Lectures related to Ergodic Theory: Chaos

Structure of Measure-Preserving Systems

Covers the abstract structure of measure-preserving systems and aims to understand their classification and ergodic decompositions.

FK-Percolation and the Six-Vertex Model: Critical Phenomena

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Essential Coexistence Phenomenon in Hamiltonian Dynamics

By Yakov Pesin delves into the essential coexistence phenomenon in Hamiltonian dynamics, exploring types I and II and providing examples and proofs.

Dynamical Approaches to Spectral Theory of Operators

Explores ergodic theory, spectral operators, and almost periodic factors in dynamical systems and spectral theory.

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Deterministic Chaos and Statistics

Explores the Lorenz System, sensitivity to initial conditions, chaotic systems, and topological mixing.

Probability and Statistics

Introduces key concepts in probability and statistics, illustrating their application through various examples and emphasizing the importance of mathematical language in understanding the universe.

Infinitesimal Deformations: One-Dimensional Maps

Explores infinitesimal deformations of one-dimensional maps, discussing common characteristics, methods, and recent results in expanding and piecewise expanding maps.

Mixing Properties of Infinite Measure Preserving Systems

Explores mixing properties of infinite measure preserving systems, focusing on suspensions, Govers transformations, and Lorentz gas.

Probability and Statistics for SIC

Delves into probability, statistics, random experiments, and statistical inference, with practical examples and insights.

Gibbs measures: Hyperbolic Attractors

Explores Gibbs measures for hyperbolic attractors, including T-invariant probability measures and perturbations of the CAT map.

Markov Chains: Ergodicity and Stationary Distribution

Explores ergodicity and stationary distribution in Markov chains, emphasizing convergence properties and unique distributions.

Statistical Physics: Systems Isolation

Explores statistical physics concepts in isolated systems, focusing on entropy and disorder.

Introduction to Quantum Chaos Log in to Mediaspace to watch this video

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Chaos: Irregular Trajectories and Sensitivity to Initial Conditions Log in to Mediaspace to watch this video

Explores chaos, irregular trajectories, and sensitivity to initial conditions in dynamical systems.

Applications of Ergodic Theory to Combinatorics Log in to Mediaspace to watch this video

Explores the applications of ergodic theory to combinatorics and number theory, including Szemerédi's Theorem and the Erdős-Kac Theorem.

Equidistribution of CM Points Log in to Mediaspace to watch this video

Explores the joint equidistribution of CM points and their properties in ergodic theory and homogeneous dynamics.

Elements of Statistics: Probability, Distributions, and Estimation Log in to Mediaspace to watch this video

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Equidistribution of CM Points Log in to Mediaspace to watch this video

Explores the equidistribution of CM points and the implications of ergodicity in measure-preserving systems.

Probability and Statistics: Fundamentals Log in to Mediaspace to watch this video

Covers the fundamental concepts of probability and statistics, including interesting results, standard model, image processing, probability spaces, and statistical testing.