BIMSA Courses

A Reinforcement Learning-Based Method for Solving High-Dimensional Integro-Differential Equations

Discover a deep learning framework using reinforcement learning to solve high-dimensional partial integro-differential equations, overcoming traditional computational limitations.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Simplicial Topology, Braids, Knots, and GLMY Theory

Explore simplicial topology's connections to braids, knots, and homotopy groups, plus GLMY theory applications in molecular biology, diseases, materials, and complex networks.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

On Mapping Class Groups of 4-Manifolds

Explore mapping class groups of 4-manifolds using configuration space invariants, including proofs about surface cross 2-sphere groups and connections to Gabai's lightbulb theorem.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Achieving Instance-Dependent Sample Complexity for Constrained Markov Decision Process

Explore advanced reinforcement learning for constrained Markov decision processes with optimal problem-dependent guarantees and novel primal-space algorithms.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Adaptive Regularized Newton-CG for Nonconvex Optimization - Optimal Global Complexity and Quadratic Local Convergence

Discover an adaptive regularized Newton-CG method achieving optimal O(ε^-3/2) global complexity while maintaining quadratic local convergence for nonconvex optimization problems.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Hecke Categories and Their (Co)center

Explore the geometrization of Hecke algebras through Hecke categories and their (co)center, with applications to Chavelley restriction theorem for reductive algebraic groups.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Structure and Computation - Algebraic Riccati Equations as an Example

Explore the interplay between mathematical structure and computational methods through algebraic Riccati equations in this advanced seminar.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Quantum Groupoids from Quantum Group Dynamics and Tannaka-Krein Duality

Explore how quantum groupoids emerge from quantum group dynamics through operator algebras, investigating quantum symmetries and their role in noncommutative geometry.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Derived Equivalences from Invariant Theory

Explore derived equivalences in algebraic geometry through invariant theory, focusing on homological algebra and category theory applications to study varieties with insights from physics and noncommutative algebra.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Noncommutative Geometry of PGL(2,Cp) and KMS States

Explore noncommutative geometry on the Berkovich projective line, focusing on representation theory of groups acting on R-trees and the construction of cross-product C*-algebras and KMS states.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Vantage Points and Sign Patterns

Explore the mathematical study of ordering points in space based on their distances from vantage points, featuring an extension of sign pattern results with applications in discrete mathematics and computer science.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Noncommutative Functional Inequalities and Applications to the Quantum KKL-conjecture

Explore noncommutative functional inequalities and their applications to the quantum KKL-conjecture, including Poincare, log-Sobolev, and Talagrand inequalities, with focus on recent advancements.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Markov Semigroups with Quantum Symmetry

Explore bimodule quantum Markov semigroups and their symmetry-preserving dynamics through von Neumann algebras, equilibrium states, and functional inequalities.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Spread Approximations and Intersection Problems

Explore the spread approximation method and its applications to intersection problems in combinatorics, including recent results on spanning trees, permutations, and forbidden sunflowers.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

A Quick Trip to Knot Theory and Knot Data Analysis

Explore knot theory and its applications in data analysis with Professor Fengchun Lei, covering 3-manifold topology and topological data analysis concepts in this BIMSA Member Seminar.

• YouTube
• 47 minutes
• Self-Paced
• Free Video