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
Salih Abdalla National Industrial Training Institute 22/03/2021 - 26/03/2021
Romain Aimino Universidade do Porto 22/03/2021 - 26/03/2021
Jaber Akbari Cheshani Shahid Beheshti University 22/03/2021 - 26/03/2021
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
Gil Astudillo Universidade Federal do Rio de Janeiro 22/03/2021 - 26/03/2021
Jason Atnip University of New South Wales 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
Simon Baker University of Birmingham 22/03/2021 - 26/03/2021
Viviane Baladi CNRS and Sorbonne University 07/03/2021 - 28/03/2021
Peter Balint BME Budapest 22/03/2021 - 26/03/2021
Polina Baron University of Chicago 22/03/2021 - 26/03/2021
Valerie Berthe Université de Paris 22/03/2021 - 26/03/2021
Zheng Bian University of Sao Paulo 22/03/2021 - 26/03/2021
Yonah Borns-Weil University of California, Berkeley 22/03/2021 - 26/03/2021
Henk Bruin University of Vienna 22/03/2021 - 26/03/2021
Clark Butler Princeton University 22/03/2021 - 26/03/2021
Ao Cai University of Lisbon 22/03/2021 - 26/03/2021
Hector Homero Canales Farias University of Vienna 22/03/2021 - 26/03/2021
Giovanni Canestrari Bologna 22/03/2021 - 26/03/2021
Stephen Cantrell University of Chicago 22/03/2021 - 26/03/2021
Jérôme Carrand Sorbonne Université 22/03/2021 - 26/03/2021
Pablo Carrasco UFMG 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
Yann Chaubet Université Paris Sud 22/03/2021 - 26/03/2021
Haipeng Chen South China University of Technology 22/03/2021 - 26/03/2021
Shuang Chen Huazhong University of Science and Technology 22/03/2021 - 26/03/2021
Ping Ngai Chung University of Chicago 22/03/2021 - 26/03/2021
Leandro Cioletti Universidade de Brasília 22/03/2021 - 26/03/2021
Julia Codas University of Sao Paulo 22/03/2021 - 26/03/2021
Solly Coles University of Warwick 22/03/2021 - 26/03/2021
Tom Conti-Leslie University of St Andrews 22/03/2021 - 26/03/2021
Deniel Correa UFRJ 22/03/2021 - 26/03/2021
Yves Coudene Sorbonne universite 22/03/2021 - 26/03/2021
Raquel Couto University of Porto 22/03/2021 - 26/03/2021
Sylvain Crovisier Université Paris-Sud 11 22/03/2021 - 26/03/2021
Jean-Claude Cuenin Loughborough 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
Tushar Das UWL 22/03/2021 - 26/03/2021
Matthew De Courcy-Ireland EPFL 22/03/2021 - 26/03/2021
Alessio Del Vigna University of Pisa 22/03/2021 - 26/03/2021
Mark Demers Fairfield University 21/03/2021 - 15/05/2021
Neil Dobbs University College Dublin 22/03/2021 - 26/03/2021
Moritz Doll Universität Bremen 22/03/2021 - 26/03/2021
Rhiannon Dougall University of Bristol 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
Gabriela Estevez Universidade Federal do Rio de Janeiro 22/03/2021 - 26/03/2021
Frédéric Faure University Grenoble Alpes 15/03/2021 - 17/04/2021
Kasun Fernando University of Toronto 22/03/2021 - 26/03/2021
Simion Filip University of Chicago 22/03/2021 - 26/03/2021
Nicholas Fleming University of Warwick 22/03/2021 - 26/03/2021
Mikolaj Fraczyk University of Chicago 22/03/2021 - 26/03/2021
Stefano Galatolo Università di Pisa 22/03/2021 - 26/03/2021
Daniele Galli University of Bologna 22/03/2021 - 26/03/2021
Manjunath Gandhi University of Pretoria 22/03/2021 - 26/03/2021
Selim Ghazouani Université d'Orsay 22/03/2021 - 26/03/2021
Paolo Giulietti Università di Pisa 22/03/2021 - 26/03/2021
Georg Gottwald University of Sydney 22/03/2021 - 26/03/2021
Sébastien Gouëzel Université de Rennes 1 22/03/2021 - 26/03/2021
Colin Guillarmou CNRS / Paris-Saclay 08/03/2021 - 18/04/2021
