Monday, March 25, 2024
Time  Items 

All day 

4:00pm 
03/25/2024  4:00pm Putting a hyperbolic metric on a complete finitetype surface gives us a linear representation (the holonomy representation) with many nice geometric and dynamical properties: for instance it is discrete and faithful, and in fact stably quasiisometrically embedded, and the group acts on its limit set with northsouth dynamics. This picture can be generalised in (at least) two ways. First, the notion of geometric finiteness generalises this picture in the context of rankone Lie groups such as PSL(2,R) or PSL(2,C). Second, Anosov representations generalise this picture to higherrank Lie groups such as PSL(d,K) for d>2.
In the first talk, I will introduce relatively Anosov representations as a common generalisation of Anosov representations on the one hand and geometric finiteness in rank one on the other. I will mention projectively visible subgroups as examples, and also discuss various variations on the notion.
In the second talk, I will briefly discuss some aspects of the proofs. The general theme here will be how the lack of compactness makes things trickier in the relative case, and some ways around this.
This generalises work of Canary–Zhang–Zimmer and is mostly joint work with Andrew Zimmer.
Location:
KT205
03/25/2024  4:30pm Among the nilpotent orbits in a simple Lie algebra are the special nilpotent orbits, which play an important role in representation theory. Some of the geometry of the closure of a nilpotent orbit can be understood by taking a transverse slice to a smaller orbit in the closure. This talk concerns a classification of two types of such transverse slices: (1) those between adjacent special nilpotent orbits; and (2) those between a special nilpotent orbit and a certain nonspecial nilpotent orbit in its closure. The slices in part (1) exhibit a duality, which extends an observation of Kraft and Procesi for type A. The slices in part (2) are related to a conjecture of Lusztig on special pieces. This talk is based on two preprints with Baohua Fu, Daniel Juteau, and Paul Levy. Location:
KT217
