# Invariant Rings of p-groups

• Katherine Horan, University of Kent
• Friday 06 November 2015, 15:00-16:00
• CMS, MR15.

Let $k$ be a field, $V$ a $k$ vector space and $G \leq GL(V)$ a finite group. In invariant theory we are interested in the invariant ring $k[V]G:=\{f \in k[V] |\, g(f) = f, \, \forall g \in G\}$, one of the questions we can ask is when is this polynomial? Are there cases when $k[V]^G$ is not even Cohen Macaulay? I will give a brief introduction to what is known in the modular and non-modular cases, with some more specific results and examples for $p$-groups, $k$ characteristic $p$.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.