Dynamical Systems - Summer School  26 - 30 August 2019

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

Organiser

Jörg Schmeling, Lund University

The summer school will provide courses from experts in the areas of the scope of the program ''Dynamics with Structures''. It is intended to provide surveys of modern directions in the theory of dynamical systems on the level of graduate students and junior researchers. The goal is to propagate modern directions of research to younger scientists and show the variety of methods and results obtained by imposing different structures on a dynamical system. It will be a unique possibility to give an insight on all three main events of the semester. The topics will reach from Conservative Dynamics and Hamiltonian Systems over Algebraic and Number Theoretic Systems and Methods, Analytic Dynamical Systems and Thermodynamic Formalism. Besides the lectures the audience is encouraged to have active discussions with the lecturers and other experts.

School programme:
Lecturer: Viktor Ginzburg (University of California Santa Cruz)
Title: Periodic orbits of Hamiltonian systems: the Conley conjecture, pseudo-rotations and holomorphic curves (in 4 parts).
Abstract: One distinguishing feature of Hamiltonian dynamical systems is that such systems, with few notable exceptions, tend to have numerous periodic orbits. For instance, for many symplectic manifolds, every Hamiltonian diffeomorphism has infinitely many periodic orbits unconditionally. This fact, usually referred to as the Conley conjecture, has by now been established for a broad class of manifolds. However, the Conley conjecture obviously fails for some, even very simple, manifolds such as the sphere. These spaces admit Hamiltonian diffeomorphisms with few periodic orbits -- the so-called pseudo-rotations -- which are of particular interest and occupy a very special place in dynamics. Symplectic topological methods and, in particular, Floer theory turn out to be the right tools to study pseudo-rotations in all dimensions and recently a connection between the existence of pseudo-rotations and the Gromov-Witten invariants has been discovered.
We will start these lectures with the background results on the Conley conjecture and then focus on the dynamics of Hamiltonian pseudo-rotations and the connection between pseudo-rotations and quantum homology.

