Spring School on Transfer Operators (Classical and Modern Techniques)  22 - 26 March 2021

08:00 - 17:00
Room : GA 3 21

Organisers

Wael Bahsoun, Loughborough University

Viviane Baladi, CNRS and Sorbonne University

Please note:
As per new sanitary recommendations, this event will take place 100% online.
For online attendance, please register by 1 March 2021 (fill above online form) and details for the connection will be sent to you a few days before the event.


This school will provide courses from experts on several aspects of the spectrum of transfer operators. Special attention will be provided to the theory of anisotropic spaces, and to applications in geometrical or physical settings.

The target audience includes PhD students and young postdocs.


► Lecturer: Mark Demers
Course structure: 6 lectures, 50 minutes
Title: Anisotropic Banach Spaces and Thermodynamic Formalism for Dispersing Billiard Maps.

Abstract: Mathematical billiards with dispersing boundaries comprise a physically interesting class of hyperbolic systems with singularities. Starting from some toy models of hyperbolic maps, we will build up a set of tools (Banach spaces and transfer operators) that we shall use to analyze the statistical properties of these systems. This framework will allow us to present recent progress in the theory of equilibrium states and topological pressure in the context of dispersing billiards, including the existence and uniqueness of a measure of maximal entropy.


► Lecturer: Semyon Dyatlov
Tutor: Malo Jézéquel
Course structure: 4 lectures, 55 minutes + 2 tutorials, 40 minutes
Title: Fractal uncertainty principle and spectral gaps.

Abstract: This minicourse describes the spectral gap problem for convex co-compact hyperbolic surfaces and the approach to it which uses the fractal uncertainty principle, a recently developed tool in harmonic analysis. Roughly speaking, the combinatorial and harmonic-analytic properties of the limit set of the surface make it possible to prove statements such as exponential remainders in the Prime Orbit Theorem or exponential local energy decay for the wave equation. Here are some of the topics that will be covered: 

  • Convex co-compact hyperbolic surfaces and their Schottky representations. Schottky limit sets and Patterson-Sullivan measure. Transfer operators.
  • The spectral gap problem, a brief overview of its applications, and known results.
  • Fractal uncertainty principles, a brief overview of the three known approaches.
  • A proof that fractal uncertainty principle gives a spectral gap using transfer operators (following Dyatlov-Zworski 2017).
  • A proof of the fractal uncertainty principle for the special case of arithmetic Cantor sets, done using each of the three approaches.

► Lecturer: Sébastien Gouézel
Course structure: 6 lectures, 50 minutes
Title: Ruelle resonances for geodesic flow on noncompact manifolds.

Abstract: Ruelle resonances are complex numbers describing the fine asymptotic properties of the correlations of smooth functions under a given flow. We will survey different situations in which one can make sense of this notion, starting with the simplest situation of expanding semi flows, and adding progressively technical tools, to be able in the end to cover more complicated flows of geometric origin, such as the geodesic flow on compact or noncompact negatively curved manifolds.


► Lecturer: Masato Tsujii
Course structure: 6 lectures, 50 minutes
Title: 3-dimensional Anosov flows.

Abstract: In this mini-course, I am going to discuss mainly about local geometric structure of the(strong) stable and unstable lamination of smooth Anosov flows, particularly in the lowest dimensional case, that is, in dimension 3. We will also explain how that structure leads to (exponential) mixing property of the flow, using a simplified model of the U(1)-extensions of Anosov diffeomorphisms. The content will be based on my joint work with Zhiyuan Zhang.


ERC Logo

This project has also received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 787304).

