International Mathematical Union Courses

Analysis with Simple Lie Groups and Lattices

Explore advanced mathematical concepts focusing on simple Lie groups and lattices, delving into their analytical properties and applications in modern algebra and geometry.

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

Arithmetic Dynamics - A Survey

Explore arithmetic dynamics, a field merging number theory and algebraic geometry with dynamical systems, examining key problems and recent advancements in this emerging area of mathematics.

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

Classification of Gapped Ground State Phases in Quantum Spin Systems

Explore quantum spin systems and gapped ground state phases with Yoshiko Ogata's in-depth analysis of classification methods and theoretical frameworks.

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

Kähler Manifolds with Curvature Bounded Below

Explore Kähler manifolds with curvature bounded below, covering Yau's uniformization conjecture, compactification of manifolds, and Gromov-Hausdorff limits in this advanced mathematical survey.

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

Hydrodynamic Limit and Stochastic PDEs Related to Interface Motion

Explore interacting particle systems and their macroscopic behavior through hydrodynamic limits, deriving models for interface motion in phase separation, species segregation, and coupled KPZ equations.

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

George Birkhoff’s Forgotten Manuscript and His Programme for Dynamics

Explore George Birkhoff's forgotten manuscript and his influential program for dynamics, uncovering its historical significance and impact on mathematical research.

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

Some Uses and Associations of Mathematics, as Seen From a Distant Historical

Explore the historical significance and diverse applications of mathematics across cultures and time periods, gaining insights into its enduring impact on society.

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

Camillo DeLellis- Regular and Singular Minimal Surfaces

Exploration of minimal surfaces, their properties, and challenges in defining generalized minimal surfaces. Discusses smoothness, singularities, and behavior at singular points, reviewing classical works and recent results.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Alice Guionnet: Random Matrices, Free Probability and the Enumeration of Maps

Explore connections between random matrices, free probability, and map enumeration in this advanced mathematical lecture by renowned expert Alice Guionnet.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

The Hedgehog and the Fox

Explore mathematical problem-solving strategies through the lens of ancient Greek archetypes, examining diverse approaches to complex mathematical challenges.

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

Bernhard Schölkopf- From Statistical to Causal Learning

Explore the evolution of AI systems, from symbolic to statistical and causal approaches, examining key challenges in machine learning and the role of causality in advancing AI understanding and modeling.

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

Tameness in Geometry and Arithmetic: Beyond O-Minimality

Explore advanced concepts in geometry and arithmetic, focusing on tameness beyond o-minimality, with mathematicians Dmitry Novikov and Gal Binyamini.

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

Ofer Gabber- Bounding the Torsion in the L-adic Cohomology of Smooth Projective Varieties Without

Explore advanced mathematical concepts in l-adic cohomology, focusing on torsion bounds in smooth projective varieties, presented by renowned mathematician Ofer Gabber.

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

Gabriella Tarantello- On a Donaldson Functional for CMC-Immersions of Surfaces into Hyperbolic

Explore CMC-immersions of surfaces into hyperbolic spaces through a Donaldson functional approach, presented by mathematician Gabriella Tarantello.

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

The Formal Model of Semi-Infinite Flag Manifolds

Explore the formal model of semi-infinite flag manifolds as explicit algebro-geometric objects, examining recent developments in affine Lie algebra representation theory and discussing implications.

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