Michael Wheeler (CU) Hyperprincipal Realizations of Ultrafilters, Part 2

Tue, Oct. 8 2pm (MATH 350)

Lie Theory

Lucas Gagnon (CU) Finding all normal subgroups of the unipotent upper triangular groups

Tue, Oct. 8 4pm (MATH 350)

Topology

Andrew Stocker (CU) Complex Bordism, MU and Complex Orientations

X

Classifying all conjugacy classes and/or irreducible representations in the family of unipotent upper triangular matrices ${\mathrm{UT}}_{n}({\mathbb{F}}_{q})$ is a wild problem, meaning that it is an essentially hopeless endeavor. In this talk, I will take up the superficially similar question of normal subgroups in ${\mathrm{UT}}_{n}({\mathbb{F}}_{q})$ and answer it with a bijection between normal subgroups and vector spaces over $\mathbb{F}}_{q$ which are parametrized by a family of Catalan-like combinatorial objects. Following this construction, I will show how supercharacter theory can turn our newfound understanding of the normal subgroup structure of ${\mathrm{UT}}_{n}({\mathbb{F}}_{q})$ into a deeper representation theoretic understanding of this family of groups.