Hausdorff Center for Mathematics Courses

Geometrically Exact Elastic Cosserat Models - Fundamentals and Analysis Part II

Delve into advanced geometrically exact elastic Cosserat models with fundamental theory and rigorous mathematical analysis techniques.

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

MCMC for Bayesian inference of the non-conducting region in intra-atrial reentrant tachycardia

Explore advanced MCMC methods for Bayesian inference in cardiac electrophysiology, focusing on estimating non-conducting regions in atrial tachycardia using personalized models.

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

Multilevel Monte Carlo Simulation of Diffusively Scaled Kinetic Equations

Explore multilevel Monte Carlo methods for simulating kinetic equations with multiscale behavior, combining asymptotic-preserving schemes to efficiently model particle dynamics.

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

Convergence Rates for Graph-Based Learning Featuring Singular PDEs

Explore convergence rates in graph-based learning through singular partial differential equations with mathematical rigor and advanced theoretical insights.

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

Multilevel Monte Carlo Methods for Comprehensive Uncertainty Quantification

Explore advanced Multilevel Monte Carlo methods for efficient uncertainty quantification, extending beyond mean estimation to capture variance, skewness, and distributional behavior.

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

Learning of Reduced Order Models Part II

Dive into advanced techniques for learning reduced order models in this mathematical framework exploration by Mario Ohlberger from Hausdorff Center.

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

Reduced Order Models for Efficient PDE-Constrained Optimization Problems - Part I

Discover reduced order modeling techniques to efficiently solve PDE-constrained optimization problems with computational cost reduction strategies.

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

Resolving Vortex Lattices in Type-II Superconductors with Multiscale Techniques

Explore advanced multiscale techniques for computing vortex lattices in superconductors using the Localized Orthogonal Decomposition method to overcome computational challenges.

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

Localised Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems

Explore the Localised Orthogonal Decomposition method for solving heterogeneous mixed-dimensional elliptic problems with optimal convergence and exponential error decay.

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

A Randomized Greedy Algorithm with Certification Over the Entire Parameter Set

Discover a randomized Greedy algorithm for constructing certified local approximation spaces for multiscale PDEs with high probability guarantees.

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

Toward Information Geometric Mechanics

Explore information geometric mechanics to solve shock wave problems in gas dynamics, avoiding numerical difficulties while preserving physical properties and enabling large-scale simulations.

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

Domain Decomposition Methods for Elastic Wave Propagation

Explore advanced numerical methods for solving elastic wave equations on Timoshenko beam networks using hybrid discontinuous Galerkin and Schwarz domain decomposition techniques.

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

Julia Robinson und die Grenzen der Mathematischen Beweiskraft

Entdecke die faszinierende Welt diophantischer Gleichungen und deren unlösbare Geheimnisse durch die Lebensgeschichten von Gödel, Turing und Julia Robinson.

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

Spectral Methods in Algebra, Geometry, and Topology

Explore advanced spectral methods across tensor triangular geometry, equivariant stable homotopy, representation theory, and chromatic homotopy theory.

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

Continuous Approaches to Discrete Optimization

Explore cutting-edge research connecting continuous optimization methods to discrete problems through expert talks on interior point methods, algorithms, and computational advances.

• YouTube
• 16 hours 4 minutes
• Self-Paced
• Free Video