Denise Dawson

Ph.D. (2011) Cornell University

First Position

Assistant professor of mathematics at Charleston Southern University

Dissertation

Complete Reducibility in Euclidean Twin Buildings

Advisor:

Kenneth Brown

Research Area:

buildings

Abstract: J.P. Serre defined completely reducible subcomplexes of spherical buildings in order to study subgroups of reductive algebraic groups. This paper begins the exploration of how one may use a similar notion of completely reducible subcomplexes of twin buildings to study subgroups of algebraic groups over a ring of Laurent polynomials and Kac-Moody groups. In this paper we explore the definitions of convexity and complete reducibility in twin buildings and some implications of the two in the Euclidean case.