Rigidity: Groups, Geometry and Cohomology

Ziel

"Our proposal has three components:

1. Unitarizable representations.

2. Spaces and groups of non-positive curvature.

3. Bounds for characteristic classes.

The three parts are independent and each one is justified by major well-known conjectures and/or ambitious goals. Nevertheless, there is a unifying theme: Group Theory and its relations to Geometry, Dynamics and Analysis.

In the first part, we study the Dixmier Unitarizability Problem. Even though it has remained open for 60 years, it has witnessed deep results in the last 10 years. More recently, the PI and co-authors have obtained new progress. Related questions include the Kadison Conjecture. Our methods are as varied as ergodic theory, random graphs, L2-invariants.

In the second part, we study CAT(0) spaces and groups. The first motivation is that this framework encompasses classical objects such as S-arithmetic groups and algebraic groups; indeed, the PI obtained new extensions of Margulis' superrigidity and arithmeticity theorems. We are undertaking an in-depth study of the subject, notably with Caprace, aiming at constructing the full ""semi-simple theory"" in the most general setting. This has many new consequences even for the most classical objects such as matrix groups, and we propose several conjectures as well as the likely methods to attack them.

In the last part, we study bounded characteristic classes. One motivation is the outstanding Chern Conjecture, according to which closed affine manifolds have zero Euler characteristic. We propose a strategy using a range of techniques in order to either attack the problem or at least obtain new results on simplicial volumes."

Wissenschaftliches Gebiet

Finanzierungsplan

ERC-AG - ERC Advanced Grant

Gastgebende Einrichtung

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE

EU-Beitrag

€ 1 332 710,40

Adresse

BATIMENT CE 3316 STATION 1
1015 Lausanne
Schweiz

Region

Schweiz/Suisse/Svizzera Région lémanique Vaud

Aktivitätstyp

Higher or Secondary Education Establishments

Kontakt Verwaltung

Caroline Vandevyver (Ms.)

Hauptforscher

Nicolas Monod (Prof.)

Links

Die Organisation kontaktieren Website

Gesamtkosten

Keine Daten

Begünstigte (1)