Computational Algebra Seminar

David Harvey
(New York University)
Computing zeta functions of projective hypersurfaces in large characteristic
3pm–4pm, Thursday 8th April, 2010
Carlaw 535
I will discuss a new algorithm for computing the zeta function of a projective hypersurface over a finite field of characteristic p whose running time dependence on p is roughly p^1/2.

Tom Fisher
(University of Cambridge)
Finding rational points on Brauer–Severi varieties
4pm–5pm, Thursday 8th April, 2010
Carlaw 535
A Brauer–Severi variety of dimension n – 1 is a twist of projective space ℙ^n-1. The Hasse principle tells us how to decide whether a Brauer–Severi variety defined over a number field has rational points, but not how to find a point. I will discuss how some of the methods for solving conics (case n = 2) generalise to other small values of n (at least if we are working over the rationals).