Lectures related to Structure of Measure-Preserving Systems

Explores elements from Ergodic Theory, transformations, invariant sets, and Lyapunov Exponents for 1-dimensional maps.

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

Mixing Properties of Infinite Measure Preserving Systems

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

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Equidistribution of CM Points

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

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.

Elements of Statistics: Probability, Distributions, and Estimation

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

Elements of Statistics: Memorylessness, Stationary Processes, Estimation using MLE

Explores memorylessness in distributions, stationary processes, and estimation using MLE.

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.

Statistical Physics: Systems Isolation

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

Applications of Ergodic Theory to Combinatorics

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

Ergodic properties of low complexity symbolic systems

Explores the influence of complexity on ergodic properties of symbolic systems, presenting the Curtis-Hedlund-Lyndon Theorem and constructions of minimal subshifts.

Correlations of the Liouville function

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Introduction to Inference

Covers the basics of probability theory, random variables, joint probability, and inference.

Chaos: Irregular Trajectories and Sensitivity to Initial Conditions

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

Statistics: Exploratory Data Analysis

Introduces statistics basics, including data analysis and probability theory, emphasizing central tendency, dispersion, and distribution shapes.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Conditional Probability: Prediction Decomposition

Explores conditional probability, Bayes' theorem, and prediction decomposition for informed decision-making.

Probability and Statistics: Fundamentals

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

Probability and Statistics

Covers inequalities, joint Gaussian distribution, risk estimation, and classification method testing in probability and statistics.