Hausdorff Center for Mathematics Courses

Comparing the Baum-Connes Conjecture and the Farrell-Jones Conjecture

Vergleich der Baum-Connes-Vermutung und der Farrell-Jones-Vermutung in der algebraischen und geometrischen Topologie, mit Fokus auf Gemeinsamkeiten und Unterschiede.

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

Spectral Truncations of Low-Dimensional Tori

Explore spectral truncations of low-dimensional tori, delving into advanced mathematical concepts and their applications in topology and geometry.

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

Rearrangement Lemma, Divided Differences & Multivariate Holomorphic Functional Calculus

Explore advanced mathematical concepts including rearrangement lemma, divided differences, and multivariate holomorphic functional calculus in this in-depth lecture.

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

Michael Baake - A Cocycle Approach to the Fourier Transform of Rauzy Fractals

Explore Fourier transforms of Rauzy fractals and their role in analyzing spectra of Pisot inflation tilings, with applications to diffraction theory and dynamical systems.

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

Manfred Einsiedler- Effective Homogenous Dynamics 1

Explore homogeneous dynamics, focusing on transformations, orbits, and effective statements in topology and number theory.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

High Mode Transport Noise Improves Vorticity Blow Up Control in 3D

Explores regularizing effects of transport noise on 3D Navier-Stokes equations, demonstrating improved vorticity control and well-posedness under specific noise conditions.

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

Rough Perturbations of the Navier Stokes System

Explore rough perturbations of Navier-Stokes equations, focusing on solution definitions, well-posedness, and physical relevance in terms of conserved quantities.

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

Sylvie Paycha: Re-Expansion Maps as Direct Connections

Explore re-expansion maps in groupoids, their connection to regularity structures, and interpretation as "gaugeoid fields" in gauge groupoids. Generalization to jet bundles in polynomial regularity structures.

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

Convergence in Hölder and Sobolev Norms for Galerkin Approximations of Generalized Whittle-Matern Fields

Optimal convergence rates for Galerkin approximations of generalized Whittle-Matern fields in Hölder and Sobolev norms, covering spectral and finite element methods for Gaussian random fields.

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

Martin Hairer: Stochastic Quantisation of Non-Abelian Yang-Mills

Explore stochastic quantisation of Yang-Mills theory, covering key concepts like canonical sections, connections, and covariant derivatives in non-Abelian gauge theories.

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

The Dynamical Systems Approach to Spatially Homogenous Einstein-Vlasov Cosmology

Explore spatially homogenous Einstein-Vlasov cosmology using dynamical systems analysis. Investigate asymptotic solutions near singularities and expanding futures, focusing on Kantowski-Sachs models with Vlasov matter.

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

Chiara Saffirio - From the Many-Body Quantum Dynamics to the Vlasov Equation

Exploring quantum dynamics to Vlasov equation: from many-body systems to kinetic theory, covering mean-field limits, semiclassical approaches, and convergence rates for interacting fermions.

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

Deterministic Solution of the Boltzmann Equation - Fast Spectral Methods

Explore fast Fourier spectral methods for solving the Boltzmann equation, addressing computational challenges and showcasing applications in rarefied gas dynamics.

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

Uncertainty Quantification for Kinetic Equations I

Overview of uncertainty quantification for kinetic equations, covering Monte Carlo methods, multi-fidelity techniques, and stochastic Galerkin particle methods. Explores computational challenges and recent advancements in the field.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Variational and Jump Inequalities

Explore variational and jump norms in mathematical analysis, covering applications in rough paths, singular integrals, and ergodic theory. Gain insights into endpoint results and their proofs.

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