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

PDEs for Neural Assemblies - Analysis, Simulations, and Behavior

Explore PDEs for neural assemblies, analyzing their behavior through simulations and mathematical techniques with Professor Benoît Perthame from Sorbonne University.

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

Swarm-Based Gradient Descent Method for Non-Convex Optimization

Explore innovative swarm-based gradient descent techniques for solving non-convex optimization problems, presented by Prof. Eitan Tadmor from the University of Maryland.

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

Coulomb Branches of 3d N=4 SUSY Gauge Theories and Bow Varieties - Part 2

Explore advanced concepts in supersymmetric gauge theories, focusing on Coulomb branches and bow varieties in 3-dimensional N=4 models with Hiraku Nakajima.

• YouTube
• 2 hours 2 minutes
• On-Demand
• Free Video

Coulomb Branches of Orthosymplectic Quiver Gauge Theories

Explore orthosymplectic quiver gauge theories, focusing on Coulomb branches, Higgs branches, and integrable systems with expert Hiraku Nakajima.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Unipotent Character Sheaves and Strata of a Reductive Group

Explore unipotent character sheaves and strata of reductive groups with George Lusztig, delving into advanced mathematical concepts and their applications.

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

Coulomb Branches of 3D N=4 SUSY Gauge Theories and Bow Varieties - Part 1

Explore Coulomb branches in 3d N=4 supersymmetric gauge theories and their connection to bow varieties, covering key concepts, technical points, and applications in integrable systems.

• YouTube
• 2 hours 2 minutes
• On-Demand
• Free Video

Semisimple Groups and the Theory of Total Positivity

Explore semisimple groups and total positivity theory with MIT's George Lusztig, delving into advanced mathematical concepts and their applications in group theory.

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

New Perspectives for Higher-order Methods in Convex Optimization

Explore advanced techniques in convex optimization, focusing on higher-order methods and their applications in mathematical problem-solving and algorithm development.

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

Set-limited Functions and Polynomial-time Interior-point Methods

Explore polynomial-time interior-point methods and set-limited functions with Yurri Nesterov, delving into advanced optimization techniques and mathematical theory.

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

Nonconvex Stochastic Programs: Chance Constraints

Explore nonconvex stochastic programs and chance constraints with Jong-Shi Pang, delving into advanced mathematical concepts for optimization under uncertainty.

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

Nonconvex Stochastic Programs - Deterministic Constraints

Explore nonconvex stochastic programs with deterministic constraints, presented by Jong-Shi Pang from USC. Gain insights into advanced mathematical concepts and their applications.

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

Primal-Dual Optimization Methods for Robust Machine Learning

Explore primal-dual optimization techniques for enhancing machine learning robustness, focusing on advanced mathematical approaches to improve model performance and reliability.

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

Optimization in Theory and Practice

Explore optimization techniques and their real-world applications with insights from Stephen Wright of University of Wisconsin-Madison, blending theoretical foundations and practical implementations.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video