International Mathematical Union Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Polyhedral Techniques in Combinatorial Optimization: Matchings and Tours

Explore recent advancements in combinatorial optimization, focusing on matching and traveling salesman problems. Learn about polyhedral techniques and linear programming formulations for designing efficient algorithms.

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

The Hug of the Scutoid

Explore the fascinating world of scutoids, a newly discovered geometric shape, and their role in biology and mathematics with mathematician Clara Grima Ruiz.

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

Convergence of the Two-Point Form Factor Series in the 1+1 Dimensional Sinh-Gordon Model

Explores convergence of form factor series in 1+1D Sinh-Gordon model, developing techniques to prove convergence and estimate large-n behavior of n-fold integrals, advancing mathematical foundations of integrable quantum field theories.

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

Aravind Asok, Jean Fasel - Vector Bundles on Algebraic Varieties

Explore vector bundles on algebraic varieties with experts Aravind Asok and Jean Fasel, delving into advanced mathematical concepts and their applications in algebraic geometry.

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

Prony’s Method, Analytic Continuation, and Quantum Signal Processing

Explore Prony's method for signal analysis and its applications in analytic continuation and quantum signal processing, with insights from Lexing Ying.

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

On Mathematical Modeling in Image Reconstruction and Beyond

Explores connections between wavelet frame-based and PDE-based approaches in image reconstruction, linking to deep learning and computational imaging advancements.

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

Keith Ball- The Probabilistic Character of Convex Domains

Explore the probabilistic nature of convex domains with mathematician Keith Ball, delving into geometric concepts and their applications in probability theory.

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