International Mathematical Union Courses

Algebraic-Geometrical Methods in the Theory of Integrable Systems

Explore algebraic-geometrical methods in integrable systems theory with renowned mathematician Igor Krichever, delving into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

ICHM May Prize Lectures

Explore ancient mathematics through cuneiform fragments and the sociocultural contexts of mathematical sciences in Islamicate societies. Gain insights into historical mathematical education and scholarly practices.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

What Is a Random Surface?

Explore the theory of random surfaces, from finite triangles to complex mathematical constructs. Discover connections to physics, probability, and geometry through accessible explanations and visual illustrations.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Geometry of PDEs

Explore the interplay between geometry and partial differential equations, examining optimal geometric structures, shape evolution, and their applications across science and mathematics.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Groups Acting on Hyperbolic Spaces - A Survey

Explore group actions on hyperbolic spaces with Mladen Bestvina in this comprehensive survey, covering key concepts, recent developments, and applications in geometric group theory.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Thermodynamic Formalism for Dispersing Billiards

Explores mathematical billiards in statistical mechanics, focusing on dispersing billiards. Discusses equilibrium states, geometric potentials, and spectral analysis, with insights into SRB measures and maximal entropy.

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

Arithmetic and Geometric Langlands Program

Explore the intricate connections between arithmetic and geometry in the Langlands program, a groundbreaking mathematical framework unifying number theory and representation theory.

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

Michael Loss - The Kac Model - Variations on a Theme

Explore the Kac Model and its variations in mathematical physics, delving into theoretical concepts and practical applications in statistical mechanics.

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

Modern Regularization Methods in Inverse Problems and Data Science

Explores recent developments in variational methods for inverse problems and machine learning, discussing convergent regularization schemes, quantitative estimates, and connections between classical regularization theory and risk minimization.

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

Emergent Complex Geometry and the Gauge/Gravity Duality

Explore emergent complex geometry and gauge/gravity duality with mathematician Robert Berman in this insightful lecture on cutting-edge mathematical physics concepts.

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

Developments in 3D Ricci Flow Since Perelman

Explore recent advancements in 3D Ricci flow theory post-Perelman, delving into mathematical breakthroughs and their implications for geometric topology and differential geometry.

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

Points on Shimura Varieties Modulo Primes

Explore the intricacies of Shimura varieties modulo primes, delving into advanced mathematical concepts and their applications in number theory and algebraic geometry.

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

The Geometry of Geometries - Matroid Theory, Old and New

Explore matroid theory's origins, connections, and recent geometric advances in combinatorial mathematics, highlighting matroid polytope, Bergman fan, and conormal fan models.

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

Wall-Crossing in Algebraic Geometry

Explore applications of Bridgeland stability conditions and wall-crossing techniques in algebraic geometry, advancing understanding of complex mathematical structures.

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

Dimitris Koukoulopoulos: Rational Approximations of Irrational Numbers

Explore rational approximations of irrational numbers with Dimitris Koukoulopoulos, delving into mathematical concepts and techniques for understanding these complex relationships.

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