Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 3
Explore geometric measure theory and optimal transport with a focus on Monge-Ampère equations and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio.
Endpoint Fourier Restriction and Unrectifiability
Explore endpoint Fourier restriction and its connection to measure unrectifiability in R^d, featuring a dichotomy between absolute continuity and 1-pure unrectifiability.
Weighted Fourier Extension Estimates and Applications
Explore weighted Fourier extension estimates and their applications in PDEs and geometric measure theory, covering topics like Fourier restriction, SME, and Falconer's distance set problem.
Exploring Variational Functions - Calculus of Variations and Geometric Measure Theory
Dive into variational problems and bounded Hessian functions with Luigi Ambrosio. Explore the intersection of Calculus of Variations and Geometric Measure Theory, inspired by machine learning insights.
Harmonic Analysis Techniques for -Almost- Minimizers
Explore harmonic analysis techniques for (almost-)minimizers, focusing on free boundary theory and calculus of variations. Learn about applications to geometric measure theory and domain geometry.
Bala Krishnamoorthy: Linear Programming in Geometric Measure Theory
Explore geometric measure theory through linear programming, examining integral currents, simplicial flat norm, and polyhedral approximation. Discover applications in median shape analysis.
Regularity Theory for Area-Minimizing Currents
Explore advanced concepts in geometric measure theory, including zero forms, currents, and rectifiability theorems, with applications to area-minimizing problems in mathematics.
Regularity Theory for Area-Minimizing Currents
Explore advanced concepts in geometric measure theory, including currents, boundaries, and regularity theory for area-minimizing surfaces, with applications to optimal transport problems.
Existence and Regularity Theories of Brakke Flow
Explore existence and regularity theories of Brakke flow, covering initial configuration, linear and alpha regularity, dispersed irregularity, and the Monotonicity Formula for minimal surfaces.
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.
The Restriction Problem and the Polynomial Method - Lecture I
Explore Stein's restriction conjecture, the Kakeya conjecture, and the polynomial method in harmonic analysis. Learn about wave packet decomposition and its applications in studying hypersurface-supported functions.
Steve Hofmann - Quantitative Rectiability, and Harmonic and Caloric Measure III
Explore advanced mathematical concepts in quantitative rectifiability and measure theory, focusing on harmonic and caloric measures in complex analytical settings.
Intrinsic Volumes on Pseudo-Riemannian Manifolds
Explore intrinsic volumes in pseudo-Riemannian geometry, covering Hadwiger's theorem, Weyl's principle, and Crofton formulas. Learn about recent developments in this advanced mathematical field.
Gaussian Isoperimetry and Related Topics III
Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.
Gaussian Isoperimetry and Related Topics II
Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.
Regularity of Free Boundaries in Obstacle Problems - Lecture IV
Explore advanced concepts in free boundary problems, focusing on regularity in obstacle problems. Learn key results, current research, and open challenges in this mathematical field.
Regularity of Free Boundaries in Obstacle Problems - Lecture II
Explore free boundary problems in PDE, focusing on regularity in obstacle problems. Learn key results, current research, and open questions in this mathematical field.
Regularity Theory for Area-Minimizing Currents - Lecture 5
Explore advanced concepts in geometric measure theory, focusing on regularity theory for area-minimizing currents. Gain insights from experts De Lellis and Spadaro in this in-depth lecture.
Existence and Regularity Theories of Brakke Flow - Lecture 4
Explore advanced theories of Brakke flow, focusing on existence and regularity aspects in this in-depth lecture by Yoshihiro Tonegawa from Tokyo Institute of Technology.
Gaussian Isoperimetry and Related Topics I
Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof techniques using geometric measure theory.