[Binghamton Geometry Topology Seminar] Seminar This Week

[Matthew R Haulmark]

Hi everyone,

This week our speaker is our very own Daniel Studenmund. The title and
abstract are below. The links for the talk and coffee are:

Zoom link for the seminar, 2:50 - 3:50:
https://binghamton.zoom.us/j/94057178271

Zoom link for the coffee, 12:30 - 1:30:
https://binghamton.zoom.us/j/96674397432

*Title*: Vanishing in top-dimensional cohomology of $GL_n(\mathcal{O})$

*Abstract*: In this talk, we will address one instance of the general
question: Given a group $G$, what is the cohomology of $G$ with
rational coefficients? A celebrated result of Borel and Serre implies
that $G = GL_n(\mathcal{O})$ has finite virtual cohomological
dimension (vcd) when $\mathcal{O}$ is the ring of integers of a number
field $K$. This implies that cohomology with rational coefficients
vanishes in dimensions greater than the vcd, but leaves open the
question of whether cohomology vanishes in the vcd. After surveying
some results in the area, I will discuss joint work with Andy Putman
which computes cohomology of $GL_n(\mathcal{O})$ in the vcd for
certain $\mathcal{O}$, and how there is a surprisingly subtle
dependence on the number ring $\mathcal{O}$.


See you on Thursday!

Best,

Matt
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