Tuesday, November 2, 2021
Time | Items |
---|---|
All day |
|
4:00pm |
11/02/2021 - 4:15pm Following up on last week's talk, I will sketch a little more about the structure and properties of uniform models for surface groups and for the general incompressible-boundary case. I will then explain how this allows us to prove Thurston's "lost" theorem: a certain self-map of Teichmuller space, used in the solution to the gluing problem, has an iterate with bounded image. Location:
LOM 214
11/02/2021 - 4:30pm The local Langlands correspondence for a connected reductive $p$-adic group $G$ partitions the set of equivalence classes of smooth irreducible representations of $G(F)$ into $L$-packets using equivalence classes of Langlands parameters. Vogan's geometric perspective gives us a moduli space of Langlands parameters, and the correspondence can be viewed as a relation between the set of equivalence classes of smooth irreducible representations of $G(F)$ and simple objects in the category of equivariant perverse sheaves on the moduli space of Langlands parameters that share a common infinitesimal parameter. This geometry gives us the notion of an ABV-packet, a set of smooth irreducible representations of $G(F)$, which conjecturally generalizes the notion of a local Arthur packet - a local Arthur packet is conjecturally an ABV-packet. In this talk, we will look at Langlands parameters coming from simple Arthur parameters in the case of $\mathrm{GL}_n.$ We will explore the geometry of the moduli space of Langlands parameters using an example. We will see work in progress towards proving that the local Arthur packet is the ABV-packet for this case. Location:
Zoom
|