Events & Seminars

  • 2020 Dec 10

    Basic Notions: Ari Shnidman "Randomness in arithmetic: class groups."

    4:00pm to 5:15pm

    Location: 

    Zoom

    For everynumber field K, there is a finite abelian group C called the
    class group, which serves as an obstruction to unique factorization.
    Since Gauss, number theorists have tried to understand questions such
    as how often is C trivial, or how often C contains an element of fixed
    order (as K varies). In the 1970's, Cohen and Lenstra observed
    empirically that when the degree and signature of K is fixed, the
    isomorphism class of C adheres to a natural probability distribution.
    I'll discuss these Cohen-Lenstra heuristics and survey what is known,

  • 2020 Dec 13

    Kazhdan seminar : Ari Shnidman "Fundamental lemmas and Fourier transform"

    Repeats every week every Sunday until Sun Jan 17 2021 .
    11:00am to 1:00pm


    Abstract: A fundamental lemma is an identity relating p-adic integrals on two different groups. These pretty identities fit into a larger story of trace formulas and special values of L-functions.  Our goal is to present recent work of Beuzart-Plessis on the Jacquet-Rallis fundamental lemma, comparing integrals on GL(n) and U(n).
  • 2020 Dec 13

    Kazhdan seminar: Tomer Schank "Sheaves with nilpotent support"

    Repeats every week every Sunday until Sun Jan 17 2021 .
    2:00pm to 4:00pm


    Abstract: Given a smooth and proper curve X and a reductive group G one can consider the stack Bun_{G,X} of principal G-bundles on X. This stack has an important role in Algebraic Geometry and Representation Theory especially with regard to the Langlands program. We shall study the geometry of Bun_{G,X} and the category 
    D(G,X) of constructible  sheaves on Bun_{G,X}. We shall be especially interested in the subcategory D_{nil}(G,X) of sheaves with nilpotent singular support.
  • 2020 Dec 13

    Kazhdan seminar: Yoel Groman and Jake Solomon "Stability conditions"

    Repeats every week every Sunday until Sun Jan 17 2021 .
    4:00pm to 6:00pm


    Abstract: We will discuss stability conditions on triangulated categories following the work of Douglas and Bridgeland. Concrete examples of stability conditions will be given from symplectic and algebraic geometry, which will also illustrate mirror symmetry. An effort will be made to give a gentle introduction to the relevant background material from category theory, symplectic geometry and algebraic geometry.
  • 2020 Dec 17

    Basic Notions: Ari Shnidman "Randomness in arithmetic: class groups."

    4:00pm to 5:15pm

    Location: 

    Zoom
    For every number fieldK, there is a finite abelian group C called the
    class group, which serves as an obstruction to unique factorization.
    Since Gauss, number theorists have tried to understand questions such
    as how often is C trivial, or how often C contains an element of fixed
    order (as K varies). In the 1970's, Cohen and Lenstra observed
    empirically that when the degree and signature of K is fixed, the
    isomorphism class of C adheres to a natural probability distribution.
    I'll discuss these Cohen-Lenstra heuristics and survey what is known,
  • 2020 Dec 20

    Kazhdan seminar : Ari Shnidman "Fundamental lemmas and Fourier transform"

    11:00am to 1:00pm


    Abstract: A fundamental lemma is an identity relating p-adic integrals on two different groups. These pretty identities fit into a larger story of trace formulas and special values of L-functions.  Our goal is to present recent work of Beuzart-Plessis on the Jacquet-Rallis fundamental lemma, comparing integrals on GL(n) and U(n).
  • 2020 Dec 20

    Kazhdan seminar: Tomer Schank "Sheaves with nilpotent support"

    2:00pm to 4:00pm


    Abstract: Given a smooth and proper curve X and a reductive group G one can consider the stack Bun_{G,X} of principal G-bundles on X. This stack has an important role in Algebraic Geometry and Representation Theory especially with regard to the Langlands program. We shall study the geometry of Bun_{G,X} and the category 
    D(G,X) of constructible  sheaves on Bun_{G,X}. We shall be especially interested in the subcategory D_{nil}(G,X) of sheaves with nilpotent singular support.

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