This weekly research seminar is a part of the trimester at IHP, Group actions and Rigidity: Around Zimmer program.
The seminar will take place in IHP. Typically, the seminar will be held on Monday and/or Wednesday at 3 pm or 3:30 pm. Please check below for the exact time of each talk.
Organizers: Homin Lee and Thang Nguyen
April 24 (Wed): Yves Benoist
Abstract:
On a cyclic group of prime order, the non-principal Dirichlet characters together with their Fourier transforms are functions that vanish at 0 and whose modulus is constant outside 0. Do there exist other functions with these properties? I will explain the history of this question and give a positive answer for non-safe primes. The proof relies on Floer homology.May 6 (Monday): Colin Guillarmou
May 13 (Mon): Barbara Schapira
Time: 2 pm (unusual time)
Title: Entropies at infinity and applications
Abstract: I will give several definitions of entropy at infinity for a dynamical system on a noncompact topological space. I will (maybe) show that they coincide. When the entropy at infinity is strictly smaller than the topological entropy of the system, in the case of geodesic flows in negative curvature, we obtain numerous interesting applications. Works in common with S Gouezel and S Tapie.
May 15 (Wed): Bruno Duchesne
Time: 3 pm
Using continuous deformations of $O(1,n)$ into $O(1,\infty)$, any representation gives rise to a «homothety class » of irreducible representations in $O(1,\infty)$. We will prove that the space of homothety classes of hyperbolic representations is actually compact. So this provides a uniform way to compactify spaces of representations such as the Teichmüller space of closed surfaces.
May 20 (Mon): holiday, no talk.
May 22 (Wed): Thibault Lefeuvre
Time: 3:00 pm
Title: Rapid mixing for isometric extensions of Anosov flows
Abstract: An isometric extension of an Anosov flow is an extension to a G-principal bundle over the base space, where G is a compact Lie group. In this talk, I will explain a recent result obtained in collaboration with M. Cekić, showing that isometric extensions exhibit rapid mixing under a natural assumption (i.e., the decay of correlations is faster than any polynomial power of time). In this problem, there is a dichotomy based on whether G is Abelian or semisimple. Interestingly, the semisimple case turns out to be easier due to a Diophantine property satisfied by semisimple Lie groups. Therefore, I will mainly focus on the Abelian case.
Workshop 2: Group Actions with Hyperbolicity and Measure Rigidity (IHP, Paris)
June 5 (Wed): Jean Lecureux
Workshop 3: Actions of Large Groups, Geometric Structures, and the Zimmer Program (IHP, Paris)
Jun 19 (Wed): Laurent Stolovitch
June 24 (Mon): Nguyen-Thi DANG
Time: 2 pm
Abstract: Bowen and Margulis independently proved in the 70s that closed geodesics on compact hyper- bolic surfaces equidistribute towards the measure of maximal entropy. From a homogeneous dynamics point of view, this measure is the quotient of the Haar measure on PSL(2,R) modulo some discrete cocompact sugroup.
In a joint work with Jialun Li, we investigate the higher rank setting of this problem by taking a higher rank Lie group (like SL(d,R) for d ≥ 3) and by studying the dynamical properties of geodesic flows in higher rank : the so-called Weyl chamber flows and their induced diagonal action. We obtain an equidistribution formula of periodic tori (instead of closed orbits of the geodesic flow).
June 24(Mon): Danyu Zhang
Title: Rigidity of fibrewise Anosov diffeomorphisms on principal torus bundles
Abstract: A fibrewise Anosov diffeomorphism is a fibre-preserving diffeomorphism on a fibre bundle that preserves an invariant stable and unstable splitting along the fibres. We discuss a result showing that every fibrewise Anosov diffeomorphism on a principal torus bundle is topologically conjugate to a map that is linear in the fibres, by a conjugacy that fibres over the identity on the base and is homotopic to the identity.
Last updated: April 4, 2024