Hausdorff Center for Mathematics Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Antonio Esposito: Nonlinear Degenerate Cross Diffusion Systems with Nonlocal Interaction

Explores nonlinear degenerate cross-diffusion systems with nonlocal interaction, proving global existence of weak solutions using a semi-implicit JKO scheme for applications in social sciences, finance, and biology.

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

A Gradient Flow Approach to Kinetic Equations

Gradient flow approach to linear kinetic equations, exploring entropy dissipation inequality and large deviation principles. Discusses potential extensions to non-linear cases and connections to Markov chains.

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

Sobolev Regularity for Maximal Operators

Explore recent developments in regularity theory for maximal operators, focusing on Sobolev and BV data. Accessible overview of an active research area with open questions.

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

Alexander Volberg - Poincaré Inequalities on Hamming Cube - Analysis, Combinatorics, Probability

Explore improved L^1-Poincaré inequality constants on Hamming cube, comparing with Gaussian space. Discuss proofs, estimates, and related mathematical concepts in analysis, combinatorics, and probability theory.

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

Dyadic Representation Meets Operator-Valued Kernels

Exploración avanzada de la teoría de representación diádica y su aplicación a integrales singulares biparamétricas, combinando ideas de Journé con nuevos enfoques en kernels con valores de operador.

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