Thursday, Feb 16 2012: 4:00 p.m. in DU 268
Speaker: Prof. Sarah Witherspoon, Texas A&M
Title: Representation Type and Varieties

Abstract: More than 50 years ago, Higman found a precise connection between the subgroup structure of a finite group and its number of representations, that is vector spaces on which it can act. Bondarenko and Drozd refined Higman's work some time later. More generally, finite dimensional algebras come in three flavors, or representation types: finite, tame, and wild. In this introductory talk, we will give an overview of representation type and of support varieties, which are useful invariants of representations. We will explain how support varieties have been used recently to obtain wildness criteria for some algebras. Specific examples include some Hopf algebras, small quantum groups, and related algebras.

Monday, March 5, 2012: 4:00 p.m. in DU 152
Speaker: Christopher French, Grinnell College
Title: The Extension Problem for Association Schemes: Semidirect Products

Abstract: The theory of association schemes arises in a large number of mathematical disciplines, from statistics to design theory, from coding theory to geometry. From one more recent point of view, association schemes may be considered as a natural generalization of groups. Some progress has been made in generalizing classical constructions and theorems from group theory to this new setting, but a great many possible generalizations remain to be considered. For example, much is known in group theory about the extension problem: given two groups $N$ and $K$, classify all groups that have a normal subgroup isomorphic to $N$, with quotient isomorphic to $K$. The first step in studying such extension problems for groups is to understand the semidirect products. In this talk, I will explain my own construction for semidirect products of groups, and illustrate how the ideas behind this construction may suggest avenues for understanding the extension problem for association schemes more generally.