International Mathematical Union Courses

Kavita Ramanan - Interacting Stochastic Processes on Sparse Random Graphs

Explores hydrodynamic limits and marginal dynamics of interacting stochastic processes on sparse random graphs, contrasting with mean-field limits and discussing applications in various scientific fields.

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

Mean-Field Limits for Quantum Systems and Nonlinear Gibbs Measures

Explore quantum systems, Bose-Einstein condensation, and nonlinear Gibbs measures in this advanced mathematics lecture on mean-field limits and symmetry-induced independence.

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

Beyond Linear Algebra

Explore advanced mathematical concepts beyond linear algebra, including critical point equations, nonlinear algebra in PDE, and geometric interpretations in optimization and statistics.

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

Mathematical Analysis and Numerical Methods for Inverse Scattering Problems

Explore mathematical analysis and numerical methods for inverse scattering problems, covering applications, challenges, algorithms, and recent progress in stability analysis and deep learning approaches.

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

Peng Shan- On Geometrical Realization of Centers

Explore connections between algebra centers and geometric cohomology, focusing on quantum groups and affine Springer fibers in Lie theory.

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

Algorithmic Aspects of Discrepancy Theory

Explore algorithmic aspects of discrepancy theory, including vector balancing, Spencer's Problem, and Banaszczyk's Theorem, with insights on geometric perspectives and partial coloring techniques.

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

Stability and Recursive Solutions in Hamiltonian PDEs

Explore stability and recursive solutions in Hamiltonian PDEs, focusing on oscillating motions near elliptic fixed points, KAM theory applications, and the interplay between chaotic and recursive phenomena.

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

Theory of Graph Neural Networks: Representation and Learning

Explore the theory behind Graph Neural Networks, covering approximation, learning properties, and connections to graph isomorphism, equivariant functions, and dynamic programming.

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

Ramsey Theory of Homogeneous Structures

Explore Ramsey theory on infinite structures, focusing on homogeneous structures. Learn about recent developments, methodologies, and ongoing research in this complex area of mathematics.

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

Canonical Kaehler Metrics and Stability of Algebraic Varieties

Explore canonical Kähler metrics, algebraic variety stability, and the Yau-Tian-Donaldson conjecture in complex geometry. Delve into Kähler manifolds, curvature, and pluripotential theory with recent progress and applications.

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

Mariusz Lemanczyk: Furstenberg Disjointness, Ratner Properties and Sarnak’s Conjecture

Explore Furstenberg disjointness, Ratner properties, and Sarnak's conjecture in number theory and ergodic theory. Delve into multiplicative functions, topological dynamics, and connections to the Chowla conjecture.

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

Structure-Preserving Model Order Reduction of Hamiltonian Systems

Explore structure-preserving model order reduction for Hamiltonian systems, focusing on symplectic geometry and reduced basis algorithms. Learn about extensions to nonlinear problems and applications in plasma physics.

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

KPZ Limit Theorems

Explores KPZ universality in particle systems, growth models, and polymers, discussing limit theorems, integrable methods, and recent results on periodic domains.

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

Georges Gonthier - Computer Proofs - Teaching Computers Mathematics, and Conversely

Explore computer-assisted mathematical proofs, from the four-color puzzle to homotopy type theory. Learn how computer science methods enhance mathematical language, leading to new insights and advancements in formal proofs.

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

Theory of Adaptive Estimation

Introduction to modern adaptive estimation theory, focusing on universal estimation procedures and oracle inequalities. Explores commutativity properties, upper functions, and applications to various statistical models.

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