Speaker: Matt Scalamandre
University of Notre Dame
Will give a PhD Defense entitled:
A Solomon-Tits theorem for rings
Abstract: An analogue of the Tits building is defined and studied for commutative rings. We prove a Solomon-Tits theorem when $R$ either satisfies a stable range condition, or is the ring of $S$-integers of a global field. We then define an analogue of the Steinberg module of $R$ and study it both as a $\mathbb{Z}$-module and as a representation. We find the rank of Steinberg when $R$ is a finite ring, and compute the length of $\text{St}_2(R)\otimes \mathbb{Q}$ as a $\text{GL}_2(R)$-
Date: 03-04-2024
Time: 12:00 pm
Location: 311 DeBartolo Hall