Institute for Mathematical Sciences Courses

An Introduction to Intertwining via Strong Stationary Duality - Developments and Open Problems

Explores advanced applications of dual chains in random walks, focusing on less symmetric scenarios and statistical applications, with examples from hyperplane arrangements and non-uniform duals.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Applications of Duality - Lecture 3

Explore applications of dual processes in Markov chains, including strong stationary times, eigenvalue interpretation, and solutions to the Peres conjecture for Birth and Death chains.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Duality and Intertwining in Markov Chains - Lecture 2

Explore advanced Markov chain analysis through embedded processes, intertwining relations, and various dualities. Gain insights into stationarity and extensions to set and measure-valued duals.

• YouTube
• 59 minutes
• On-Demand
• Free Video

An Introduction to Intertwining via Strong Stationary Duality - First Examples and Basic Setup

Explore Markov chains, mixing times, and card shuffling techniques. Learn about strong stationary times and their properties in this advanced probability theory lecture.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Hypoelliptic Laplacian and the Trace Formula

Explore geometric formulas for semisimple orbital integrals, connecting heat equation methods to Selberg's trace formula through Laplacian deformations and Fokker-Planck operators.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

The Hypoelliptic Laplacian in Real and Complex Geometry

Explores the hypoelliptic Laplacian's construction and applications in real and complex geometry, focusing on de Rham and Dolbeault theories and its role as a geometric Fokker-Planck operator.

• YouTube
• 56 minutes
• On-Demand
• Free Video

From Mosquitoes to ChatGPT - The Birth and Strange Life of the Random Walk

Explore the fascinating history and diverse applications of random walks, from mosquito control to AI, and their impact on modern technology and scientific understanding.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Scientific Research in the Time of AI

Explore AI's impact on scientific progress, from leveraging fundamental principles to utilizing data. Discover ongoing projects shaping new research infrastructure.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Optimal Transport and High Dimensional Probability - Introduction to Optimal Transport

Explore optimal transport theory and its applications in high-dimensional probability, focusing on fundamental concepts and recent developments in this mathematical field.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Optimal Transport and High Dimensional Probability in Wasserstein Spaces

Explore optimal transport theory and high-dimensional probability in Wasserstein spaces, delving into advanced mathematical concepts and their applications.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Optimal Transport and High-Dimensional Probability

Explore functional inequalities, convergence of flows, and logconcavity of probability measures in high-dimensional spaces through optimal transport theory.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Optimal Transport and High-Dimensional Probability - Functional Inequalities and Concentration of Measure

Explore functional inequalities, concentration of measure, and transport inequalities in high-dimensional probability, including sub-Gaussian variables and the entropy method.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Optimal Transport and High-Dimensional Probability - Langevin Dynamics via Calculus

Explore optimal transport, high-dimensional probability, and Langevin dynamics through advanced calculus techniques in this mathematical deep dive.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Optimal Transport and High-Dimensional Probability - Otto's Calculus on Wasserstein Space

Explore optimal transport and high-dimensional probability through Otto's Calculus on Wasserstein spaces, delving into advanced mathematical concepts and their applications.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Approximately Hadamard Matrices and Random Frames

Explore approximately Hadamard matrices and random frames with Mark Rudelson, delving into advanced mathematical concepts and their applications in signal processing and data analysis.

• YouTube
• 48 minutes
• On-Demand
• Free Video