Name University Dates of visit
Romain Aimino Faculdade de Ciências da Universidade do Porto 21/03/2021 - 04/04/2021
Shayan Alikhanloo Bielefeld University 22/03/2021 - 26/03/2021
Lucas Amorim Vilas Boas University of Porto and Centre de Physique Theorique Marseille 22/03/2021 - 26/03/2021
Catalin Badea Univ Lille 22/03/2021 - 26/03/2021
Wael Bahsoun Loughborough University 21/03/2021 - 06/04/2021
Viviane Baladi CNRS and Sorbonne University 07/03/2021 - 28/03/2021
Valerie Berthe Université de Paris 22/03/2021 - 26/03/2021
Zheng Bian University of Sao Paulo 22/03/2021 - 26/03/2021
Jérôme Carrand Sorbonne Université 22/03/2021 - 26/03/2021
Roberto Castorrini University of Rome Tor Vergata 22/03/2021 - 26/03/2021
Mihajlo Cekić Université Paris-Saclay 22/03/2021 - 26/03/2021
Shuang Chen Huazhong University of Science and Technology 22/03/2021 - 26/03/2021
Solly Coles University of Warwick 22/03/2021 - 26/03/2021
Raquel Couto University of Porto 22/03/2021 - 26/03/2021
Latifa DEBBI Polytechnic National school, Algiers 22/03/2021 - 26/03/2021
David Damanik Rice University 22/03/2021 - 26/03/2021
Mark Demers Fairfield University 21/03/2021 - 15/05/2021
Moritz Doll Universität Bremen 22/03/2021 - 26/03/2021
Semyon Dyatlov MIT 22/03/2021 - 26/03/2021
Nikolai Edeko University of Tübingen 22/03/2021 - 26/03/2021
Frédéric Faure University Grenoble Alpes 15/03/2021 - 17/04/2021
Sébastien Gouëzel Université de Rennes 1 22/03/2021 - 26/03/2021
Colin Guillarmou CNRS / Paris-Saclay 08/03/2021 - 18/04/2021
William Hide Durham University 22/03/2021 - 26/03/2021
Boukhecham Houssam Eddine Université Paris Est Créteil 22/03/2021 - 26/03/2021
Long Jin Tsinghua University 22/03/2021 - 26/03/2021
Malo Jézéquel LPSM, Sorbonne Université 22/03/2021 - 26/03/2021
Minsung Kim University of Maryland 22/03/2021 - 26/03/2021
Andrew Larkin Loughborough University 22/03/2021 - 26/03/2021
Jungwon Lee CNRS and Sorbonne Université 22/03/2021 - 26/03/2021
Martin Leguil Université de Picardie Jules Verne 22/03/2021 - 26/03/2021
Marco Lenci University of Bologna 22/03/2021 - 26/03/2021
Diego Liberati National research council of Italy 22/03/2021 - 26/03/2021
Nicolò Paviato University of Warwick 22/03/2021 - 26/03/2021
Françoise Pène Univ Brest 22/03/2021 - 26/03/2021
Hadi Roopaei Fazel institute of higher education 22/03/2021 - 26/03/2021
Barbara Schapira Rennes 1 22/03/2021 - 26/03/2021
Anastasios Stylianou University of Warwick 22/03/2021 - 26/03/2021
Fanni Sélley CNRS and Sorbonne Université 22/03/2021 - 26/03/2021
Airi Takeuchi Karlsruhe Institute of Technology 22/03/2021 - 26/03/2021
Samuel Tapie Nantes 22/03/2021 - 26/03/2021
Toby Taylor-Crush Loughborough University 22/03/2021 - 26/03/2021
Masato Tsujii Kyushu University 14/03/2021 - 20/04/2021
Lucas Vacossin Université Paris-Saclay 22/03/2021 - 26/03/2021
Caroline Wormell LPSM, CNRS 22/03/2021 - 26/03/2021
Dmitri Yafaev Rennes and Saint-Petersburg 22/03/2021 - 26/03/2021
Liyang Zhang Fairfield University 22/03/2021 - 26/03/2021
Maciej Zworski University of California, Berkeley 17/03/2021 - 29/03/2021
Total Guests : 48
Name University Dates of visit
Mark Demers Fairfield University 21/03/2021 - 15/05/2021
Semyon Dyatlov MIT 22/03/2021 - 26/03/2021
Sébastien Gouëzel Université de Rennes 1 22/03/2021 - 26/03/2021
Malo Jézéquel LPSM, Sorbonne Université 22/03/2021 - 26/03/2021
Masato Tsujii Kyushu University 14/03/2021 - 20/04/2021
Total Guests : 5
Conference in Honor of the 70th Birthday of Tudor Ratiu, 20 to 24 July 2020.
Registration fees of CHF 50.- are mandatory for visits from 1 day to full attendance of the conference.
Cancellations and no-shows are not eligible for a refund.
I hereby agree to the conditions of the registration fees and to settling the amount by 28 February 2020.

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