--- robots: noindex, nofollow --- # Lodha 1st period (october 5-9) All the lectures are in the Harish-Chandra seminar room. Monday 10:00-11:15 Chritophe Pittet: The rapid decay property 11:30-12:45 Mitul Islam: Recent Developments in the Zimmer Program LUNCH 15:00-16:15 Tullia Dymarz: Quasi-isometric rigidity TEA Tuesday 10:00-11:15 Christophe Pittet: The rapid decay property 11:30-12:45 Mitul Islam: Recent Developments in the Zimmer Program LUNCH 15:00-16:15 Tullia Dymarz: Quasi-isometric rigidity TEA Wednesday 10:00-11:15 Indira Chatterji: The rapid decay property 11:30-12:45 Ignacio Vergara: Property (T) for uniformly bounded representations LUNCH 15:00-16:15 Ralph Spatzier: Recent Developments in the Zimmer Program TEA Thursday 10:00-11:15 Indira Chatterji: Median spaces 11:30-12:45 Ignacio Vergara: Property (T) for uniformly bounded representations LUNCH 15:00-16:15 Ralph Spatzier: Recent Developments in the Zimmer Program TEA 17:00-18:00 Inhyeok Choi: Animations on hyperbolicity 18:00 Movie night (in the lecture hall) followed by GOOD FOOD Friday 10:00-11:15 Tullia Dymarz: Quasi-isometric rigidity 11:30-12:45 Indira Chatterji: The rapid decay property LUNCH 15:00-16:15 tba TEA # Titles and abstract here: Name: Christophe Pittet and Indira Chatterji Title: The rapid decay property Part I and II (Pittet): Heat kernels and the rapid decay property Abstract: Property RD (rapid decay) says that the matrix coefficients of a unitary representation of a locally compact group decay fast with respect to a length function. We will explain some relations of property RD with the Harish-Chandra function of a semisimple group. Part III, IV and V (Chatterji): Rapid decay, median geometry and beyond. Abstract: I will list what group do and don't have rapid decay (Coxeter groups, hyperbolic, mapping class groups, etc), discuss open questions and some applications of the rapid decay property (Baum-Connes conjecture). I will also discuss roughly median geometry, which is the geometry of a product of rank one Lie groups, and a class of groups that have rapid decay property. I will also discuss the problems that arise in higher rank. --- Name: Mitul Islam and Ralph Spatzier Title: Recent Developments in the Zimmer Program *Part I&II (Islam): Boundary actions of lattices and rigidity* Abstract: A lattice in a higher rank Lie group G (e.g. SL(n,R) for n at least 3) acts naturally on several compact G-homogeneous spaces: the so-called Furstenberg boundaries of the G-symmetric space. I will discuss the question of what happens to these natural actions under small perturbations. There are several classical theorems establishing that such actions are “stable” under perturbations in G as well as via smooth diffeomorphisms. However the case of continuous deformations - bereft of any regularity - had been elusive. I will discuss my joint work with Connell, Nguyen, and Spatzier establishing a rigidity result in this continuous case. We also show that this rigidity vanishes in the visual boundary action. *Part III & IV (Spatzier): On Hyperbolic Actions of Higher Rank Semisimple Lie groups*. These lectures describe recent work with Danijela Damjanovic, Kurt Vinhage and Disheng Xu. *Part III: Background and Statement of Results* This talk will introduce the dynamical notions and ideas that allows to formulate our result such as Anosov actions, partially hyperbolic actions, accessibility, bi-homogeneous actions We will exhibit examples such actions. Our main result classifies such actions up to smooth conjugacy as bi-homogeneous actions. *Part IV: Main Ideas in the proofs* I will discuss the main steps in the proof of our classification theorems - and in particular, how to take brackets of Hoelder vector fields. --- Name: Tullia Dymarz Title: Quasi-isometric rigidity Abstract: Finitely generated groups can be treated as metric spaces when assigned a word metric. However, these metrics depend on picking a generating set and so we usually consider these groups up to quasi-isometric equivalence. Quasi-isometric rigidity involves finding classes of groups that are closed under this equivalence. In these talks we will explore the basics of quasi-isometric rigidity with a focus on the Eskin-Fisher-Whyte program of understanding quasi-isometries of lattices in solvable Lie groups but other groups and techniques will be surveyed as well. --- Name: Ignacio Vergara Title: Property (T) for uniformly bounded representations Abstract: Kazhdan’s property (T) is defined as a rigidity property of unitary representations of groups. In these talks, I will focus on a strengthening of this property for uniformly bounded representations. Special attention will be given to the characterisation of property (T) in terms of Kazhdan projections and invariant means. I will also explain how these ideas extend to the setting of relative property (T) for pairs of groups. --- Name: Inhyeok Choi Title: Animations on hyperbolicity Abstract: We will play with inhyeokchoi48.github.io/research/binary . If time allows, we will move on to inhyeokchoi48.github.io/research/poincare . If time still permits, I will explain some maths behind it. Based on joint work with Donggyun Seo.