Generalizations of the Bernstein Problem
Dive into Otis Chodosh's exploration of the Bernstein Problem's generalizations, examining minimal surface equations and their connections to higher dimensions.
Fluid Equations - Regularity and Kolmogorov’s Turbulence Theory
Explore fluid dynamics, Navier-Stokes equations, and Kolmogorov's turbulence theory. Gain insights into regularity results and mathematical confirmations of phenomenological theories.
The Regularity Problem for the Landau Equation
Explore the intricacies of the Landau equation's regularity problem with François Golse, delving into advanced mathematical concepts and their applications.
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.
Sobolev Regularity for Maximal Operators
Explore recent developments in regularity theory for maximal operators, focusing on Sobolev and BV data. Accessible overview of an active research area with open questions.
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.
Partial Differential Equations - Lecture 22
Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in various scientific fields.
Partial Differential Equations - Lecture 16
Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
Partial Differential Equations - Lecture 10
Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
Edgard Pimentel - Regularity Theory for Nonlinear PDEs
Explore recent developments in regularity theory for nonlinear PDEs, covering compactness, stability, and scaling arguments. Learn about fully nonlinear PDEs, Isaacs equation, and free boundary problems.
On the Regularity Implied by the Assumptions of Geometry
Explore the theory of Regularity Transformation equations and their impact on non-regular spacetime geometry, including applications in General Relativity and Einstein-Euler equations.
The Multiple Membrane Problem
Explore the N-membranes problem in mathematics, focusing on equilibrium positions of ordered elastic membranes and their free boundary regularity.
Geometric Variational Problems: Regularity vs Singularity Formation
Explore techniques for existence, regularity, and singularity formation in geometric problems, focusing on harmonic maps, Yang-Mills connections, and nematic liquid crystals. Learn about new gluing methods for parabolic flows.
Generic Regularity in Obstacle Problems
Explore the classical obstacle problem, its free boundary, and recent developments in regularity theory with insights from renowned mathematician Alessio Figalli.
Singularities of Minimizing Harmonic Maps
Explore singularities of minimizing harmonic maps, delving into mathematical concepts and theories with expert insights from Michał Miśkiewicz.
An Excursion into Mean Curvature Flow
Explore mean curvature flow's regularity theory, focusing on distinctions between one-dimensional and higher-dimensional flows in this geometric analysis lecture.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond
Explore countable subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions. Examine model theory applications.