Past Seminars- Algebra

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  • Steven Sam
    Wed Oct 11, 2017
    2:00 pm
    Given a projective variety X over a field of characteristic 0, and a positive integer r, we study the rth secant variety of Veronese re-embeddings of X. In particular, I'll explain recent work which shows that the degrees of the minimal equations (and more generally, syzygies) defining these secant varieties can be bounded in terms of X and r...
  • 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...