Description The Abdus Salam International Centre for Theoretical Physics (ICTP), in collaboration with International School for Advanced Studies - Trieste (SISSA), is organizing a School on Algebraic, Geometric and Probabilistic Aspect of Dynamical Systems and Control Theory, which will be held at ICTP, Trieste, Italy, from 4 to 15 July 2016.

Analyzing the interplay between different sub areas of mathematics is one of the fascinating goals of researchers in this area. The ideas from probability theory and algebra are ubiquitous in ergodic theory of dynamical systems. The deep works of many dynamicists had proved the power of ergodic theory methods to solve celebrated problems in number theory and algebra. The aim of this workshop is to gather some of the experts of these areas and discuss recent developments with mostly young researchers.

The workshop will consist of long courses, invited and contributed talks, as well as an open problem session and a poster session.The idea is to have sufficient time to have discussion sections with students and post-docs and help young researchers to define new projects.

MINICOURSES

• Counting Techniques (S. Filip)
• Introduction to smooth group actions and rigidity (F. Hertz)
• Symbolic dynamics for low-dimensional systems with positive entropy (Y. Lima)
• Dynamics of group actions on homogeneous spaces (A. Mohammadi)
• Kerov-Vershik method in Pickrell's classification (Y. Qiu)
• Brownian motion, evolving geometries and entropy formulas (A. Thalmaier)

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement No 647133 (ICHAOS).

