Kinetic Theory - Junior Trimester Program

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Explore advanced kinetic theory through this comprehensive lecture series from the Hausdorff Center for Mathematics' Junior Trimester Program. Delve into cutting-edge research spanning indirect diffusion effects, mean field limits of particle systems, gradient flow approaches to kinetic equations, and hypocoercivity for linear kinetic equations. Master scaling limits and effective equations in kinetic theory through detailed presentations by Mario Pulvirenti, while examining uncertainty quantification methods with Lorenzo Pareschi. Investigate the coupling of kinetic and fluid equations in spray theory, kinetic modeling of social phenomena, and Boltzmann-type equations in socio-economic applications. Study numerical methods including fast spectral approaches for the Boltzmann equation, asymptotic-preserving schemes, and micro-macro discretizations. Analyze specialized topics such as the Vlasov-Poisson-Boltzmann system, quantum dynamics with band-crossing, multi-species kinetic models, and the derivation of fundamental equations like the Vlasov equation. Examine applications ranging from traffic flow control and particle suspensions to Bose-Einstein condensates and fermionic systems in the mean-field regime. Learn about spectral gaps, entropy production, hydrodynamic limits, and the mathematical foundations connecting microscopic particle interactions to macroscopic behavior through presentations by leading experts in mathematical physics and kinetic theory.

