Professor Anne Shepler invites you to attend the Doctoral Dissertation Defense of Dillon Hanson

"Invariant Differential Derivations for Modular Reflection Groups"

ABSTRACT:

The invariant theory of finite reflection groups has rich connections to geometry, topology, representation theory, and combinatorics. We consider finite reflection groups acting on vector spaces over fields of arbitrary characteristic, where many arguments of classical invariant theory break down. When the characteristic of the underlying field is positive, reflections may be nondiagonalizable. A group containing these so-called transvections has order which is divisible by the characteristic of the underlying field, so is in the modular setting. In this defense, we will examine the action on differential derivations, which include products of differential forms and derivations, and will identify the structure of the set of invariants under the action of groups fixing a single hyperplane, groups with maximal transvection root spaces acting on vector spaces over prime fields, as well as special linear groups and general linear groups over finite fields.

Cake and coffee will be served in GAB 472 following this event.