Part of the Semester : Dynamics with Structures

Name University Dates of visit
Magnus Aspenberg Lund University 18/08/2019 - 27/08/2019
Cengiz Aydin Université de Neuchâtel 26/08/2019 - 30/08/2019
Polina Baron National Research University "Higher School of Economics" 26/08/2019 - 30/08/2019
David Bechara Ruhr Universität Bochum 26/08/2019 - 30/08/2019
Michael Benedicks Uppsala University 18/08/2019 - 30/08/2019
Joé Brendel Université de Neuchâtel 26/08/2019 - 30/08/2019
Mats Bylund Lund University 26/08/2019 - 30/08/2019
Haipeng Chen South China University of Technology 26/08/2019 - 30/08/2019
Solly Coles University of Warwick 26/08/2019 - 30/08/2019
Lucas Dahinden Universität Heidelberg 26/08/2019 - 30/08/2019
David Damanik Rice University 25/08/2019 - 31/08/2019
Henrik Ekström Lund University 26/08/2019 - 30/08/2019
Gerard Farré Puiggalí KTH 26/08/2019 - 30/08/2019
Mohamadreza Farshidfar University of Neuchâtel 26/08/2019 - 30/08/2019
Yaniv Ganor Tel Aviv University 26/08/2019 - 30/08/2019
Anish Ghosh Tata Institute of Fundamental Research 25/08/2019 - 31/08/2019
Viktor Ginzburg University of California Santa Cruz 25/08/2019 - 31/08/2019
Vasilii Goriachkin Lund University 26/08/2019 - 30/08/2019
Oliver Katsikas Université de Fribourg 26/08/2019 - 30/08/2019
Seongchan Kim Université de Neuchâtel 26/08/2019 - 30/08/2019
Rakesh Kumar Indian Institute of Technology (Banaras Hindu University), Varanasi 26/08/2019 - 30/08/2019
Philipp Kunde Hamburg 26/08/2019 - 30/08/2019
Joaquín Lema Universidad de la República 26/08/2019 - 30/08/2019
Bing Li South China University of Technology 26/08/2019 - 30/08/2019
Shuxia Li Univeristy of Texas Rio Grande Valley 26/08/2019 - 30/08/2019
Yaoqiang Li Sorbonne Université - Campus Pierre et Marie Curie (Paris 6) 26/08/2019 - 30/08/2019
Shiling Liang EPFL 26/08/2019 - 30/08/2019
Bowen Liu Universität Augsburg 26/08/2019 - 30/08/2019
Ezequiel Maderna Universidad de la República 26/08/2019 - 30/08/2019
Khudoyor Mamayusupov National Research University Higher School of Economics 26/08/2019 - 30/08/2019
Rodica Georgiana Marineac Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest 26/08/2019 - 30/08/2019
Benjamin Meco Uppsala Universitet 26/08/2019 - 30/08/2019
Robert Nicholls University of Augsburg 26/08/2019 - 30/08/2019
Ryuma Orita Tokyo Metropolitan University 26/08/2019 - 30/08/2019
Ashraf Owis Cairo 26/08/2019 - 30/08/2019
Yakov Pesin Pennsylvania State University 17/08/2019 - 31/08/2019
Boris Petkovic KTH Royal Institute of Technology 26/08/2019 - 30/08/2019
Abror Pirnapasov Ruhr University Bochum 26/08/2019 - 30/08/2019
Zhijun (George) Qiao University of Texas Rio Grande Valley 26/08/2019 - 30/08/2019
Pedram Safaee UNINE 26/08/2019 - 30/08/2019
Felix Schlenk Université de Neuchâtel 26/08/2019 - 30/08/2019
Jörg Schmeling Lund University 18/08/2019 - 02/09/2019
Samuel Senti Universidade Federal do Rio de Janeiro 26/08/2019 - 30/08/2019
Nessim Sibony Université Paris-Sud (Orsay) 25/08/2019 - 31/08/2019
Iryna Sivak EPFL 26/08/2019 - 30/08/2019
Anastasios Stylianou University of Warwick 26/08/2019 - 30/08/2019
Dennis Ulbrich Universität Bremen 25/08/2019 - 30/08/2019
Polina Vytnova University of Warwick 26/08/2019 - 30/08/2019
Vijay Kumar Yadav Indian Institute of Technology (Banaras Hindu University) 26/08/2019 - 30/08/2019
Lixuan Zheng Universite Paris-Est Creteil Val de Marne 26/08/2019 - 30/08/2019
Total Guests : 50
Name University Dates of visit
David Damanik Rice University 25/08/2019 - 31/08/2019
Anish Ghosh Tata Institute of Fundamental Research 25/08/2019 - 31/08/2019
Viktor Ginzburg University of California Santa Cruz 25/08/2019 - 31/08/2019
Nessim Sibony Université Paris-Sud (Orsay) 25/08/2019 - 31/08/2019
Total Guests : 4
Monday 26 August
08:30-09:30 CIB front desk registration and Welcome Coffee
09:30-10:30 Viktor Ginzburg - Part I
10:30-11:00 Coffee Break
11:00-12:00 Talk 2
12:00-14:00 Lunch
14:00-15:00 Talk 3

Tuesday 27 August
09:30-10:30 Talk 4
10:30-11:00 Coffee Break
11:00-12:00 Viktor Ginzburg - Part II
12:00-14:00 Lunch
14:00-15:00 Talk 6
15:00-15:30 Coffee Break
15:30-16:30 Talk 7

Wednesday 28 August
09:30-10:30 Talk 8
10:30-11:00 Coffee Break
11:00-12:00 Talk 9
12:00-14:00 Lunch
14:00-15:00 Viktor Ginzburg - Part III
Social Dinner

Thursday 29 August
09:30-10:30 Talk 11
10:30-11:00 Coffee Break
11:00-12:00 Talk 12
12:00-14:00 Lunch
14:00-15:00 Talk 13
15:00-15:30 Coffee Break
15:30-16:30 Viktor Ginzburg - Part IV

Friday 30 August
09:30-10:30 Talk 15
10:30-11:00 Coffee Break
11:00-12:00 Talk 16