Hausdorff Center for Mathematics Courses

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

Aspects of Convex, Nonconvex, and Geometric Optimization

Explore advanced optimization techniques in convex, nonconvex, and geometric contexts with expert insights on signal processing applications and mathematical foundations.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

Fundamentals of Optimization in Signal Processing

Explore essential optimization techniques for signal processing, including first-order methods, regularization, and stochastic gradient approaches, to solve complex problems efficiently.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Stephen Wright: Fundamentals of Optimization in Signal Processing

Explore key optimization techniques for signal processing, including first-order methods, regularization, stochastic gradient, and matrix optimization, with applications and algorithmic approaches.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Polynomial Approximation of Random PDEs by Discrete Least Squares with Observations

Polynomial approximation of random PDEs using discrete least squares with random point observations. Explores stability, error bounds, and optimal index set selection for metamodel construction in high-dimensional parameter spaces.

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