news

Undergraduate Prizes 2020-2021

Below are undergraduate prizes awarded in Mathematics for the 2020-2021 academic year. Alexander Prize • Hanna Mularczyk Friends Prize • Kenz Kallal • Lux Zhao...
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announcements

The Azat Miftakhov Day
June 16, 2021      10:00 am
In solidarity with Azat Miftakhov *Starting at 4pm Central European Summer Time (UTC+2)* It will be organized online by the Azat Miftakhov committee in solidarity with Azat...
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upcoming events

  • June 14, 2021
    3:00 pm
    Special Colloquium

    COLLOQUIUMS

    Speaker: Michael Douglas - Harvard CMSA & Stony Brook University   Title: Special Colloquium
  • June 15, 2021
    10:00 am
    via Zoom Video Conferencing

    MATHEMATICAL PICTURE LANGUAGE SEMINAR

    Speaker: Jeongwan Haah - Microsoft   Title: TBD
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  • MATHEMATICAL PICTURE LANGUAGE SEMINAR

    MATHEMATICAL PICTURE LANGUAGE SEMINAR
    TBD

    10:00 AM-11:00 AM
    June 1, 2021
  • COLLOQUIUMS

    COLLOQUIUMS
    Special Colloquium

    3:00 PM-4:00 PM
    June 1, 2021

    Title: From Ramanujan to Rokhlin, via quantum groups

    Abstract: In this talk, intended for a broad audience, I will describe recent work on new q-series invariants of 3-manifolds labeled by Spin-C structures. While the original motivation for studying these invariants is rooted in topology, they exhibit a number of unexpected properties and connections to other areas of mathematics, e.g. turn out to be characters of logarithmic vertex algebras.

    Registration is required to receive the Zoom information.

    Please go here to register.

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  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Ultra Unification: Quantum Fields Beyond the Standard Model
    10:30 AM-12:00 PM
    June 2, 2021
    Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects,  etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.

    Zoom: https://harvard.zoom.us/j/977347126

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  • COLLOQUIUMS

    COLLOQUIUMS
    Special Colloquium

    3:00 PM-4:00 PM
    June 8, 2021

    Title: The two-dimensional Ising model revisited

    Abstract: I will describe joint work with Constantin Teleman, in which we cast topological eyes on a well-studied system in condensed matter physics.  In particular, we use the symmetry in a strong form and apply the technology of extended topological field theory.  We obtain a proof of duality, construct a new dual theory for models based on a nonabelian group, and make dynamical predictions.  The lecture will not assume any physics background.

    Registration is required to receive the Zoom information.

    Please go here to register.

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  • COLLOQUIUMS

    COLLOQUIUMS
    Special Colloquium

    3:00 PM-4:00 PM
    June 14, 2021

    Title: Topics in computers and mathematics

    Abstract: Advances in computation and machine learning are changing the way we do pure mathematics and theoretical physics. Using examples from differential geometry, finite group theory and other fields, I will survey some directions which I believe will have major impact during the coming decade: machine learning, ML inspired numerical methods, computer assisted proofs and interactive theorem proving.

    Registration is required to receive the Zoom information.

    Please go here to register.

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  • ANNOUNCEMENTS
    10:00 AM-1:15 PM
    June 16, 2021

    In solidarity with Azat Miftakhov

    *Starting at 4pm Central European Summer Time (UTC+2)*

    It will be organized online by the Azat Miftakhov committee in solidarity with Azat Miftakhov, a graduate student from Moscow State University who has been arbitrarily detained by Russian state authorities for almost two years and a half.

    4:00 pm Cédric Villani (Member of the French National Assembly)
    Opening speech

    4:15 pm Maryna Viazovska (École Polytechnique Fédérale de Lausanne, Switzerland)
    tba

    5:15 pm Alexander Bufetov (CNRS & Institut de Mathématiques de Marseille, France & Steklov, IITP RAS, Russia)
    Determinantal point processes: quasi-symmetries, minimality and interpolation

    6:15 pm Peter Scholze (Universität Bonn, Germany)
    Condensed Mathematics

    * Tokyo at 11pm, Moscow at 5pm, Bonn, Paris and Warsaw at 4pm, London at 3pm, New York at 10am, San Francisco at 7am

    The webinar will be broadcast live on several websites whose
    addresses will be announced a few days before. Further
    the information available at caseazatmiftakhov.org

  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Uses of Wilson Operator Expansion in Gauge Theories
    10:30 AM-12:00 PM
    June 16, 2021

    I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.

    It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.

    Zoom: https://harvard.zoom.us/j/977347126

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  • MATHEMATICAL PICTURE LANGUAGE SEMINAR
    10:00 AM-11:00 AM
    June 22, 2021

    The commutative graph complex, defined by contracting edges in graphs, was introduced by Kontsevich in 1993. Recently, Chan-Galatius-Payne have shown that its cohomology can be identified with a piece of the cohomology of  moduli spaces of curves, and Willwacher showed that graph cohomology in degree zero it is related to the Grothendieck-Teichmuller Lie algebra.  Nevertheless, the cohomology of the graph complex remains mysterious, and little is known explicitly.

    In this talk I will explain how to use invariant trace forms to construct differential forms on a moduli space of metric graphs. By integrating these forms, one can canonically assign integrals to graphs, which are very closely related to Feynman integrals in perturbative quantum field theory, but have the property that they always converge.  A Stokes formula enables us to deduce some information about the cohomology of the graph complex, and leads to new predictions about its structure, and its relation to physics.

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

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