Kinetic Equations Courses and Certifications

PCS Institute for Basic Science

Dynamics of Oscillator Populations: Exact Finite-Dimensional Reduction and Beyond

Explore finite-dimensional reduction in oscillator populations, extending Ott-Antonsen theory. Learn about transients, circular cumulants, and transfer matrix methods for complex oscillator systems.

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

Hausdorff Center for Mathematics

Uncertainty Quantification for Kinetic Equations II

Explore uncertainty quantification for kinetic equations, focusing on Monte Carlo methods, multi-fidelity approaches, and stochastic Galerkin particle techniques to address high-dimensional challenges.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

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

Institut des Hautes Etudes Scientifiques (IHES)

Regularity Theory of Kinetic Equations with Rough Coefficients - Lecture 3

Delve into the extension of De Giorgi-Nash-Moser theory to hypoelliptic PDEs in kinetic theory, focusing on Kolmogorov equations with rough coefficients and connections to control theory and hypocoercivity.

• YouTube
• 2 hours 5 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Regularity Theory of Kinetic Equations with Rough Coefficients - Part 1

Delve into the extension of De Giorgi-Nash-Moser theory to hypoelliptic PDEs in kinetic theory, focusing on Kolmogorov equations with rough coefficients and connections to control theory and hypocoercivity.

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

Institut des Hautes Etudes Scientifiques (IHES)

Regularity Theory of Kinetic Equations with Rough Coefficients - Lecture 2

Delve into the extension of De Giorgi-Nash-Moser theory to hypoelliptic PDEs in kinetic theory, focusing on Kolmogorov equations with rough coefficients and connections to control theory and hypocoercivity.

• YouTube
• 2 hours 1 minute
• On-Demand
• Free Video

Hausdorff Center for Mathematics

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
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Scaling Limits and Effective Equations in Kinetic Theory I

Explores scaling limits and effective equations in kinetic theory, focusing on Boltzmann and Landau equations for rarefied gases and weakly interacting plasmas, discussing mathematical challenges in rigorous derivation.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

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
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Regularity Theory of Kinetic Equations with Rough Coefficients - Lecture 4

Delve into the extension of De Giorgi-Nash-Moser theory to hypoelliptic PDEs in kinetic theory, focusing on Kolmogorov equations with rough coefficients and connections to control theory and hypocoercivity.

• YouTube
• 2 hours 10 minutes
• On-Demand
• Free Video

Dublin Institute for Advanced Studies DIAS

Dynamics of Correlations and Kinetic Equations

Explore the mathematical foundations of correlation dynamics and their connection to kinetic equations in statistical mechanics and many-body systems.

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

Centre International de Rencontres Mathématiques

Numerical Methods, Uncertainty Quantification, and Optimal Transport Theory - CEMRACS 2022

Master advanced mathematical methods including kinetic equations, Schrödinger bridges, evolutionary adaptation models, and optimal transport theory through expert lectures.

• YouTube
• 15 hours 10 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Propagation of Chaos for Exotic Interactions

Explore alignment mechanisms in N-particle models with topological interactions, examining the kinetic equation's derivation and statistical independence in mean-field limits.

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

Hausdorff Center for Mathematics

Swarming Models with Local Alignment Effects

Explores phase transitions in kinetic equations for swarming models, focusing on noise-driven transitions and their applications in mathematical physics and interacting particle systems.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Non-equilibrium Fermi Polarons in Driven-Dissipative Systems

Explore non-equilibrium Fermi polarons in driven-dissipative systems, focusing on kinetic equations, relaxation, and non-equilibrium distributions in two-dimensional materials and ultracold atomic gases.

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