International Mathematical Union Courses

Kathryn Mann- Groups Acting at Infinity

Explore rigidity in group actions, lattices, and infinity, with applications to surface groups, boundaries, and Anosov flows. Gain insights into mathematical concepts and their interconnections.

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

Aaron Brown- Lattice Subgroups Acting on Manifolds

Explore lattice subgroups' actions on manifolds, covering definitions, theorems, and Zimmer's conjecture. Gain insights into isometric and projective actions, standard modifications, and ongoing research.

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

Gradient Descent on Infinitely Wide Neural Networks - Global Convergence and

Explore gradient descent on infinitely wide neural networks, examining global convergence and optimization techniques for non-convex problems in machine learning.

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

Jan Philip Solovej: The Ground State of Quantum Gases

Explore quantum gases' ground state, thermodynamic limits, and Bogolubov approximation in this mathematical physics lecture, bridging theory and experimental verification.

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

Restricted Extremal Problems in Hypergraphs

Exploration of extremal problems in 3-uniform hypergraphs, focusing on restricted variants motivated by quasirandom hypergraphs. Discusses recent progress and a unifying framework for these challenging mathematical problems.

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

The Arithmetic of Quadratic Twists of Elliptic Curves

Explore quadratic twists of elliptic curves, Selmer groups, and L-values. Delve into the congruent number problem and progress on the BSD conjecture. Gain insights into advanced number theory concepts.

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

Ronen Eldan- Revealing the Simplicity of High-Dimensional Objects via Pathwise Analysis

Explore high-dimensional geometry through pathwise analysis, revealing simple structures in complex spaces and their applications in probability theory and statistical physics.

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

Isabella Novik - Face Numbers - The Upper Bound Side of the Story

Explore face numbers in simplicial polytopes and sphere triangulations, examining upper bounds, maximizers, and central symmetry implications. Recent developments and open problems are discussed.

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

Stable Homotopy Groups of Spheres and Motivic Homotopy Theory

Survey of stable homotopy groups of spheres computation, covering classical methods, Mahowald's Uncertainty Principles, and new techniques using motivic homotopy theory. Includes recent computations and future research directions.

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

Weingarten Calculus and Its Applications

Explore Weingarten calculus and its applications in compact groups, quantum probability, and random matrix theory, with insights on theoretical properties and recent developments.

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

Tamas Hausel - Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems

Explore enhanced mirror symmetry for Langlands dual Hitchin systems, covering topics from SYZ mirror symmetry to equivariant cohomology and Kirillov algebras.

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

Numerical Stability of Algorithms at Extreme Scale and Low Precisions

Explore numerical stability in extreme-scale computing and low-precision arithmetic, focusing on error bounds, blocked algorithms, and probabilistic analysis for matrix computations.

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

Tianyi Zheng- Asymptotic Behaviors of Random Walks on Countable Groups

Explore asymptotic behaviors of random walks on countable groups, covering Kesten's theorems, entropy, and applications to group theory and graph analysis.

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

Fractal Uncertainty Principle and Quantum Chaos

Explore quantum chaos and fractal uncertainty principle in wave equations, with applications to eigenfunctions, Schrödinger equation, and hyperbolic surfaces. Gain insights beyond classical/quantum correspondence.

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

New Trends in Nonlinear Optimization

Explore new trends in nonlinear optimization, including gradient methods, quasi-Newton techniques, and approaches for constrained problems, with a focus on recent developments and efficient algorithms.

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