David Wehlau, Queen's University
"Modular Invariants and Classical Invariant Theory"
Let F be a field, G a group and V a finite dimensional representation of G defined over F. The ring of polynomial functions on V, denoted k[V] inherits a natural G-action. The subring of polynomials fixed pointwise by this action is the ring of invariants denoted F[V]G. Invariant Theory is the study of these rings and their generators and relations.
Classical Invariant Theory flourished in the late nineteenth century and was the dominant field of study in algebra at that time. Giants such as David Hilbert, Emmy Noether, Arthur Cayley and J.J. Sylvester and others were particularly interested in the case G = SL(2, C) and F = C.
In the last thirty years, there has been a great deal of work on modular invariant theory, i.e., the case where G is a finite group, F is some field of characteristic p > 0 and p divides |G|. Of particular interest and importance here is the case where G = Z/p.
I will describe how a theorem published in 1861 provides an unexpected bridge which connects the classical and modern problems. I will show how this connection can be used to prove that these two problems are in fact equivalent.
Refreshments will be served in MC 5046 at 3:30 p.m. Everyone is welcome to attend.