Description
Commutative algebra seminar
Thursday 09 August, 2.00-3.30 pm
Venue: Room 215
Speaker: Sudhir R Ghorpade
Title:
A Finite Field Nullstellensatz and the Number of Zeros of Polynomials over Finite Fields.
Abstract:
In this series of two talks, we will begin by discussing some Nullstellensatz-like results when the base field is finite, and outline the proofs. Next, we will discuss a combinatorial approach to determining or estimating the number of common zeros of a system of multivariate polynomials with coefficients in a finite field. Here
we will outline a remarkable result of Heijnen and Pellikaan about the maximum number of zeros
that a given number of linearly independent multivariate polynomials of a given degree can have
over a finite field. A projective analogue of this result about multivariate homogeneous polynomials
has been open for quite some time, although there has been considerable progress in the last two
decades, and especially in the last few years. We will outline some results and conjectures here,
including a recent joint work with Peter Beelen and Mrinmoy Datta.