
Bryden Cais
Thu Dec 13, 2012
3:00 pm
What is the probability that a random abelian variety over F_q is ordinary? Using (semi)linear algebra, we will answer an analogue of this question, and explain how our method can be used to answer similar statistical questions about prank and anumber. The answers are perhaps surprising, and deviate from what one might expect via naive reasoning...

Andrei Jorza
Thu Nov 15, 2012
3:00 pm
To a Hilbert modular form one may attach a padic analytic
Lfunction interpolating certain special values of the usual Lfunction.
Conjectures in the style of Mazur, Tate and Teitelbaum prescribe the order
of vanishing and first Taylor coefficient of such padic Lfunctions, the
first coefficient being controlled by an Linvariant which has...

Daniel Litt
Thu Nov 8, 2012
3:00 pm
There are beautiful and unexpected connections between algebraic topology, number theory, and algebraic geometry, arising from the study of the configuration space of (not necessarily distinct) points on a variety. In particular, there is a relationship between the DoldThom theorem, the analytic class number formula, and the "motivic...

Shahed Sharif
Thu May 31, 2012
3:00 pm
Let $C$ be a curve over a local field whose reduction is totally
degenerate. We discuss the related problems of 1) determining the
group structure of the torsion subgroup of the Jacobian of $C$, and 2)
determining if a given line bundle on $C$ is divisible by a given
integer $r$. Under certain hypotheses on the reduction of $C$, we
exhibit...

Mitya Boyarchenko
Tue May 8, 2012
3:00 pm
In the early 1970s Drinfeld introduced a family of rigid analytic
spaces parameterizing deformations of certain formal groups with level
structure. This family is called the LubinTate tower. He found an
open affinoid in the first level of this tower whose reduction is
isomorphic to what is now known as a DeligneLusztig variety for GL_n
over...

Maurice Rojas
Thu Apr 12, 2012
3:00 pm
We show how to efficiently count exactly the number of solutions of a system of n polynomials in n variables over certain local fields L, for a new class of polynomials systems. The fields we handle include the reals and the padic rationals. The polynomial systems amenable to our methods are made up of certain Adiscriminant chambers, and our...

Vladimir Baranovsky
Thu Dec 1, 2011
1:00 pm
A very useful technique in homological algebra, is the Basic Peturbation Lemma which tells how cohomology of a complex changes when a differential is perturbed. It has numerous applications in algebra, topology, and computational methods in algebra; some of which will be reviewed in the talk.