
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 CampbellBakerHausdorf 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 NPcomplete 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 SylvesterGallai theorem states the following: Given a finite set of points in the 2dimensional 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...