Computational Algebra Seminar: Voight -- Computing zeta functions using Dwork cohomology

Speaker: John Voight (IMA, University of Minnesota)
Title: Computing zeta functions using Dwork cohomology
Time & Place: 3:05-4pm, Thursday 7 June, Carslaw 535

Abstract:
Let X be a variety defined by a set of polynomial equations in several
variables over a finite field F_q with q elements.  In many
applications, one is interested in the number of solutions of these
equations over finite extensions F_{q^r} of F_q.  One can package
these integers together into a generating series in a suitable way to
obtain the zeta function of X, which possesses a marvelous structure
and is a fundamental object in algebraic geometry.

In the first part of this talk, intended for a general audience, we
will introduce the zeta function from scratch, provide several
examples, and discuss its properties and applications.  In the second
part, we will discuss a new result on the computation of zeta
functions using Dwork cohomology, and conclude with several
interesting combinatorial and geometric implementational issues.