Tuesday, March 26, 2024
Time  Items 

All day 

10am 
03/26/2024  10:30am 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 on Monday, 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 Tuesday morning, 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:
KT801

1pm 
03/26/2024  1:30pm Many recent developments in matrix models and topological string theory have been driven by resurgence methods. I will introduce basic resurgence concepts in the context of hermitian matrix models (and their double scaling limits) and demonstrate the natural appearance of negative dbranes associated to antieigenvalue tunneling (tunneling on the non physical sheet of the spectral curve). Furthermore I will illustrate how such negative dbranes are a feature of the t’Hooft limit and necessary for a full non perturbative resurgent large N description, but at the same time are turned off at finite N. Furthermore I will introduce the concept of diagonal framing for resurgent transseries that include negative dbranes. This gives rise to an identification of the non perturbative partition functions of hermitian matrix models and certain topological strings, which I will illustrate using the example of (2,3) minimal strings/H_0 Argyres Douglas Theory. Location:
KT 801

4pm 
03/26/2024  4:00pm We exhibit in any dimension n>2 and for any positive integer m a collection of m pairwise incommensurable closed hyperbolic nmanifolds of the same volume each possessing a unique shortest closed geodesic of the same length less than 1/m. Location:
KT 205