Syllabus

Bao Quoc Tang: Indirect diffusion effect and convergence to equilibrium
Li Chen: Mean field limit of many particle system with non Lipschitz force
Giada Basile: A gradient flow approach to kinetic equations
Josephine Evans: Using Harris’s theorem to prove hypocoercivity for linear kinetic equations with..
Matias Delgadino: Mean ﬁeld limit by Gamma convergence
Martin Burger: Propagation of gradient ﬂow structures from microscopic to macroscopic models
Antonio Esposito: Nonlinear degenerate cross diﬀusion systems with nonlocal interaction
Amit Einav: Weak Poincaré inequalities in the absence of spectral gaps
Hagop Tossounian: On Kac’s model, ideal Thermostats, and finite Reservoirs
Giambattista Giacomin: Interacting diffusions on random graphs and PDE limits
Joaquin Fontbona: Quantitative uniform propagation of chaos for Maxwell molecules
Mario Pulvirenti: A local mean-field stochastic particle system for the Bolzmann equation
Simone Fagioli: Solutions to aggregation
A. Eberle: Couplings & converg. to equilibrium f. Langevin dyn. & Hamiltonian Monte Carlo methods
Franca Hoffmann: Reversed Hardy Littlewood Sobolev Inequalities
Lecture Lorenzo Pareschi: Uncertainty quantification for kinetic equations II
Lecture Lorenzo Pareschi: Uncertainty quantification for kinetic equations III
Lecture Lorenzo Pareschi: Uncertainty quantification for kinetic equations I
Talk Axel Klar: Asymptotic methods for kinetic and hyperbolic evolution problems on
Talk Jani Lukkarinen: Kinetic theory of lattice waves
Talk Christian Schmeiser: Decay to equilibrium of diffusive and kinetic transport
Talk Thomas Rey: Projective integration of collisional kinetic equations
Lecture Mario Pulvirenti: Scaling limits and eﬀective equations in kinetic theory III
Lecture Mario Pulvirenti: Scaling limits and exective equations in kinetic theory II
Lecture Mario Pulvirenti: Scaling limits and effective equations in kinetic theory I
Talk Jingwei Hu: Deterministic solution of the Boltzmann equation Fast spectral methods
Talk Andrea Tosin: Kinetic modelling of traffic flow control
Lecture Laurent Desvillettes: Coupling kinetic and fluid equations in the theory of sprays I
Lecture Laurent Desvillettes: Coupling kinetic and fluid equations in the theory of sprays II
Lecture Laurent Desvillettes: Coupling kinetic and fluid equations in the theory of sprays III
Lipschitz Lecture III: Kinetic limit for classical particle and waves
Talk Jose Antonio Carrillo: Swarming models with local alignment effects
Ludovic Cesbron: A fractional Fick Law method for diffusion limits of kinetic equations
Karel Pravda-Starov: Sufficient geometric conditions for the null-controllability of evolution...
Arnaud Münch: Asymptotic and null controllability of an advection-diffusion equation
Talk Bertrand Maury: Accounting for congestion in finite size particle systems micro macro issues
Lecture Giuseppe Toscani: Kinetic theory of social phenomena II
Lecture Giuseppe Toscani: Kinetic theory of social phenomena III
Lecture Giuseppe Toscani: Kinetic theory of social phenomena I
Lecture Marie Therese Wolfram: On Boltzmann type equations in socio economic applications
Talk Raphael Winter: From interacting particle systems with long range to kinetic equations
Carlos Castro: Numerical approximation of the decay rate for some dissipative systems
Helge Dietert: Trend to equilibrium for a spatially degenerate kinetic Fokker-Planck equation
Maxime Breden: On the equilibria of Boltzmann like kinetic equations
Frédéric Hérau: A Korn Wirtinger inequality
Donghyun Lee: Vlasov Poisson Boltzmann equation in bounded domains
Miguel Rodrigues: Large magnetic field regimes and asymptotic preserving schemes
Laurent Lafleche: Fractional Hypocoercitivity
Anais Crestetto: Micro-macro discretizations
Havva Yoldas: Harris's Theorem and its applications to some kinetic and biological models
Ning Jiang: Vlasov-Maxwell-Boltzmann system
Liu Liu: Micro-macro decomposition based asymptotic-preserving numerical schemes
Maxime Herda: Asymptotic behaviors of the Vlasov-Poisson-Fokker-Planck equation
Chiara Saffirio: From the many-body quantum dynamics to the Vlasov equation
Pierre Monmarche: Bouncing with velocity jump process
Gernot Heißel: The dynamical systems approach to spatially homogenous Einstein-Vlasov cosmology
Erica Belen De La Canal: L^p estimates for the solution of the system of Boltzmann equations
Marina Ferreira: Multicomponent coagulation equation for aerosol dynamics
Alexander Bobylev: On BGK models for gas mixtures
Shi Jin: Semiclassical computational methods for quantum dynamics with band-crossing and uncertainty
Christian Klingenberg: On a multi-species kinetic model of plasma, theory and numerics
Alessia Nota: Homoenergetic Solutions for the Boltzmann Equation
Laurent Boudin: Stability of the spectral gap for the Boltzmann multi-species operator
Lipschitz Lecture IV: Kinetic limit for particles interacting through a short range potential
Francis Filbet: Asymptotics of the three dimensional Vlasov equation in...
Laurent Desvillettes: From Boltzmann equations for mixtures towards thin spray equations
Richard Höfer: On the sedimentation of particle suspensions in Stokes flows
Jens Marklof: Kinetic transport in the Lorentz gas classical and quantum
Robert M. Strain: Global mild solutions of the Landau and non cutoff Boltzmann equation
Herbert Spohn: Hydrodynamics of the classical Toda chain
Maria Carvalho: Spectral Gaps and Entropy Production...
Mario Pulvirenti: Propagation of chaos for exotic interactions
Robert Patterson: Interaction Clusters for the Kac Process
Alexander Bobylev: On some properties of Vlasov-Poisson-Landau kinetic equations
Benjamin Schlein: Excitation spectrum and time evolution of Bose-Einstein condensates
Miguel Escobedo Martínez: Some remarks on the three waves collision integral+condensate
Marcello Porta: On the correlation energy of interacting fermionic systems in the mean-field regime
Peter Pickl: Derivation of the Vlasov equation
Irene M. Gamba: Multi component gas system models: The billiard mixing for mixtures
Marianne B. C.: Hypocoercivity & diﬀusion limit of a ﬁnite volume scheme for linear kinetic eq.