a detailed schedule of lectures and events.

    Friday, April 5

    Saturday, April 6

    • 1:30 p.m. – 2:20 p.m. Part 1
    • 2:20 p.m. – 2:30 p.m. Break
    • 2:30 p.m. – 3:20 p.m. Part 2

    Jiaoyang Huang

    Random Matrix Statistics and Airy Line Ensembles

    • 9:05 a.m. – 9:55 a.m. Part 1
    • 9:55 a.m. – 10:05 a.m. Break
    • 10:05 a.m. – 10:55 a.m. Part 2

    Daniel Litt

    Motives, mapping class groups, and monodromy

    3:20 p.m. – 3:35 p.m.

    Break

    10:55 a.m. – 11:10 a.m.

    Break

    • 3:35 p.m. – 4:25 p.m. Part 1
    • 4:25 p.m. – 4:35 p.m. Break
    • 4:35 p.m. – 5:25 p.m. Part 2

    Lisa Piccirillo

    Exotic phenomena in dimension 4

    • 11:10 a.m. – 12 p.m. Part 1
    • 12 p.m. – 1:30 p.m. Lunch
    • 1:30 p.m. – 2:20 p.m. Part 2

    Samit Dasgupta

    Stark’s conjectures and explicit class field theory

    2:20 p.m. – 2:35 p.m.

    Break

    • 2:35 p.m. – 3:25 p.m. Part 1
    • 3:25 p.m. – 3:35 p.m. Break
    • 3:35 p.m. – 4:25 p.m. Part 2

    Dan Cristofaro-Gardiner

    Low-dimensional topology and dynamics

    Organizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau, Shing-Tung Yau (Harvard).

    Sponsored by the National Science Foundation, Harvard University Mathematics, and the Massachusetts Institute of Technology.

    Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here.

  • HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Szemer\’edi’s theorem and nilsequences

    Speaker: James Leng – UCLA

    3:00 PM-4:00 PM
    April 6, 2024-April 27, 2024

    Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

    In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

    ===============================

    For more info, see https://math.mit.edu/combin/

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  • OTHER MATHEMATICS DEPARTMENT EVENTS: Special Lecture: Equivariant Topology in Combinatorics

    OTHER MATHEMATICS DEPARTMENT EVENTS
    Special Lecture: Equivariant Topology in Combinatorics

    Speaker: Dora Woodruff – Harvard AB 2024

    10:00 AM-10:25 AM
    April 12, 2024
    1 Oxford Street, Cambridge, MA 02138 USA

    My thesis discusses a bridge between equivariant topology and combinatorics. The kind of problem I look at is an inherently discrete problem which can be solved by translating the problem into showing the nonexistence of a certain map of topological spaces. We will see examples stemming from graph theory, such as the Lovász Conjecture discrete geometry, such as the Randakumar and Rao Conjecture, and general combinatorics.

  • OTHER MATHEMATICS DEPARTMENT EVENTS: Special Lecture: The Atiyah-Singer Index Theorem and Almost Complex Spheres

    Speaker: Dhruv Goel – Harvard AB 2024

    10:30 AM-10:55 AM
    April 12, 2024
    1 Oxford Street, Cambridge, MA 02138 USA

    When is a real smooth manifold secretly a complex manifold? For this, it is necessary, but not sufficient, for the manifold’s tangent bundle to be a complex vector bundle, a condition called being “almost complex”. In this talk, I will give several examples of complex, almost complex, and (orientable, even-dimensional) not-even-almost complex manifolds. I will then discuss how the Atiyah-Singer Index Theorem can be used to show that certain smooth manifolds are not almost complex, focusing on the case of the twisted Dirac operator on spinor bundles on spheres.

  • CMSA EVENT: CMSA Member Seminar: 3d quantum trace map

    Speaker: Sunghyuk Park – Harvard

    12:00 PM-1:00 PM
    April 12, 2024

    I will speak about my recent work (joint with Sam Panitch) constructing the 3d quantum trace map, a homomorphism from the Kauffman bracket skein module of an ideally triangulated 3-manifold to its (square root) quantum gluing module, thereby giving a precise relationship between the two quantizations of the character variety of ideally triangulated 3-manifolds. Our construction is based on the study of stated skein modules and their behavior under splitting, especially into face suspensions.


    Friday, Apr. 12th at 12pm, with lunch, lounge at CMSA (20 Garden Street).

