Monday, September 24, 2018
09/24/2018 - 8:00pm
Let G be a split reductive p-adic group. In the Iwahori-invariants of an unramified principal series representation of G, there are two bases, one of which is the so-called Casselman basis. In this talk, we will prove a conjecture of Bump–Nakasuji–Naruse about certain transition matrix between these two bases. The ingredients of the proof include Maulik–Okounkov’s stable envelopes and Brasselet–Schurmann–Yokura’s motivic Chern classes for the Langlands dual groups. This is based on joint work with P. Aluffi, L. Mihalcea and J. Schurmann.
09/24/2018 - 8:15pm
The thermodynamic formalism of uniformly hyperbolic dynamical systems is by now a fairly well understood subject. This is mainly because for such systems we have at our disposal a finite Markov partition. If we allow our ambient space to be non-compact, then (in general) we do not have a Markov partition, and some new methods are necessary to study its thermodynamic formalism. In this talk I will explain what is known about the thermodynamic formalism of the geodesic flow in a non-compact negatively curved manifold. In particular I will discuss the role of the entropy “at infinity” of the geodesic flow. I will put emphasis in the comparison with the situation for countable Markov shifts.