Hausdorff Center for Mathematics Courses

Numerical Homogenization Based Fast Solver for Multiscale PDEs

Explore numerical homogenization for multiscale PDEs, covering Bayesian approaches, exponential decaying bases, and efficient solvers. Learn about applications in geophysics, materials science, and biology.

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

Nonlocal Theories for Free Crack Propagation in Brittle Materials

Explora la teoría y modelado de la fractura dinámica en sólidos frágiles, desde enfoques clásicos hasta modelos no locales multiescala, abordando desafíos computacionales y simulaciones peridinámica.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• Free Video

The Slices of Hermitian K-Theory

Explore Hermitian K-theory's slices, their construction, and applications in algebraic geometry. Gain insights into Milnor's conjecture on quadratic forms through this advanced mathematical lecture.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Ricci Curvature and Functional Inequalities for Interacting Particle Systems

Explore entropic Ricci curvature bounds and their applications to interacting particle systems, focusing on functional inequalities and convergence rates to equilibrium in nonnegative curvature scenarios.

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

Drinfeld Center, Tube Algebra, and Representation Theory of Monoidal Categories

Explore connections between category theory, subfactor theory, and quantum groups. Learn about Drinfeld center, tube algebra, and representation theory of monoidal categories.

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

Mathematics of Signal Design for Communication Systems and Szemerédi’s and Green-Tao’s Theorems

Explore signal design for communication systems, focusing on orthogonal transmission schemes and their dynamics. Delve into mathematical connections with functional analysis and additive combinatorics.

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

Hans Feichtinger- Fourier Analysis via the Banach Gelfand Triple

Explore Gabor analysis foundations using MATLAB, focusing on finite Abelian groups and matrix analysis methods. Learn to apply abstract harmonic analysis concepts to signal processing problems.

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

Gabor Analysis and Its Mysteries

Einführung in die Gabor-Analyse: Grundlagen, Anwendungen und mathematische Konzepte für Signalverarbeitung, Quantenmechanik und Kommunikationstechnik.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Stephen Wright: Fundamentals of Optimization in Signal Processing

Explore optimization in signal processing, covering first-order methods, regularization, and advanced algorithms. Gain insights into matrix optimization and parallel implementations for solving complex problems.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Large Scale Machine Learning and Convex Optimization - Lecture 3

Explore advanced stochastic optimization techniques for large-scale machine learning, including novel Newton-based methods and combinations of batch and online algorithms for improved convergence rates.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Cut Generating Functions

Explore cut generating functions in mixed integer programming, focusing on subadditive functions, their properties, and applications in deriving cutting planes. New results and open questions discussed.

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

A Market for Scheduling, with Applications to Cloud Computing

Explore a novel market model for resource allocation and scheduling, with applications to cloud computing. Learn about equilibrium computation and its challenges in this unique marketplace.

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

Edith Elkind- Coalitional Games on Sparse Social Networks

Explore coalitional games on social networks, analyzing graph structures, computational complexity, and solution concepts for connected subsets of agents.

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

Panorama of Mathematics - Clusters, Loops and Trees in the Ising Model

Explore clusters, loops, and trees in the Ising model with Fields Medalist Stanislav Smirnov, covering topics from conformal field theory to discrete complex analysis and random cost representation.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Panorama of Mathematics - Alfio Quarteroni

Explore reduced order models for solving partial differential equations, focusing on complexity reduction and efficient simulations in multiphysics problems.

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