Past Seminars- Algebra

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  • Abdul Basit
    Wed Nov 30, 2016
    2:00 pm
    The classical Sylvester-Gallai theorem states the following: Given a finite set of points in the 2-dimensional Euclidean plane, not all collinear, there must exist a line containing exactly 2 points (referred to as an ordinary line). In a recent result, Green and Tao were able to give optimal lower bounds on the number of ordinary lines for large...
  • Daniel Krashen
    Mon Nov 21, 2016
    3:00 pm
    In this talk, I'll describe conjectures and recent work concerning field invariants and their complexity, relating to quadratic forms, Galois cohomology, and similar concepts.
  • Angela Gibney
    Mon Nov 7, 2016
    3:00 pm
    I will discuss recent work, with Prakash Belkale, where we show the section ring for the pair (Bun, D) is finitely generated, for D the determinant of cohomology line bundle on the stack Bun = Bun_{SL(r)}(C) parameterizing principal SL(r)-bundles on a singular stable curve C.  I'll define these things, put the result into some historical...
  • Ralph Greenberg
    Tue May 3, 2016
    2:00 pm
    There is a classical theorem of Iwasawa which concerns certain modules X for the formal power series ring Λ = Zp[[T]] in one variable.  Here p is a prime and Zp is the ring of p-adic integers.  Iwasawa's theorem asserts that X has no nonzero, finite Λ-submodules. We will begin by describing...
  • Kiran Kedlaya
    Tue Apr 12, 2016
    2:00 pm
  • Yuri G. Zarhin
    Tue May 5, 2015
    2:00 pm
    We study the monodromy of a certain class of semistable hyperelliptic curves over the rationals that was introduced by Shigefumi Mori forty years ago (before his Minimal Model Program). Using ideas of Chris Hall, we prove that the corresponding $\ell$-adic monodromy groups are (almost) ``as large as possible". We also discuss an explicit...
  • Herbert Lange
    Fri Feb 20, 2015
    3:30 pm