Past Seminars- Algebra

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  • Professor Michael Fried
    Thu Apr 15, 2010
    2:00 pm
    Modular curves are the most famous example of the title. As moduli space towers they exhibit a "Frattini property," based on their monodromy groups as covers of the j-line. Using the goals of Serre's "l-adic representations" book I will treat, in parallel, two cases of general ideas. Modular curves here derive from the semi-direct product of Z/2...
  • Robert Guralnick
    Thu Apr 8, 2010
    2:00 pm
    We shall discuss some results which classify the smallest degree representations of simple groups. We will then discuss various applications of these ideas including the solution of a conjecture of Serre on semisimplicity of certain representations and a conjecture of Kollar and Larsen on the non-irreducibility of symmetric powers.
  • Rachel Pries
    Thu Nov 5, 2009
    2:00 pm
  • Ivan Cheltsov
    Fri May 8, 2009
    4:00 pm
    The only known sufficient condition for the existence of a Kahler-Einstein metric on a Fano manifold can be formulated in terms of so-called alpha-invariant introduced by Tian and Yau more than 20 years ago. This invariant can be naturally defined for log Fano varieties with log terminal singularities using purely algebraic language. Using a...
  • Yuri Zarhin
    Thu May 7, 2009
    2:00 pm
    The Hodge group (aka special Mumford-Tate group) of a complex abelian variety $X$ is a certain linear reductive algebraic group over the rationals that is closely related to the endomorphism ring of $X$. (For example, the Hodge group is commutative if and only if $X$ is an abelian variety of CM-type.) In this talk I discuss" lower bounds" for...
  • Oscar Villareal
    Thu Mar 5, 2009
    3:00 pm
    Many constructions in algebraic geometry require one to choose a point outside a countable union of subvarieties. Over $\C$ this is always possible. Over a countable field, a countable union of subvarieties can cover all the closed points. Let $k$ be a finitely generated field of characteristic zero and let $\kbar$ be an algebraic closure. Let $A...
  • Assistant Professor Vasiliy Dolgushev
    Wed Oct 22, 2008
    1:00 pm
    Problems of deformation theory are often motivated by questions from physics. In my talk I will first consider deformation theory of an associative algebra. Then I will describe a problem of deformation quantization and formulate Kontsevich's result which closes this problem with a positive answer. Finally, I will talk about the application of...