Isoperimetric Inequalities in High Dimensional Convex Sets - Lecture 1, Part 2
Explore isoperimetric inequalities in high-dimensional convex sets, focusing on Bourgain's slicing problem and the KLS conjecture. Gain insights from expert Bo'az Klartag.
Isoperimetric Inequalities in High Dimensional Convex Sets - Lecture 1, Part 1
Explore isoperimetric inequalities in high-dimensional convex sets, focusing on Bourgain's slicing problem and the KLS conjecture. Gain insights from expert Bo'az Klartag in this advanced mathematics lecture.
Smoothing by Ricci-DeTurck Flow and Applications to Scalar Curvature
Explore Ricci-DeTurck flow's existence theory for non-smooth initial metrics and its applications to scalar curvature rigidity problems in geometry.
Conjugate Points and the MC Criterion in Volume-Preserving Diffeomorphisms - Lecture
Explore conjugate points on volume-preserving diffeomorphisms, focusing on the MC criterion and its applications in fluid dynamics and Riemannian geometry.
Geometric Laplacians on Self-Conformal Fractal Curves in the Plane
Explore geometric Laplacians on self-conformal fractal curves, examining heat kernels, eigenvalue asymptotics, and their relation to fractal geometry. Delve into construction methods and applications in complex analysis.
Geometric Aspects of the Planar Least Gradient Problem
Explore geometric aspects of the planar least gradient problem, delving into mathematical concepts and analytical techniques.
Distance, Curvature and Symmetry - A Haphazard Tour Through Metric Geometry
Explore metric geometry through distance, curvature, and symmetry concepts, gaining insights into fundamental mathematical principles and their applications in spatial analysis.
Twisted Ruelle Zeta Function on Locally Symmetric Spaces - Fried's Conjecture and Applications
Explore Twisted Ruelle zeta functions, Fried's conjecture, and applications in locally symmetric spaces. Gain insights into spectral geometry and refined analytic torsion.
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.
Complexity of Submanifolds and Colding-Minicozzi Entropy
Explore Colding-Minicozzi entropy's role in analyzing submanifold complexity and its applications to mean curvature flow singularities and hypersurface simplicity.
Riesz Inequality for Polygons: Symmetry and Symmetry Breaking
Explore counterparts of Hardy-Littlewood and Riesz inequalities for polygons, examining symmetry and symmetry breaking in nonlocal isoperimetric problems.
Eigenvalues and Minimal Surfaces
Explore Laplace operator eigenvalues, their physical significance, and connection to minimal surfaces. Discover recent findings in isoperimetric eigenvalue problems for Riemannian surfaces.
Parametric Geometric Inequalities and Weyl Law for the Volume Spectrum
Explore parametric geometric inequalities and their connection to the volume spectrum, examining proofs, applications, and implications for minimal surfaces and stationary geodesic nets.
Around the Alexandrov-Fenchel Inequality - Convex Geometry and Its Applications
Explore the history and recent progress in convex geometry, focusing on Minkowski's theory and its connections to various mathematical disciplines.
Integrable Billiards and Rigidity - Lecture 1
Explore integrable billiards and the Birkhoff-Poritsky conjecture, focusing on Hopf-type rigidity and its extension to Twist symplectic maps and billiards.
Minimal Surfaces and the Allen-Cahn Equation on 3-Manifolds
Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.
Geometric Analysis of Phase Retrieval
Explore geometric analysis of phase retrieval, examining nonconvex heuristics and proving benign geometric structure for efficient signal recovery using iterative optimization methods.
The Singular Set of Stable Minimal Hypersurfaces
Explore stable minimal hypersurfaces, their singularities, and recent findings on constructing metrics with specific singular sets in higher dimensions.
Optimal Estimates for Neumann Eigenvalues
Explore optimal estimates for Neumann eigenvalues, including award-winning research on maximizing second eigenvalues and recent findings on convex set bounds.
Generic Dynamics of the Mean Curvature Flows
Explore generic dynamics of mean curvature flows, including perturbation of shrinkers and isolatedness of cylindrical singularities in hypersurface evolution.
Recent Progress on Self-Expanders of Mean Curvature Flow and Applications
Explore recent advancements in self-expanders of mean curvature flow, their role in modeling singularities, and applications in geometric analysis.