Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 1
Explore advanced harmonic analysis concepts: Nikodym sets and maximal functions associated with spheres. Gain insights from expert Jongchon Kim in this comprehensive lecture.
Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 2
Explores advanced concepts in harmonic analysis, focusing on Nikodym sets and maximal functions related to spheres. Builds on previous lecture, deepening understanding of these mathematical structures.
Distance Problems and Their Many Variants - Lecture 2
Explores distance problems in harmonic analysis, focusing on variants and recent developments. Discusses polynomial methods and discrete approaches, offering insights for researchers in the field.
Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 2
Explores advanced concepts in harmonic analysis, focusing on Nikodym sets and maximal functions related to spheres. Builds on recent developments in the field.
Complex Monge-Ampère Operators and Functional Hermitian Intrinsic Volumes
Explore geometric construction of Monge-Ampère operators on finite convex functions, examining their properties and related valuations as functional versions of Hermitian intrinsic volumes.
Around the Nash Problem for Smooth Valuations
Explore smooth valuations on manifolds, their relation to translation-invariant valuations, and Crofton formulas. Discover surprising flexibility properties in finite subspace families.
Geometric Functionals of Polyconvex Excursion Sets of Poisson Shot Noise Processes
Explore geometric functionals of polyconvex excursion sets in Poisson shot noise processes, including asymptotics, variance bounds, and central limit theorems for intrinsic volumes.
Boundary Regularity of Minimal Surfaces
Explore boundary regularity of minimal surfaces with Camillo De Lellis. Gain insights into advanced mathematical concepts and their applications in geometric analysis.
Rigidity of Mass-Preserving 1-Lipschitz Maps from Integral Current Spaces into Euclidean Spaces
Explore rigidity of mass-preserving 1-Lipschitz maps from integral current spaces to Euclidean balls, proving isometry conditions and discussing stability of positive mass theorem for graphical manifolds.
Curvature Tensors and Measures of Singular Spaces - Lecture 3
Explore advanced concepts in geometry, focusing on curvature tensors and measures of singular spaces in this in-depth mathematical lecture.
Curvature Tensors and Measures of Singular Spaces - Part I
Explore curvature tensors and measures of singular spaces in advanced geometry, focusing on concepts beyond Riemannian geometry.
On the Radon-Carleman Problem in Uniformly Rectifiable Domains
Explore the Radon-Carleman Problem in uniformly rectifiable domains with mathematician Irina Mitrea. Gain insights into advanced mathematical concepts and their applications in analysis.
Length Functions on Currents
Explore length functions on currents, delving into advanced concepts in dynamics and geometric measure theory.
On the Entropy of Rectifiable and Stratified Measures
Explore entropy concepts for rectifiable and stratified measures, delving into mathematical intricacies and theoretical foundations.
Recent Developments in Constant Mean Curvature Hypersurfaces - Part I
Explore recent developments in constant mean curvature hypersurfaces, focusing on existence theory using min-max methods and discussing open problems in the field.
Currents on Metric Spaces and Intrinsic Flat Convergence
Explore Ambrosio-Kirchheim's Theory of Currents on Metric Spaces and delve into integral current spaces and intrinsic flat convergence, providing essential background for Antoine Song's talk.
Self-Similar Solutions to Extension and Approximation Problems - Lecture
Explore self-similar solutions in extension and approximation problems, focusing on Lipschitz and Hölder maps with unique properties in higher dimensions.
Area-Minimizing Integral Currents: Singularities and Structure - Lecture
Explore area-minimizing integral currents, their singularities, and structure. Delve into dimension bounds, fractal properties, and recent progress towards proving key conjectures in geometric measure theory.
The David-Semmes Problem, Rectifiability, and Harmonic Measure - ICBS 2024
Explore the David-Semmes problem, its solution in codimension one, and its impact on harmonic measure problems. Gain insights into Riesz transforms and n-rectifiability.
Hausdorff Dimension of Three-Dimensional Kakeya Sets
Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
Exponential Decay of Intersection Volume and Applications
Explore exponential decay of intersection volume and its applications in extremal and probabilistic combinatorics with distinguished researcher Hong Liu.