Named Lecture Series

  • 2017 Jan 09

    Lecture 3: Cohen-Lenstra in the Presence of Roots of Unity

    Lecturer: 

    Prof. Jacob Tsimerman, University of Toronto
    4:00pm

    Location: 

    Ross 70
    (joint with Lipnowski, Sawin) The class group is a natural abelian group one can associated to a number field, and it is natural to ask how it varies in families. Cohen and Lenstra famously proposed a model for families of quadratic fields based on random matrices of large rank, and this was later generalized by Cohen-Martinet. However, their model was observed by Malle to have issues when the base field contains roots of unity.
  • 2017 Jan 08

    Lecture 2: Torsion In Class Groups

    Lecturer: 

    Prof. Jacob Tsimerman, University of Toronto
    12:00pm

    Location: 

    Ross 70A
    (joint with Bhargava,Shankar,Taniguchi,Thorne, and Zhao) Zhang’s conjecture asserts that for fixed positive integers m, n, the size of the m-torsion in the class group of a degree n number field is smaller than any power of the discriminant. In all but a handful of cases, the best known result towards this conjecture is the ”convex” bound given by the Brauer-Siegel Theorem. We make progress on this conjecture by giving a”subconvex” bound on the size of the 2-torsion of the class group of a number field in terms of its discriminant, for any value of n.
  • 2017 Jan 05

    Lecture 1: Counting Number Fields

    Lecturer: 

    Prof. Jacob Tsimerman, University of Toronto
    2:30pm

    Location: 

    Lecture Hall 2
    Number fields are fields which are finite extensions of Q. They come with a canonical invariant called the discriminant, which can be thought of as the volume of a certain canonically associated lattice. While these objects are central to modern number theory, it turns out that counting them is extremely difficult. More precisely, what is the asymptotic behavior of N (n,X) the number of degree n field extensions of Q with discriminant at most X as X grows, while n remains fixed?
  • 2016 Jun 13

    Lecture 2: Homology and cohomology of tropical varieties

    Lecturer: 

    Dr. June Huh, IAS & Princeton
    10:30am

    Location: 

    Rothberg building(s), Room B220
    A tropical variety is a piecewise linear object that (sometimes) appears as a shadow of an algebraic variety. In this talk, a gentle introduction to the Chow homology and cohomology of tropical varieties will be given. Two family of examples of combinatorial nature will be emphasized: the Stanley-Reisner ring of the boundary of a simplicial polytope, modulo linear system of parameters, and the Chow ring of a matroid.

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