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.
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.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 3
Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into advanced mathematical concepts and techniques.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 4
Explore Bourgain's groundbreaking proof of the circular maximal function theorem in this advanced mathematical lecture by Jonathan Hickman.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 2
Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into advanced mathematical concepts and techniques.
Bourgain's Proof of the Circular Maximal Function Theorem - Part 1
Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into its mathematical intricacies and significance in harmonic analysis.
Dynamically Defined Random Fractals
Explore dynamically defined random fractals and their mathematical properties through expert insights from Karoly Simon of Budapest University of Technology and Economics.
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.
面積0の集合と関連する問題 - 2021年4月
Dive into 面積0の集合の数学的探究、Hausdorff測度と次元の概念、そして掛谷予想について学ぶ数学フロンティア講座。
C^0 Convex Integration for Incompressible Euler - Lecture 4
Explore C^0 convex integration for incompressible Euler equations, focusing on a novel iteration method producing continuous solutions, drawing parallels with Nash's theorem from Lecture 3.
Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2
Explore optimal transportation and Monge Ampère equations, covering key concepts like super differentials, isoperimetric problems, and probability measures in this advanced mathematics lecture.
The Kakeya Needle Problem for Rectifiable Sets
Explore the Kakeya needle problem for rectifiable sets, covering basic theorems, discrete sets, differential structures, and dimensions, with insights from mathematician Marianna Csőrnyei.
The Onsager Theorem and Beyond - Lecture Series
Explore advanced topics in fluid dynamics and differential geometry with renowned mathematician Camillo De Lellis, covering Onsager's theorem, Euler equations, and isometric embeddings.