Armando W. Gutiérrez INRIA Saclay and Ecole Polytechnique 22/03/2021 - 26/03/2021
Jérôme Guérizec Nantes 22/03/2021 - 26/03/2021
Ola Hajj Sleiman American University Of Beirut 22/03/2021 - 26/03/2021
Boumediene Hamzi ICL 22/03/2021 - 26/03/2021
William Hide Durham University 22/03/2021 - 26/03/2021
Boukhecham Houssam Eddine Université Paris Est Créteil 22/03/2021 - 26/03/2021
David Hui HKUST 22/03/2021 - 26/03/2021
Sebastian Hurtado University of Chicago 22/03/2021 - 26/03/2021
Jonny Imbierski Leiden 22/03/2021 - 26/03/2021
Godofredo Iommi Pontificia Universidad Catolica de Chile 22/03/2021 - 26/03/2021
Seung uk Jang The University of Chicago 22/03/2021 - 26/03/2021
Long Jin Tsinghua University 22/03/2021 - 26/03/2021
Natalia Jurga University of St Andrews 22/03/2021 - 26/03/2021
Charlene Kalle Leiden University 22/03/2021 - 26/03/2021
Solomon Keedle-Isack Loughborough 22/03/2021 - 26/03/2021
Osama Khalil University of Utah 22/03/2021 - 26/03/2021
Niloofar Kiamari Roma Tre University 22/03/2021 - 26/03/2021
Minsung Kim University of Maryland 22/03/2021 - 26/03/2021
Anna Kis University of Waterloo 22/03/2021 - 26/03/2021
Benoît Kloeckner Université Paris-Est Marne-la-Vallée 22/03/2021 - 26/03/2021
Yuri Kordyukov Ufa Federal Research Centre Russian Academy of Sciences 22/03/2021 - 26/03/2021
Alexey Korepanov University 22/03/2021 - 26/03/2021
Benjamin Küster Paderborn University 22/03/2021 - 26/03/2021
Georgios Lamprinakis Lund University 22/03/2021 - 26/03/2021
Niels Langeveld Leiden 22/03/2021 - 26/03/2021
Erwan Lanneau Universite Grenoble Alpes 22/03/2021 - 26/03/2021
Andrew Larkin Loughborough University 22/03/2021 - 26/03/2021
François Ledrappier Université Pierre-et-Marie-Curie, Paris IV 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
Yuri Lima Universidade Federal do Ceará 22/03/2021 - 26/03/2021
Yuxuan Liu Kyushu University 22/03/2021 - 26/03/2021
Artur Oscar Lopes UFRGS 22/03/2021 - 26/03/2021
Marco Lopez Wake Forest University 22/03/2021 - 26/03/2021
Liangang Ma Binzhou University 22/03/2021 - 26/03/2021
Keivan Mallahi-Karai Jacobs University 22/03/2021 - 26/03/2021
Matheus Manso Del Valle IMPA - Instituto de Matemática Pura e Aplicada 22/03/2021 - 26/03/2021
Carlos Matheus CNRS 22/03/2021 - 26/03/2021
Pouya Mehdipour UFV 22/03/2021 - 26/03/2021
Philippe Michel EPFL 22/03/2021 - 26/03/2021
Daniel Mitsutani University of Chicago 22/03/2021 - 26/03/2021
Joe Myers Hill University of Leeds 22/03/2021 - 26/03/2021
Rainer Nagel Tübingen 22/03/2021 - 26/03/2021
Katsukuni Nakagawa Hiroshima University 22/03/2021 - 26/03/2021
Yushi Nakano Tokai University 22/03/2021 - 26/03/2021
Calvin Nesbitt University of Reading 22/03/2021 - 26/03/2021
Angxiu Ni UC Berkeley 22/03/2021 - 26/03/2021
Davi Obata University of Chicago 22/03/2021 - 26/03/2021
Alexey Okunev Loughborough University 22/03/2021 - 26/03/2021
Lea Oljaca University of Exeter 22/03/2021 - 26/03/2021
Izak Oltman University of California, Berkeley 22/03/2021 - 26/03/2021
Ashraf Owis Cairo 22/03/2021 - 26/03/2021
Wenyu Pan The University of Chicago 22/03/2021 - 26/03/2021
Kiho Park University of Chicago 22/03/2021 - 26/03/2021
David Parmenter University of Warwick 22/03/2021 - 26/03/2021
Nicolò Paviato University of Warwick 22/03/2021 - 26/03/2021
Tomas Persson Lund University 22/03/2021 - 26/03/2021
Maxence Phalempin Université de brest 22/03/2021 - 26/03/2021
Andrey Piatnitski The Arctic University of Norway 22/03/2021 - 26/03/2021
Sergey Pirogov IITP RAS 22/03/2021 - 26/03/2021
Mark Pollicott University of Warwick 22/03/2021 - 26/03/2021
