Past Seminars- Algebra

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  • Ralph Greenberg
    Tue Feb 25, 2014
    3:00 pm
    We will discuss the question of defining a p-adic L-function and formulating a main conjecture for an Artin representation. The case where the Artin representation is totally even (or odd) is classical. The corresponding main conjecture has been proven by Wiles.  This talk will discuss the special case where the representation is 2-...
  • Vladimir Baranovsky
    Thu Jun 6, 2013
    2:00 pm
  • Jennifer Balakrishnan
    Thu May 23, 2013
    2:00 pm
    We give a Chabauty-like method for finding p-adic approximations to integral points on hyperelliptic curves when the Mordell-Weil rank of the Jacobian equals the genus. The method uses an interpretation of the component at p of the p-adic height pairing in terms of iterated Coleman integrals.  This is joint work with Amnon Besser and...
  • Steven Sam
    Thu May 9, 2013
    2:00 pm
    The theory of polynomial functors allows one to make sense of the stable polynomial representation theory of the general linear group over a field of characteristic 0. It also has a good notion of specialization, so that calculations done in the "infinite limit" can be used to get information in the usual finite-dimensional siutation. (...
  • Jeremy Pecharich
    Thu Apr 25, 2013
    10:00 am
    For A an associative algebra we will introduce a scheme attached to A that parametrizes finite dimensional representations of A called the representation scheme. We will then discuss a theorem of V. Ginzburg which relates non-commutative symplectic geometry to commutative symplectic geometry on the representation scheme. If time permits we will...
  • Ruochuan Liu
    Thu Apr 11, 2013
    2:00 pm
    This is a joint seminar with Number theory seminar. A classical result of Fontaine-Colmez in p-adic Hodge theory says that one can classify crystalline representations of Galois groups of p-adic fields using certain semi-linear objects, namely the weakly admissible (filtered, phi)-modules. In this talk we propose a notion of (...
  • Yuri Zarhin
    Thu Mar 7, 2013
    2:00 pm
    We study the map that sends a monic degree n complex polynomial f(x) without multiple roots to the collection of n values of its derivative at the roots of f(x). It turns out that the differential (tangent map) of this map always has rank n-1.