International Mathematical Union Courses

A Mathematical Perspective on Machine Learning

Explore deep learning's impact on AI and science, its theoretical foundations, and its potential for solving high-dimensional problems in scientific computing and beyond.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

The Horocycle Flow on the Moduli Space of Translation Surfaces

Explore the intricate dynamics of horocycle flows on translation surface moduli spaces, delving into mathematical concepts and their applications in geometry and dynamical systems.

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

The Master Equation for Mean Field Games

Explore the mathematical foundations of mean field games and their master equation, delving into advanced concepts and applications in game theory and optimization.

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

Xiaohua Zhu - Kähler-Ricci Flow on Fano Manifolds

Explore the Kähler-Ricci flow on Fano manifolds, delving into complex geometry and differential equations. Gain insights into this advanced mathematical topic through expert analysis and explanations.

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

The Cohomology of Shimura Varieties with Torsion Coefficients and Applications

Explore Shimura varieties' cohomology with torsion coefficients and its applications in advanced mathematics, presented by Ana Caraiani.

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

Graphs of Large Chromatic Number

Explore the fascinating world of graph theory, focusing on graphs with high chromatic numbers and their intriguing properties in this engaging mathematical lecture.

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

Formation of Singularities in Nonlinear Dispersive PDEs

Explore the formation of singularities in nonlinear dispersive partial differential equations with mathematician Galina Perelman in this insightful lecture on advanced mathematical concepts.

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

Gapped Quantum Systems

Explore gapped quantum systems with Matthew Hastings, delving into advanced mathematical concepts and their applications in quantum physics and information theory.

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

Raphaël Beuzart-Plessis- Relative Trace Formulae and the Gan-Gross-Prasad Conjectures

Explore relative trace formulae and their application to the Gan-Gross-Prasad conjectures in advanced number theory and representation theory.

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

Elchanan Mossel: Combinatorial Statistics and the Sciences

Explore the intersection of combinatorial statistics and scientific applications with insights from renowned mathematician Elchanan Mossel in this thought-provoking lecture.

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

The Horocycle Flow on the Moduli Space of Translation Surfaces

Explore the intricate dynamics of horocycle flows on translation surface moduli spaces, delving into mathematical concepts and their applications in geometry and dynamical systems.

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

Marie-France Vignéras- Modular Representations of P-Adic Groups

Explore modular representations of p-adic groups in the Langlands program, examining their connections to number theory and geometry using various vector spaces and modules.

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

30 Years of Modularity - Number Theory Since the Proof of Fermat's Last Theorem

Explore advancements in number theory since Fermat's Last Theorem, focusing on modularity and its impact on mathematical research over the past three decades.

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

Homological Algebraic Geometry

Explore semiorthogonal decompositions in algebraic geometry, including their properties, geometric significance, and novel applications in categorical constructions and singularity resolutions.

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

Michel van den Bergh- Noncommutative Crepant Resolutions

Explore noncommutative crepant resolutions in algebraic geometry with Michel van den Bergh, delving into advanced mathematical concepts and their applications.

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