## Speaker:

John Voight

## Institution:

UC Berkeley

## Time:

Friday, April 22, 2005 - 4:00pm

## Location:

MSTB 254

The number of solutions to a set of polynomial equations defined over a

finite field of $q=p^a$ elements is encoded by its zeta function, which is a

rational function in one variable. A question of fundamental interest is

how to compute this function efficiently. We describe a method to solve

this problem (due to Wan) using a $p$-adic trace formula of Dwork. We

examine how well this method works in practice on some explicit examples

coming from a certain class of varieties known as $\Delta$-regular

hypersurfaces. Our experience suggests several potential avenues of further

research.