GENERAL
SEMINAR

“Modular
Invariant Theory”

by

JIM
SHANK

University
of Kent

Abstract:  Let S:=F[x_1,...,x_n] denote the ring of polynomials
in n variables with coefficients in the field F. A subgroup G of the general linear
group GL_n(F) acts on the span of the x_i by linear transformations. This
action extends to an action on S by ring automorphisms. The subring consisting
of those polynomials fixed by this

action, S^G, is known as the ring of invariants. Invariant Theorists are interested
in the structure of S^G, in relating properties of G and S^G, and in algorithms
for constructing generators for S^G. The subject has a rich history with
natural links to representation theory, algebraic geometry and algebraic
topology. I will discuss a variety of results and examples paying particular
attention to the case when G is finite and the characteristic of F is a prime
number dividing the order of G, i.e., modular invariant theory.

Date : May  4, 2011 (Wednesday)

Time : 15.40-16.30

Place: Bilkent University ,Mathematics Seminar Room
SA141

Tea and cookies will be served before the seminar.