Explore the intersection of algebraic, geometric, and probabilistic methods in dynamical systems and control theory through this comprehensive mathematical school organized by ICTP Mathematics. Delve into six intensive minicourse series covering counting techniques, smooth group actions and rigidity, symbolic dynamics for low-dimensional systems with positive entropy, dynamics of group actions on homogeneous spaces, the Kerov-Vershik method in Pickrell's classification, and Brownian motion with evolving geometries and entropy formulas. Engage with expert-led lectures that demonstrate how probability theory and algebraic concepts permeate ergodic theory, while discovering how ergodic theory methods solve fundamental problems in number theory and algebra. Participate in contributed talks covering topics such as quantum ergodicity, thermodynamics of dynamical systems, invariant measures, equilibrium states, random matrix theory, and functional limit theorems. Benefit from discussion sessions, open problem presentations, and poster sessions designed to foster collaboration between established researchers and emerging mathematicians, providing opportunities to define new research projects and explore cutting-edge developments in these interconnected mathematical fields.

Syllabus

Brownian motion, evolving geometries and entropy formulas - A. Thalmaier - Lecture 01
Brownian motion, evolving geometries and entropy formulas - A. Thalmaier - Lecture 02
Brownian motion, evolving geometries and entropy formulas - A. Thalmaier - Lecture 03
Brownian motion, evolving geometries and entropy formulas - A. Thalmaier - Lecture 04
Symbolic dynamics for low-dimensional systems with positive entropy - Y. Lima - Lecture 01
Symoblic dynamics for low-dimensional systems with positive entropy - Y. Lima - Lecture 02
Symoblic dynamics for low-dimensional systems with positive entropy - Y. Lima - Lecture 03
Symoblic dynamics for low-dimensional systems with positive entropy - Y. Lima - Lecture 04
Dynamics of group actions on homogeneous spaces - A. Mohammadi - Lecture 01
Dynamics of group actions on homogeneous spaces - A. Mohammadi - Lecture 02
Dynamics of group actions on homogeneous spaces - A. Mohammadi - Lecture 03
Dynamics of group actions on homogeneous spaces - A. Mohammadi - Lecture 03
Kerov-Vershik method in Pickrell's classification - Y. Qiu - Lecture 01
Kerov-Vershik method in Pickrell's classification - Y. Qiu - Lecture 02
Kerov-Vershik method in Pickrell's classification - Y. Qiu - Lecture 03
Kerov-Vershik method in Pickrell's classification - Y. Qiu - Lecture 04
Introduction to smooth group actions and rigidity - F. Hertz - Lecture 01
Introduction to smooth group actions and rigidity - F. Hertz - Lecture 02
Introduction to smooth group actions and rigidity - F. Hertz - Lecture 03
Introduction to smooth group actions and rigidity - F. Hertz - Lecture 04
Cohomological equations for suspension flows over Vershik automorphisms - D. Zubov
Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces - T. Sahlsten
Thermodynamics of the Katok map - Y. Pesin
Regularity of the drift in negative curvature - F. Ledrappier
Totally non-free actions and invariant random subgroups - R. Grigorchuk
Zero entropy subgroups of the mapping class group - K. Parwani
Toeplitz determinants with merging singularities - I. Krasovsky
Invariant measures for the actions of infinite classic groups - P. Nikitin
Rigidity for partially hyperbolic diffeomorphisms - R. Varao
Limit theorem for interval exchange maps - A. Klimenko
Equilibrium states for geodesic flow in non-positive curvature - V. Climenhaga
Random Matrix Theory and Infinite-dimensional Stochastic Differential Equations - H. Osada
Functional Limit Theorem for the Sine-process - A. Dymov
Integrability of continuous bundles - K. M. War
Equilibrium states are determined by their unstable conditionals - P. Carrasco
Entropy for partially hyperbolic diffeomorphisms with low dimensional center - R. Saghin
Strong hyperbolicity of high entropy measures - A. Tahzibi
Counting Techniques - S. Filip - Lecture 04
Counting Techniques - S. Filip - Lecture 03
Counting Techniques - S. Filip - Lecture 02
Counting Techniques - S. Filip - Lecture 01