After completing the discussion from last week on the examples PGL(2) and SL(2), I will discuss parabolic subgroups. We will look at them from two points of view: (1) Lie theoretic: via certain subsets of roots (2) Geometric: as stabilizers of certain subspaces I will then explain how these two points of view interact in the case of the exceptional group of G_2. This will make use of a very useful, but perhaps(?) little known/used basis of the octonians.

Let $M}_{n$ be an $n\times n$ random matrix whose entries are i.i.d. copies of a discrete random variable $\xi$. It has been conjectured that the dominant reason for the singularity of $M}_{n$ is the event that a row or column of $M}_{n$ is zero, or that two rows or columns of $M}_{n$ coincide (up to a sign). I will discuss joint work with Ashwin Sah (MIT) and Mehtaab Sawhney (MIT), towards the resolution of this conjecture.

Singularity of discrete random matrices

Thu, Apr. 28 4pm (Zoom)

Topology

Lucas Gagnon (CU Boulder)

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This talk will be an overview if the paper

An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson

by Julianna S. Tymoczko. See https://arxiv.org/abs/math/0503369.