Rafael Potrie Universidad de la República 22/03/2021 - 26/03/2021
Françoise Pène Univ Brest 22/03/2021 - 26/03/2021
Daniel Qin Kalamazoo College 22/03/2021 - 26/03/2021
Gabriel Rivière Université de Nantes 22/03/2021 - 26/03/2021
Donald Robertson University of Manchester 22/03/2021 - 26/03/2021
Hadi Roopaei Fazel institute of higher education 22/03/2021 - 26/03/2021
Edmilson Roque dos Santos University of São Paulo 22/03/2021 - 26/03/2021
Jan Rozendaal Institute of Mathematics, Polish Academy of Sciences 22/03/2021 - 26/03/2021
Luciana Salgado UFRJ-BR 22/03/2021 - 26/03/2021
Shrey Sanadhya University of Iowa 22/03/2021 - 26/03/2021
Bruno Santiago Universidade Federal Fluminense 22/03/2021 - 26/03/2021
Edson Santos University of Sao Paulo 22/03/2021 - 26/03/2021
Mohammed Saqlain Khan Rheinische Friedrich-Wilhelms-Universität Bonn 22/03/2021 - 26/03/2021
Barbara Schapira Rennes 1 22/03/2021 - 26/03/2021
Philipp Schuette Paderborn University 22/03/2021 - 26/03/2021
Julien Sedro LPSM, CNRS 22/03/2021 - 26/03/2021
Cagri Sert University of Zurich 22/03/2021 - 26/03/2021
Abolfazl Shabani Shahid Beheshti University 22/03/2021 - 26/03/2021
Jaqueline Siqueira Federal University of Rio de Janeiro 22/03/2021 - 26/03/2021
Daniel Smania University of Sao Paulo 22/03/2021 - 26/03/2021
Anastasios Stylianou University of Warwick 22/03/2021 - 26/03/2021
Adriana Cristina Sánchez Chavarría Universidad de Costa Rica 22/03/2021 - 26/03/2021
Fanni Sélley CNRS and Sorbonne Université 22/03/2021 - 26/03/2021
Hiroki Takahasi Keio University 22/03/2021 - 26/03/2021
Airi Takeuchi Karlsruhe Institute of Technology 22/03/2021 - 26/03/2021
Matteo Tanzi New York University 22/03/2021 - 26/03/2021
Zhongkai Tao UC Berkeley 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
Dalia Terhesiu Mathematical Institute Leiden 22/03/2021 - 26/03/2021
Hisayoshi Toyokawa Hokkaido University 22/03/2021 - 26/03/2021
Masato Tsujii Kyushu University, Japan 14/03/2021 - 20/04/2021
Lucas Vacossin Université Paris-Saclay 22/03/2021 - 26/03/2021
Paulo Varandas Univerdade Federal da Bahia 22/03/2021 - 26/03/2021
Victor Vargas National University of Colombia 22/03/2021 - 26/03/2021
Helder Vilarinho Universidade da Beira Interior 22/03/2021 - 26/03/2021
Helmuth Villavicencio Fernández Universidad Nacional de Ingenieria 22/03/2021 - 26/03/2021
Polina Vytnova University of Warwick 22/03/2021 - 26/03/2021
Jian Wang University of California, Berkeley 22/03/2021 - 26/03/2021
Yaping Wang East China Normal University 22/03/2021 - 26/03/2021
Tobias Weich Paderborn University 22/03/2021 - 26/03/2021
Amie Wilkinson University of Chicago 22/03/2021 - 26/03/2021
Caroline Wormell LPSM, CNRS 22/03/2021 - 26/03/2021
Shengquan Xiang EPFL 22/03/2021 - 26/03/2021
Hui Xiao Universität Hildesheim 22/03/2021 - 26/03/2021
Haoren Xiong University of California at Berkeley 22/03/2021 - 26/03/2021
Dmitri Yafaev Rennes and Saint-Petersburg 22/03/2021 - 26/03/2021
Jin Yan Queen Mary University of London 22/03/2021 - 26/03/2021
Nasab Yassine University of Brest 22/03/2021 - 26/03/2021
Daofei Zhang University of Warwick 22/03/2021 - 26/03/2021
Liyang Zhang Fairfield University 22/03/2021 - 26/03/2021
Zhiyuan Zhang Paris 13 22/03/2021 - 26/03/2021
Maciej Zworski University of California, Berkeley 17/03/2021 - 29/03/2021
Total Guests : 180
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
Masato Tsujii Kyushu University, Japan 14/03/2021 - 20/04/2021
Total Guests : 4
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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Participation
CHF
 
