International Mathematical Union Courses

Asaf Shapira - Local vs Global Combinatorics

Explore extremal combinatorics through the Brown-Erdős-Sós conjecture, hypergraph theory, and removal lemmas. Gain insights into local-global principles and their applications in mathematics.

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

Sylvie Méléard- Multiscale Eco-Evolutionary Models- From Individuals to Populations

Exploring eco-evolutionary models from individual to population scales, focusing on small population effects, mutation dynamics, and long-term behaviors using stochastic processes and mathematical approximations.

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

Neena Gupta- The Zariski Cancellation Problem and Related Problems in Affine Algebraic Geometry

Explore Zariski Cancellation Problem and related topics in affine algebraic geometry, including Asanuma rings, affine fibration, epimorphism theorems, and notable examples from leading mathematicians.

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

Stuart White- Classification of Simple Amenable C-Algebras

Explore the classification of simple amenable C*-algebras with Stuart White, covering operator algebras, group actions, inductive limits, and the Elliott programme in this mathematical lecture.

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

Marsha Berger - Towards Adaptive Simulations of Dispersive Tsunami Propagation

Explore adaptive simulations for tsunami propagation, focusing on shallow water equations, mesh refinement, and Boussinesq models. Learn about computational techniques for predicting tsunami impacts from various sources.

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

Integrable Fluctuations in One-Dimensional Random Growth

Explores recent findings on asymptotic fluctuations in KPZ universality class, covering random growth models, directed polymers, and particle systems. Discusses solvability, explicit formulas, and integrable differential equations.

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

Mathematics of Computation Through the Lens of Linear Equations and Lattices

Explore mathematical foundations of computation through linear equations and lattices, covering error correction, vector problems, and lattice theory with implications for future computing.

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

Recent Progress in General Relativity

Explore recent advancements in general relativity, covering topics from Lorentzian manifolds to black hole stability and many-black-hole spacetimes.

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

Noncommutative Ergodic Theory of Higher Rank Lattices

Explore recent advancements in noncommutative ergodic theory, focusing on dynamics of positive definite functions and character rigidity in higher rank lattices, with applications to various mathematical fields.

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

Random Algebraic Dynamics in Complex Dimension 2

Explore dynamics of automorphism groups on projective surfaces, covering measure classification, orbit closures, and finite orbits. Techniques from geometry and dynamical systems are discussed.

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

Self-Similar Sets and Measures on the Line

Explore fractal geometry through self-similar sets and measures, focusing on recent developments in determining their dimensions. Gain insights into classical fractals and cutting-edge research.

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

The Positive Grassmannian, the Amplituhedron, and Cluster Algebras

Explore the positive Grassmannian and amplituhedron, delving into their combinatorial structures and connections to physics, integrable systems, and scattering amplitudes using oriented matroids, tropical geometry, and cluster algebras.

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

Yuri Prokhorov - Effective Results in the Three-Dimensional Minimal Model Program

Explore recent developments in 3D minimal model program, covering basic operations, terminal singularities, classification strategies, and effective boundedness of Q-Fano 3-folds.

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

Independent Learning Dynamics for Stochastic Games - Where Game Theory Meets

Explore independent learning dynamics in stochastic games, bridging game theory and reinforcement learning. Discover convergent algorithms for multi-agent scenarios in dynamic environments.

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

Atsushi Ichino- Theta Lifting and Langlands Functoriality

Explore theta lifting, seesaw identities, and Langlands functoriality in number theory, focusing on modular forms and local Shimura-Waldspurger correspondence.

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