International Mathematical Union Courses

Lagrange Multiplier Functionals

Explore Lagrange multiplier functionals in mathematics and physics, focusing on Rabinowitz' action functional in symplectic geometry and its applications in string topology and closed geodesics.

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

Sausages and Butcher Paper

Explore geometric principles through everyday objects, unraveling complex mathematical concepts with accessible examples and innovative visualizations.

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

Homological Stability - A Tool for Computations

Explore homological stability as a powerful computational tool in mathematics, focusing on its applications and theoretical foundations.

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

Alexander Gamburd- Arithmetic and Dynamics on Varieties of Markoff Type

Explore arithmetic and dynamics on Markoff-type varieties with Alexander Gamburd, delving into mathematical concepts and their applications in this engaging lecture.

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

Olivier Wittenberg- Some Aspects of Rational Points and Rational Curves

Explore rational points and curves in algebraic geometry, examining their properties and connections to other mathematical concepts.

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

Dynamics of Dilute Gases: A Statistical Approach

Explore statistical approaches to understanding dilute gas dynamics with mathematician Laure Saint-Raymond in this insightful lecture on advanced mathematical physics concepts.

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

Nikolai Andreev - Leelavati Prize

Explore the mathematical contributions and educational impact of Nikolai Andreev, recipient of the prestigious Leelavati Prize for outstanding public outreach in mathematics.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Small Denominators and Multiplicative Jensen's Formula

Explore small denominators and multiplicative Jensen's formula in mathematical physics, delving into their applications and implications for quantum systems and dynamical models.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Larry Guth- Decoupling Estimates in Fourier Analysis

Explore recent developments in decoupling, a Fourier analysis technique with applications in harmonic analysis, PDE, and number theory. Survey key applications and proof concepts.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

On the Complexity of Quantum Many Body Systems

Explores recent advancements in representing and computing ground states of 1D quantum systems efficiently using concepts from quantum computation and information theory.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Craig B. Gentry: Homomorphic Encryption

Explore groundbreaking advancements in cryptography with Craig B. Gentry's lecture on homomorphic encryption, a revolutionary technique for secure data processing in untrusted environments.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Counting Lattice Points in Moduli Spaces of Quadratic Differentials

Explore lattice point counting in moduli spaces of quadratic differentials, examining applications in Masur-Veech volumes, geodesic multicurves, and meander enumeration.

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

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