International Mathematical Union Courses

Hydrodynamic Stability at High Reynolds Number and Transition Threshold Problem

Explores hydrodynamic stability theory, focusing on laminar flow instability and turbulence transition at high Reynolds numbers. Discusses key physical effects and recent progress in linear inviscid damping and enhanced dissipation for shear flows.

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

Constraint Satisfaction Problem - What Makes the Problem Easy

Explore constraint satisfaction problems, their complexity, and variants. Learn about polynomial-time solvable cases and NP-complete instances in this mathematical deep dive.

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

Entropy in Mean Curvature Flow

Explore entropy in hypersurfaces and its role in mean curvature flow. Survey recent progress on conjectures about sharp lower bounds and extensions in geometric complexity.

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

Joel Kamnitzer- Perfect Bases in Representation Theory- Three Mountains and Their Springs

Exploration of perfect bases in representation theory, examining three approaches and their combinatorial implications for tensor product multiplicities in semisimple groups.

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

Graphons and Graphexes as Limits and Models of Large Sparse Graphs

Explore graphons and graphexes as mathematical tools for analyzing large sparse graphs, with applications in network science and complex systems modeling.

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

Reverse Mathematics from Multiple Points of View

Explore reverse mathematics through diverse perspectives, examining its foundations, applications, and implications for mathematical logic and computability theory.

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

Lieb-Thirring Inequalities: What We Know and What We Want to Know

Explore Lieb-Thirring inequalities, their applications in mathematical physics, PDEs, and functional analysis, and recent developments in harmonic analysis with orthonormal functions.

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

Finitary Analysis in Homogeneous Spaces

Explore finitary analysis in homogeneous spaces with Amir Mohammadi, delving into advanced mathematical concepts and their applications in this specialized field.

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

Scaling Limits and Universality of Ising and Dimer Models

Explore scaling limits and universality in statistical mechanics, focusing on non-planar Ising models and interacting dimers. Gain insights into critical phenomena and macroscopic behavior of interacting systems.

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

Brigitte Stenhouse, François Lê - ICHM Montucla Prize Lecture

Explore Mary Somerville's mathematical education and the historical development of the genus concept in algebraic geometry through two insightful lectures by prize-winning historians of mathematics.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Mean Curvature and Variational Theory

Explores recent developments in prescribing mean curvature equations, focusing on existence theory, min-max theory for CMC/PMC surfaces, and Morse theory for area functional. Includes solution to Multiplicity One Conjecture.

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

The Beauty of Braids - From Knot Invariants to Higher Categories

Explore the fascinating world of braids, knot invariants, and higher categories in mathematics with insights from renowned expert Catharina Stroppel.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

The Distribution of Values of Zeta and L-Functions

Explore the intricate world of zeta and L-functions, delving into their value distribution patterns and mathematical implications with renowned number theorist Kannan Soundararajan.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

CDC Panel – Online Cooperation

Exploring challenges and solutions for international mathematical cooperation during limited mobility, with focus on leveraging technology to support mathematicians in developing countries.

• YouTube
• 2 hours
• On-Demand
• Free Video

Lower Bounds on the Top Lyapunov Exponent of Stochastic Systems

Explore lower bounds on top Lyapunov exponents in stochastic systems, examining mathematical techniques and implications for understanding system behavior and stability.

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