Past Seminars- Algebra

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  • Michael O'Sullivan
    Mon Apr 24, 2017
    3:00 pm
    For each  random n-vector there is an entropy vector of length 2^n-1.  A fundamental question in information theory is to characterize the region formed by these  entropic vectors. The region is bounded by Shannon's inequalities, but not tightly bounded for n>3. Chan and Yeung discovered that random vectors constructed from...
  • Herbert Lange
    Wed Mar 1, 2017
    3:00 pm
    Let f: C' -> C be a cyclic cover of smooth projective curves. Its Prym variety is by definition the complement of the pullback of the Jacobian of C in the Jacobian of C'. It is an abelian variety with a polarization depending on the genus of C, the degree of f and the ramification type of the covering f. This gives a map from...
  • Alexander Grishkov
    Fri Feb 10, 2017
    3:00 pm
    We will discuss the exponential map (from a Lie algebra to the corresponding Lie group) in the case of positive characteristic p, and its relation to the Campbell-Baker-Hausdorf formula which expresses the group product via the Lie brackets. If time permits, we will also talk about loops (algebraic structures similar to groups where only a weaker...
  • Umut Isik
    Wed Feb 1, 2017
    4:00 pm
    I will describe a natural sequence of generalizations going from Turing style computational complexity theory and the P vs NP problem to the complexity theory of algebraic varieties. I will then explain how to use universal circuits to make an NP-complete sequence of projective varieties.
  • Peter Stevenhagen
    Tue Jan 17, 2017
    2:00 pm
    We show how the Galois representation of an elliptic curve over a number field can be used to determine the structure of the (topological) group of adelic points  of that elliptic curve. As a consequence, we find that for "almost all" elliptic curves over a number field K,  the adelic point group is a universal topological...
  • 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.