The Monge-Ampère Equations and the Bergman Kernel - Lecture 1
Explore complex analysis in higher dimensions, focusing on Cauchy-Riemann equations, L2 theory, and applications to geometry. Learn about Bergman kernels and extension theorems in this advanced mathematics lecture.
Calderon Problem - Introduction and Historical Context - Lecture 1
Explore the Calderon problem in inverse theory, covering its history, dimensions, approaches, and solutions. Gain insights into this fundamental concept in partial differential equations.
Deep Learning and Computations of PDEs by Siddhartha Mishra
Explore deep learning applications in PDEs, uncertainty quantification, and optimization. Learn about operator learning, DeepOnet decomposition, and high-dimensional PDEs in this advanced lecture.
Statistical Inverse Problems and PDEs: Progress and Challenges
Explore statistical inverse problems and PDEs, covering Bayesian approaches, computational challenges, and mathematical guarantees for algorithms in high-dimensional settings.
Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids
Explores semi-Lagrangian discretisation of Monge-Ampère operator on P1 finite element spaces, discussing challenges and solutions for numerical methods in solving Monge-Ampère equations, with applications in inverse reflector problems.
Axel Målqvist - Localization of Multiscale Problems
Explore multiscale problem-solving techniques, focusing on Local Orthogonal Decomposition for PDEs. Learn about convergence, high-contrast data, and applications to time-dependent problems.
Solving the 4NLS with White Noise Initial Data
Explore white noise initial data in solving 4NLS, covering Hamiltonian PDE, globalization arguments, and limit equations. Gain insights into complex mathematical concepts and proofs.
Entropy Method for Hypocoercive BGK and Fokker-Planck Equations
Explore entropy methods for hypocoercive equations, focusing on BGK and Fokker-Planck models. Learn about decay rates, auxiliary functionals, and regularization techniques in non-symmetric systems.
Phase-Field Models for Motion by Mean Curvature - Lecture 2
Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.
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.
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.
Regularity of Free Boundaries in Obstacle Problems - Lecture III
Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.
Regularity of Free Boundaries in Obstacle Problems Lecture I
Explore regularity of free boundaries in obstacle problems, covering key concepts, proofs, and current research in this mathematical field of PDE and Geometric Measure Theory.
Panorama of Mathematics - Alfio Quarteroni
Explore reduced order models for solving partial differential equations, focusing on complexity reduction and efficient simulations in multiphysics problems.
Harmonic Maps Between Surfaces and Teichmüller Theory - Lecture 1
Explore harmonic maps between surfaces, their applications, and connections to Teichmüller theory in this advanced lecture on geometric analysis and complex geometry.
Geometry of PDEs
Explore the interplay between geometry and partial differential equations, examining optimal geometric structures, shape evolution, and their applications across science and mathematics.
Lieb-Thirring Inequalities: What We Know and What We Want to Know
Explore Lieb-Thirring inequalities, their applications in mathematical physics, PDEs, and functional analysis, and recent developments in harmonic analysis with orthonormal functions.
Patricia Gonçalves- On Hydrodynamic Limits of Fractional PDEs From Stochastic Interacting
Explores hydrodynamic limits of fractional PDEs derived from stochastic interacting particle systems, focusing on recent advances in scaling limit procedures and boundary conditions.
The Regularity Problem for the Laplace Equation in Rough Domains
Explores recent advances in Boundary Value Problems for the Laplace operator in rough domains, focusing on the equivalence between Dirichlet and regularity problem solvability.
Guido De Philippis - PDE Constrained Measures III
Explore advanced concepts in PDE-constrained measures with Guido De Philippis, delving into complex mathematical theories and applications in this advanced lecture.
Frequency Function Methods in PDE I
Explore frequency function methods in partial differential equations, focusing on applications and theoretical foundations for solving complex mathematical problems.