Optimal Transportation - Junior Trimester Program

Hausdorff Center for Mathematics via YouTube

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Explore advanced mathematical concepts through this comprehensive lecture series from the Junior Trimester Program on Optimal Transportation held at the Hausdorff Research Institute for Mathematics. Delve into cutting-edge research presentations covering variational modeling, gradient flows, large deviations, martingale optimal transport, and Ricci curvature bounds. Learn about diverse applications including the Mullins effect in filled rubber, many particle dynamics, multivariate quantile regression, and discrete Gaussian free fields. Examine theoretical frameworks such as the Weighted Energy Dissipation principle, Monge-Kantorovich approaches, and intrinsic flat convergence. Discover connections between optimal transport theory and quantum systems, Langevin samplers, and hyperbolic systems. Study specialized topics including the Vlasov-Fokker-Planck equation, zero range processes, Coulomb cost problems, and sticky particle dynamics. Gain insights into mathematical analysis techniques for boundary layers, variance reduction methods, and semi-infinite asymmetric exclusion processes. Access expert presentations on metric spaces, tangent structures, energy superdiffusion, and convex duality with transaction costs, providing a comprehensive overview of contemporary research in optimal transportation theory and its interdisciplinary applications.

Syllabus

Thomas Hudson: Explaining the Mullins effect in filled rubber
Marco Morandotti: Many particle dynamics via differential inclusions
Xiaolu Tan: On the martingale optimal transport duality in the Skorokhod space
Mark Peletier: Variational Modelling Energies, gradient flows and large deviations (part 1)
Guillaume Carlier: A Monge-Kantorovich approach to multivariate quantile regression
Yashar Memarian: A Brunn Minkowski type inequality on the sphere
Shouhei Honda: Elliptic PDEs on compact Ricci limit spaces and applications
Marek Biskup: Extreme points of two dimensional discrete Gaussian free field part 1
Jan Maas: Optimal transport methods for discrete and quantum systems (part 1)
Julian Tugaut: Exit time of a self stabilizing diffusion
Daniel Sutton: An effective description of Hamiltonian dynamics via the Maupertuis principle
Tony Lelievre: Entropy techniques for nonlinear partial differential equations a few examples
Giuseppe Savaré: The Weighted Energy Dissipation WED principle for gradient flows (part 3)
Patrick van Meurs: Analysis of a boundary layer in a discrete to continuum problem
William Minvielle: Variance reduction in random homogenization special quasirandom structures
Grigorios A Pavliotis: Accelerating convergence and reducing variance for Langevin samplers
Emanuel Milman: 1 D Localization part 1
Michiel Renger: The inverse problem from gradient flows to large deviations
Richard Kraaij: A Lagrangian formalism for large deviations of independent copies...
Mark Peletier: Variational Modelling Energies, gradient flows and large deviations part 3
Upanshu Sharma: Overdamped limit of the Vlasov Fokker Planck equation a variational approach
Marios G. Stamatakis: Hydrodynamic limits and condensing zero range processes
Nicola Gigli: Spaces with Ricci curvature bounded from below part 2
Gero Friesecke: Optimal transport with Coulomb cost
Christina Sormani: A Course on Intrinsic Flat Convergence part 1
Ali Üstünel: Some variational problems on the Wiener space and applications
Ionel Popescu: Free functional inequalities on the circle
Giuseppe Savaré: The Weighted Energy Dissipation WED principle for gradient flows (part 4)
Nicolas Juillet: Martingale transport problem and PCOCs
Nicola Gigli: Spaces with Ricci curvature bounded from below part 3
Johannes Zimmer: The semi infinte asymmetric exclusion process large deviations via matrix products
Marek Biskup: Extreme points of two dimensional discrete Gaussian free field (part 4)
Jan Maas: Optimal transport methods for discrete and quantum systems part 3
Marek Biskup: Extreme points of two dimensional discrete Gaussian free field part 2
Yan Dolinsky: Convex Duality with Transaction Costs
Giovanni Bonaschi: Quadratic and rate independent limits for a large deviations functional
Christina Sormani: A Course on Intrinsic Flat Convergence part 2
Julien Reygner: Multitype sticky particles and probabilistic solutions to hyperbolic systems...
Nicola Gigli: Spaces with Ricci curvature bounded from below part 4
Tapio Rajala: Tangents and dimensions of metric spaces
Gabriel Stoltz: Energy superdiffusion for systems with two conserved quantities
Christina Sormani: A Course on Intrinsic Flat Convergence part 3
Emanuel Milman: 1 D Localization part 4
Emanuel Milman: 1 D Localization part 3
Marek Biskup: Extreme points of two dimensional discrete Gaussian free field part 3
Christina Sormani: A Course on Intrinsic Flat Convergence part 5
Emanuel Milman: 1 D Localization part 5
Christina Sormani: A Course on Intrinsic Flat Convergence part 4