    Also by Zoom: https://harvard.zoom.us/j/92410768363

  • CMSA EVENT: CMSA Member Seminar: Global weak solutions of 3+1 dimensional vacuum Einstein equations

    Speaker: Puskar Mondal – CMSA

    12:00 PM-1:00 PM
    April 12, 2024

    It is important to understand if the `solutions’ of non-linear evolutionary PDEs persist for all time or become extinct in finite time through the blow-up of invariant entities. Now the question of this global existence or finite time blow up in the PDE settings is well defined if the regularity of the solution is specified. Most physically interesting scenarios demand control of the point-wise behavior of the solution. Unfortunately, most times this level of regularity is notoriously difficult to obtain for non-linear equations. In this talk, I will discuss very low regularity solutions namely distributional (or weak) solutions of vacuum Einsten’s equations in 3+1 dimensions. I prove that on a globally hyperbolic spacetime foliated by closed connected oriented negative Yamabe slices, weak solutions of the Einstein equations exist for all time. The monotonicity of a Coercive Entity called reduced Hamiltonian that controls the minimum regularity required for the weak solution is employed. This is in the same spirit as Leray’s global weak solutions of Navier-Stokes in 3+1 dimensions and the first result in the context of Einstein equations.


    Friday, Apr. 12th at 12pm, with lunch, lounge at CMSA (20 Garden Street).

    Also by Zoom: https://harvard.zoom.us/j/92410768363

  • OTHER MATHEMATICS DEPARTMENT EVENTS: Special Lecture: Algebraicity, Transcendence, and Periods

    Speaker: Salim Tayou – Harvard University

    2:00 PM-2:45 PM
    April 12, 2024
    1 Oxford Street, Cambridge, MA 02138 USA

    Transcendental numbers form a mysterious and large class of complex numbers: they are defined as complex numbers that are not the solution of a polynomial equation, and include the numbers pi and e, for example. Within this class, we find the periods that were first studied by Newton and Kepler in the context of celestial mechanics, and which present many curious properties that are the subject of very active research. In this talk, I will give a glimpse of almost 500 years of history of periods, right up to the most recent developments.

  • HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: On the evolution of structure in triangle-free graphs

    Speaker: Will Perkins – Georgia Tech

    3:00 PM-4:00 PM
    April 12, 2024

    Erdos-Kleitman-Rothschild proved that the number of triangle-free graphs on n vertices is asymptotic to the number of bipartite graphs; or in other words, a typical triangle-free graph is a random subgraph of a nearly balanced complete bipartite graph. Osthus-Promel-Taraz extended this result to much lower densities: when m >(\sqrt{3}/4 +eps) n^{3/2} \sqrt{\log n}, a typical triangle-free graph with m edges is a random subgraph of size m from a nearly balanced complete bipartite graph (and this no longer holds below this threshold). What do typical triangle-free graphs at sparser densities look like and how many of them are there? We consider what we call the “ordered” regime, in which typical triangle-free graphs are not bipartite but do align closely with a nearly balanced bipartition. In this regime we prove asymptotic formulas for the number of triangle-free graphs and give a precise probabilistic description of their structure. Joint work with Matthew Jenssen and Aditya Potukuchi.

    ===============================

    For more info, see https://math.mit.edu/combin/

  • HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Szemer\’edi’s theorem and nilsequences

    Speaker: James Leng – UCLA

    3:00 PM-4:00 PM
    April 12, 2024-April 27, 2024

    Suppose A is a subset of the natural numbers with positive density. A classical result in additive combinatorics, Szemeredi’s theorem, states that for each positive integer k, A must have an arithmetic progression of nonzero common difference of length k.

    In this talk, we shall discuss various quantitative refinements of this theorem and explain the various ingredients that recently led to the best quantitative bounds for this theorem. This is joint work with Ashwin Sah and Mehtaab Sawhney.

    ===============================

    For more info, see https://math.mit.edu/combin/

  • OTHER MATHEMATICS DEPARTMENT EVENTS: Special Lecture: Symmetry in quantum field theory

    OTHER MATHEMATICS DEPARTMENT EVENTS
    Special Lecture: Symmetry in quantum field theory

    Speaker: Daniel S. Freed – Harvard University

    3:15 PM-4:00 PM
    April 12, 2024
    1 Oxford Street, Cambridge, MA 02138 USA

    The notion of an abstract group encapsulates and illuminates concrete manifestations of symmetry. Recently in quantum field theory there have been discussions of “higher symmetry” and “noninvertiblesymmetry” and their applications.  In joint work with Greg Moore and Constantin Teleman, we propose a conceptual framework for symmetry in quantum field theory, built on the ongoing developments in topological field theory.  It incorporates these newer forms of symmetry, at least with sufficient finiteness conditions.

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