Hausdorff Center for Mathematics Courses

Fluctuations in Stochastic Homogenization

Explore fluctuations in stochastic homogenization, focusing on the homogenization commutator and its role in driving path-wise fluctuations of key quantities in the field.

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

A Family of Crouzeix-Raviart Non-Conforming Finite Elements in Two- and Three Spatial Dimensions

Explore non-conforming finite elements in 2D and 3D, focusing on Crouzeix-Raviart type. Learn about optimal a priori estimates, jump conditions, and explicit representations of local basis functions.

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

Homogenization Methods for Weakly Compressible Elastic Materials Forward and...

Explore homogenization methods for weakly compressible elastic materials, focusing on modeling, effective elasticity tensors, and estimating tissue porosity using mechanical responses.

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

Nonlocal Theories for Free Crack Propagation in Brittle Materials - Lecture 2

Explores mathematical upscaling of nonlocal fracture models, focusing on weak convergence, compactness, and Gamma-convergence for bridging mesoscopic and macroscopic scales in brittle material dynamics.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video

Convergence Theory of Adaptive Finite Element Methods

Explore the convergence theory of adaptive finite element methods for elliptic PDEs, including approximation classes and optimal convergence rates.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Adaptive Numerical Solution Methods for PDEs

Explore adaptive methods for PDEs, including error estimation, vertex bisection, and finite element techniques, enhancing numerical solutions for complex mathematical problems.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Adaptive Wavelet Methods and Applications

Explore adaptive wavelet methods for solving complex PDEs, including tensor product approximation and reformulation techniques for optimal solutions in various domains.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Winfried Scharlau: Die fünfziger Jahre - eine Zeit des Aufbruchs (Mathematischer Salon)

Einblick in die mathematische Entwicklung der 1950er Jahre: Eine Ära des Fortschritts und der Innovation in der Wissenschaft nach dem Zweiten Weltkrieg.

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

Introduction to Higher Grothendieck Witt Groups

Explore advanced algebraic topology concepts with a focus on Higher Grothendieck Witt groups in this comprehensive lecture by Marco Schlichting.

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

The 2-Completion of L-Theory for C-Algebras

Explores the relationship between algebraic K-theory and L-theory for C*-algebras, focusing on C2-actions, Tate constructions, and 2-completions in topological K-theory.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

On Density of Sobolev Functions on Euclidean Domains

Explore recent findings on Sobolev space density, removability of measure zero sets, and extension operators in Euclidean domains. Gain insights into advanced mathematical concepts and their applications.

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

New Stability Results for Sequences of Metric Measure Spaces With Uniform Ricci Bounds

Explore new stability results for metric measure spaces with uniform Ricci bounds, including applications to Cheeger's isoperimetric constants and an almost suspension theorem.

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

Matthias Liero- On Entropy Transport Problems and the Hellinger Kantorovich Distance

Explores entropy-transport minimization problems, introducing the Hellinger-Kantorovich distance as an interpolation between Hellinger and Kantorovich-Wasserstein distances, with applications in dynamic processes involving mass creation/annihilation.

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

Yoann Dabrowski- Free Entropy and a Laplace Principle for Hermitian Brownian Motion

Explores Voiculescu's free entropy, ultraproducts, continuous model theory, and free stochastic differential equations, with implications for Connes embedding conjecture.

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

Operator Algebras of Locally Compact Groups Acting on Trees

Explore C*-simplicity in locally compact groups, focusing on tree actions. Covers reduced group C*-algebras, examples of C*-simple groups, and the type I conjecture for Aut(T) subgroups.

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