Monday 22 March
10:10-11:00 Masato Tsujii ( Slides )
3-dimensional Anosov flows - Session I
11:10-12:00 Sébastien Gouézel ( Slides )
Ruelle resonances for geodesic flow on noncompact manifolds - Session I
12:00-14:00 Break
14:00-14:50 Sébastien Gouézel ( Slides )
Session II
15:00-15:55 Semyon Dyatlov ( Slides -  Exercice)
Fractal uncertainty principle and spectral gaps - Session I
16:10-17:00 Mark Demers ( Slides )
Anisotropic Banach Spaces and Thermodynamic Formalism for Dispersing Billiard Maps - Session I

Tuesday 23 March
10:10-11:00

Masato Tsujii ( Slides )

Session II
11:10-12:00

Masato Tsujii ( Slides )

Session III
12:00-14:00 Break
14:00-14:50 Sébastien Gouézel ( Slides )
Session III
15:00-15:55 Semyon Dyatlov ( Slides )
Session II
16:10-17:00 Mark Demers ( Slides )
Session II

Wednesday 24 March
10:10-11:00

Masato Tsujii ( Slides )

Session IV
11:10-12:00 Sébastien Gouézel ( Slides )
Session IV
12:00-14:00 Break
14:00-14:50 Mark Demers ( Slides )
Session III
15:00-15:55 Mark Demers ( Slides )
Session IV
16:00-16:40 Malo Jézéquel ( Slides )
Session I

Thursday 25 March
10:10-11:00

Masato Tsujii ( Slides )

Session V
11:10-12:00 Sébastien Gouézel ( Slides + Notes )
Session V
12:00-14:00 Break
14:00-14:55 Semyon Dyatlov ( Slides )
Session III
15:05-16:00 Semyon Dyatlov ( Solutions )
Session IV
16:10-17:00 Mark Demers ( Slides  )
Session V
17:15-18:15 Bernoulli Lecture ( Slides )
Internal waves and homeomorphism of the circle
Professor Maciej Zworski
University of California, Berkeley

Friday 26 March
10:10-11:00

Masato Tsujii ( Slides )

Session VI
11:10-12:00 Sébastien Gouézel  ( Slides )
Session VI
12:00-14:00 Break
14:00-14:40 Malo Jézéquel  ( Slides )
Session II
14:50-15:40 Mark Demers ( Slides )
Session VI