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SUMMARY:The spectrum of Anosov representations
DTSTART:20251208T150000Z
DTEND:20251208T161500Z
DTSTAMP:20260425T120100Z
UID:indico-event-15539@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Thibault Lefeuvre (Université Paris-Saclay)\n\nI wi
 ll report on an ongoing project in collaboration with Yannick Guedes Bonth
 onneau and Tobias Weich. The goal of this work is to define a natural spec
 trum associated with Anosov representations\, consisting of complex hypers
 urfaces in the complexified dual Cartan subalgebra. The leading hypersurfa
 ce corresponds to a well-known object in the literature — the so-called 
 critical hypersurface of the representation. To some extent\, this spectru
 m generalizes a similar notion in the rank-one case\, known as the set of 
 Pollicott-Ruelle resonances (and the leading resonance)\, which is known t
 o encode the exponential decay of correlations\, among other properties. I
  will describe the main consequences of this spectral approach\, namely th
 e meromorphic extension (to the full complexified dual Cartan subalgebra) 
 of dynamical zeta functions and Poincaré series associated with the repre
 sentation. If time permits\, I will discuss specific values of these funct
 ions\, the sharp quantitative decay of correlations for the refraction flo
 w\, and the perspectives for future work.\n \n\nhttps://indico.math.cnrs.
 fr/event/15539/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/15539/
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