Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 4
Explore finitely generated subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions.
Harmonic Maps with Free Boundary: Regularity, Singularity Formation and Geometric Applications
Explore harmonic maps with free boundary, covering existence, regularity, and parabolic blow-up. Examine elliptic and parabolic problems, recent advances in regularity theory, and geometric applications to the Steklov problem.
Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps
Explore sharp rectifiability results for singular sets of minimizing harmonic maps, with uniform Minkowski bounds and integrability. Analyze quantitative stratification and dimension-reduction techniques.
Regularity for Stationary Varifolds
Explore advanced concepts in geometric measure theory, focusing on regularity properties of stationary varifolds and their applications in minimal surface theory.
Dimers on a Riemann Surface and Compactified Free Field
Explore dimer models on Riemann surfaces, height function convergence, and connections to compactified free fields. Gain insights into probabilistic methods and discrete complex analysis in statistical mechanics.
Turbulence and Singularities in Fluid Flows - Mathematical Considerations
Explore turbulence, singularities, and fluid dynamics through mathematical considerations, multiscale solutions, and incompressible fluid pressure. Gain insights into Navier-Stokes equations and regularity criteria.
Rough Paths for Physicists - Course 2: Rough Paths, Combinatorics and Regularity
Explore rough paths, combinatorics, and regularity in physics, focusing on Brownian motion and its applications in mathematical analysis.
Conserved Quantities and Regularity in Fluid Mechanics
Explore conserved quantities and regularity in fluid mechanics, gaining insights into fundamental principles and advanced concepts in this field.
Regularity of Vortex and SQG Patches - Lecture
Explore regularity of vortex and SQG patches, covering existence, global irregularity, numerical simulations, and geometric analysis in fluid dynamics.
Fluid Equations: From Leray to Ladyzhenskaya and Beyond
Explore incompressible fluid theory, from Leray's weak solutions to Ladyzhenskaya's contributions, and recent findings on Navier-Stokes equations and turbulence.