Erez Lapid (Weizmann Institute of Science and Institute for Advanced Study)
 

"Parabolic induction of representations of the general linear group over
a non-archimedean local field and geometry"

Abstract: Determining irreducibility of parabolic induction is important for the
analysis of the automorphic discrete spectrum, as well as in its own
right. I will present some results and conjectures about the case of
the general linear group, which goes back to the seminal work of
Joseph Bernstein and Andrei Zelevinsky in the 1970s.  In particular,
we prove a special case of a (strong form of a) conjecture of
Geiss-Leclerc-Schröer.  This is joint work with Alberto Mínguez.  
I will also discuss an apparently new conjecture about certain
parabolic Kazhdan-Lusztig polynomials.  We verified this conjecture
numerically in a small range by computing all Kazhdan-Lusztig
polynomials for the symmetric group S(12).

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George Pappas (Michigan State University)

"Good and semi-stable reduction of Shimura varieties"

Abstract: We will describe a classification of Shimura varieties that have good
or semi-stable reduction at a prime where the level subgroup is
parahoric. This is joint work with X. He and M. Rapoport.

3:00-4:00PM ~ Eriz Lapid

4:00-4:30PM ~ Break

4:30-5:30PM ~ George Pappas