International Mathematical Union Courses

Polyhedral Techniques in Combinatorial Optimization: Matchings and Tours

Explore recent advancements in combinatorial optimization, focusing on matching and traveling salesman problems. Learn about polyhedral techniques and linear programming formulations for designing efficient algorithms.

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

The Hug of the Scutoid

Explore the fascinating world of scutoids, a newly discovered geometric shape, and their role in biology and mathematics with mathematician Clara Grima Ruiz.

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

Convergence of the Two-Point Form Factor Series in the 1+1 Dimensional Sinh-Gordon Model

Explores convergence of form factor series in 1+1D Sinh-Gordon model, developing techniques to prove convergence and estimate large-n behavior of n-fold integrals, advancing mathematical foundations of integrable quantum field theories.

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

Aravind Asok, Jean Fasel - Vector Bundles on Algebraic Varieties

Explore vector bundles on algebraic varieties with experts Aravind Asok and Jean Fasel, delving into advanced mathematical concepts and their applications in algebraic geometry.

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

Prony’s Method, Analytic Continuation, and Quantum Signal Processing

Explore Prony's method for signal analysis and its applications in analytic continuation and quantum signal processing, with insights from Lexing Ying.

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

On Mathematical Modeling in Image Reconstruction and Beyond

Explores connections between wavelet frame-based and PDE-based approaches in image reconstruction, linking to deep learning and computational imaging advancements.

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

Keith Ball- The Probabilistic Character of Convex Domains

Explore the probabilistic nature of convex domains with mathematician Keith Ball, delving into geometric concepts and their applications in probability theory.

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

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video