GRANTS A limited number of grants are available to support the travel and living expenses of selected participants, with priority given to participants working in a developing country and who are at the early stages of their career.
Go to day
  • Monday, 4 July 2016
    • 08:15 - 21:00
      • 08:15 Registration 45' ( Leonardo Building - Lobby )
      • 09:00 Opening 30'
        Speakers: S. Luzzatto (ICTP), S. Bufetov (CNRS - Steklov Mathematical Institute)
      • 09:30 Kerov-Vershik method in Pickrell's classification 45'
        Speaker: Y. Qiu (Universite' Paul Sabatier)
        Material: References Video
      • 10:15 Break 30'
      • 10:45 Introduction to smooth group actions and rigidity 45'
        Speaker: F. Hertz (The Pennsylvania State University)
        Material: References Video
      • 11:30 Break 15'
      • 11:45 Dynamics of group actions on homogeneous spaces 45'
        Speaker: A. Mohammadi (The University of Texas at Austin)
        Material: Abstract Video
      • 12:30 Lunch break 2h0'
      • 14:30 Exercise class 2h0'
      • 19:00 Welcome Reception 2h0' ( Mignon ( Terrace ) )
  • Tuesday, 5 July 2016
    • 09:00 - 16:00
      • 09:00 Introduction to smooth group actions and rigidity 45'
        Speaker: F. Hertz (The Pennsylvania State University)
        Material: Video
      • 09:45 Break 30'
      • 10:15 Kerov-Vershik method in Pickrell's classification 45'
        Speaker: Y. Qiu (Universite' Paul Sabatier)
        Material: Video
      • 11:00 Break 15'
      • 11:15 Dynamics of group actions on homogeneous spaces 45'
        Speaker: A. Mohammadi (The University of Texas at Austin)
        Material: Video
      • 12:00 Lunch break 2h0'
      • 14:00 Poster session 2h0'
  • Wednesday, 6 July 2016
    • 09:00 - 16:30
      • 09:00 Kerov-Vershik method in Pickrell's classification 45'
        Speaker: Y. Qiu (Universite' Paul Sabatier)
        Material: Video
      • 09:45 Break 30'
      • 10:15 Dynamics of group actions on homogeneous spaces 45'
        Speaker: A. Mohammadi (The University of Texas at Austin)
        Material: Video
      • 11:00 Break 15'
      • 11:15 Introduction to smooth group actions and rigidity 45'
        Speaker: F. Hertz (The Pennsylvania State University)
        Material: Video
      • 12:00 Group photo 10'
      • 12:10 Lunch break 1h50'
      • 14:00 Exercise class 2h0'
      • 16:00 Entropy for partially hyperbolic diffeomorphisms with low dimensional center 30'
        Speaker: R. Saghin (Universidad Valparaiso Chile)
        Material: Video
  • Thursday, 7 July 2016
    • 09:00 - 18:00
      • 09:00 Dynamics of group actions on homogeneous spaces 45'
        Speaker: A. Mohammadi (The University of Texas at Austin)
        Material: Video
      • 09:45 Break 30'
      • 10:15 Introduction to smooth group actions and rigidity 45'
        Speaker: F. Hertz (The Pennsylvania State University)
        Material: Video
      • 11:00 Break 15'
      • 11:15 Kerov-Vershik method in Pickrell's classification 45'
        Speaker: Y. Qiu (Universite' Paul Sabatier)
        Material: Video
      • 12:00 Lunch break 2h0'
      • 14:00 Equilibrium States are determined by their unstable conditionals 30'
        Speaker: P. Carrasco (Universidade de Sao Paulo)
        Material: Abstract Slides Video
      • 14:30 Integrability of continuous bundles 30'
        Speaker: K.M. War (SISSA)
        Material: Abstract Video
      • 15:00 Strong hyperbolicity of high entropy measures 1h0'
        Speaker: A. Tahzibi (University of São Paulo (on leave) - Université Paris-Sud)
        Material: Abstract Video
      • 16:00 Group discussions 2h0'
  • Friday, 8 July 2016
    • 09:00 - 21:00
      • 09:00 Functional Central Limit Theorem for the Sine-process 45'
        Speaker: A. Dymov (National Research University Higher School of Economics)
        Material: Abstract Video
      • 09:45 Break 30'
      • 10:15 Random Matrix Theory and Infinite-dimensional Stochastic Differential Equations 45'
        Speaker: H. Osada (Kyushu University)
        Material: Abstract Video
      • 11:00 Break 15'
      • 11:15 Equilibrium states for geodesic flow in non-positive curvature 45'
        Speaker: V. Climenhaga (University of Houston)
        Material: Abstract Video
      • 12:00 Lunch break 2h0'
      • 14:00 Limit theorem for interval exchange maps 30'
        Speaker: A. Klimenko (Russian Academy of Sciences Steklov Mathematical Institute)
        Material: Abstract Video
      • 14:30 Rigidity for partially hyperbolic diffeomorphism 30'
        Speaker: R. Varao (University of Campinas/ Unicamp)
        Material: Abstract Video
      • 15:00 Invariant measures for the actions of infinite classic groups on the spaces of infinite matrices 30'
        Speaker: P. Nikitin (Institut de Mathematiques de Marseille)
        Material: Abstract Video
      • 15:30 Toeplitz determinants with merging singularities 30'
        Speaker: I. Krasovsky (Imperial College London)
        Material: Abstract Video
      • 19:00 Social Dinner 2h0' ( Mignon ( Restaurant ) )
        You are kindly requested to confirm your participation to the dinner to the secretary by 4.00 pm of Tuesday, 5 July.
  • Monday, 11 July 2016
    • 09:00 - 16:30
      • 09:00 Brownian motion, evolving geometries and entropy formulas 45'
        Speaker: A. Thalmaier (University of Luxembourg)
        Material: Abstract Slides Video
      • 09:45 Break 30'
      • 10:15 Counting Techniques 45'
        Speaker: S. Filip (University of Chicago)
        Material: Abstract Video
      • 11:00 Break 15'
      • 11:15 Symbolic dynamics for low-dimensional systems with positive entropy 45'
        Speaker: Y. Lima (Paris Sud University)
        Material: Abstract Lecture notes Video
      • 12:00 Lunch break 2h0'
      • 14:00 Exercise class 2h0'
      • 16:00 Examples of new partially hyperbolic diffomorphism 30'
        Speaker: K. Parwani (Eastern Illinois University)
        Material: Abstract Video
  • Tuesday, 12 July 2016
    • 09:00 - 17:15
      • 09:00 Counting Techniques 45'
        Speaker: S. Filip (University of Chicago)
        Material: Video
      • 09:45 Break 30'
      • 10:15 Symbolic dynamics for low-dimensional systems with positive entropy 45'
        Speaker: Y. Lima (Paris Sud University)
        Material: Video
      • 11:00 Break 15'
      • 11:15 Brownian motion, evolving geometries and entropy formulas 45'
        Speaker: A. Thalmaier (University of Luxembourg)
        Material: Slides Video
      • 12:00 Lunch break 2h0'
      • 14:00 Totally non-free actions and invariant random subgroups 1h0'
        Speaker: R. Grigorchuk (Texas A&M University)
        Material: Abstract Video
      • 15:00 Regularity of the drift in negative curvature 1h0'
        Speaker: F. Ledrappier (University of Notre Dame)
        Material: Abstract Video
      • 16:30 Palm Measures 45'
        Speaker: S. Bufetov (CNRS - Steklov Mathematical Institute)
        Material: Abstract
  • Wednesday, 13 July 2016
    • 09:00 - 16:00
      • 09:00 Symbolic dynamics for low-dimensional systems with positive entropy 45'
        Speaker: Y. Lima (Paris Sud University)
        Material: Video
      • 09:45 Break 15'
      • 10:00 Brownian motion, evolving geometries and entropy formulas 45'
        Speaker: A. Thalmaier (University of Luxembourg)
        Material: Slides Video
      • 10:45 Break 15'
      • 11:00 Counting Techniques 45'
        Speaker: S. Filip (University of Chicago)
        Material: Video
      • 11:45 Lunch break 2h15'
      • 14:00 Exercise class 2h0'
  • Thursday, 14 July 2016
    • 09:00 - 23:00
      • 09:00 Brownian motion, evolving geometries and entropy formulas 45'
        Speaker: A. Thalmaier (University of Luxembourg)
        Material: Slides Video
      • 09:45 Break 30'
      • 10:15 Counting Techniques 45'
        Speaker: S. Filip (University of Chicago)
        Material: Video
      • 11:00 Break 15'
      • 11:15 Symbolic dynamics for low-dimensional systems with positive entropy 45'
        Speaker: Y. Lima (Paris Sud University)
        Material: Video
      • 12:00 Lunch break 2h0'
      • 14:00 Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces 30'
        Speaker: T. Sahlsten (University of Bristol)
        Material: Abstract Video
      • 14:30 Cohomological equations for suspension flows over Vershik automorphisms 30'
        Speaker: D. Zubov (National Research University Higher School of Economics)
        Material: Abstract Video
      • 15:00 Thermodynamics of the Katok Map 1h0'
        Speaker: Y. Pesin (The Pennsylvania State University)
        Material: Abstract Video
      • 19:30 ICTP Cuban Party 3h30' ( Leonardo Building - Terrace )
  • Friday, 15 July 2016
    • 09:00 - 15:00
      • 09:00 Group discussions 1h15'
      • 13:00 Lunch break 2h0'