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#Geometric Measure Theory

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ICTP Mathematics

Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 3

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Explore geometric measure theory and optimal transport with a focus on Monge-Ampère equations and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Endpoint Fourier Restriction and Unrectifiability

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Explore endpoint Fourier restriction and its connection to measure unrectifiability in R^d, featuring a dichotomy between absolute continuity and 1-pure unrectifiability.
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8 Lesons
29 minutes
On-Demand
Free-Video
International Mathematical Union

Weighted Fourier Extension Estimates and Applications

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Explore weighted Fourier extension estimates and their applications in PDEs and geometric measure theory, covering topics like Fourier restriction, SME, and Falconer's distance set problem.
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8 Lesons
43 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Exploring Variational Functions - Calculus of Variations and Geometric Measure Theory

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Dive into variational problems and bounded Hessian functions with Luigi Ambrosio. Explore the intersection of Calculus of Variations and Geometric Measure Theory, inspired by machine learning insights.
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1 Lesons
48 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Harmonic Analysis Techniques for -Almost- Minimizers

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Explore harmonic analysis techniques for (almost-)minimizers, focusing on free boundary theory and calculus of variations. Learn about applications to geometric measure theory and domain geometry.
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12 Lesons
45 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Bala Krishnamoorthy: Linear Programming in Geometric Measure Theory

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Explore geometric measure theory through linear programming, examining integral currents, simplicial flat norm, and polyhedral approximation. Discover applications in median shape analysis.
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13 Lesons
58 minutes
On-Demand
Free-Video
ICTP Mathematics

Regularity Theory for Area-Minimizing Currents

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Explore advanced concepts in geometric measure theory, including zero forms, currents, and rectifiability theorems, with applications to area-minimizing problems in mathematics.
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17 Lesons
1 hour 40 minutes
On-Demand
Free-Video
ICTP Mathematics

Regularity Theory for Area-Minimizing Currents

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Explore advanced concepts in geometric measure theory, including currents, boundaries, and regularity theory for area-minimizing surfaces, with applications to optimal transport problems.
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15 Lesons
1 hour 53 minutes
On-Demand
Free-Video
ICTP Mathematics

Existence and Regularity Theories of Brakke Flow

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Explore existence and regularity theories of Brakke flow, covering initial configuration, linear and alpha regularity, dispersed irregularity, and the Monotonicity Formula for minimal surfaces.
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11 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems - Lecture III

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Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.
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10 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems Lecture I

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Explore regularity of free boundaries in obstacle problems, covering key concepts, proofs, and current research in this mathematical field of PDE and Geometric Measure Theory.
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10 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Restriction Problem and the Polynomial Method - Lecture I

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Explore Stein's restriction conjecture, the Kakeya conjecture, and the polynomial method in harmonic analysis. Learn about wave packet decomposition and its applications in studying hypersurface-supported functions.
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17 Lesons
55 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Steve Hofmann - Quantitative Rectiability, and Harmonic and Caloric Measure III

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Explore advanced mathematical concepts in quantitative rectifiability and measure theory, focusing on harmonic and caloric measures in complex analytical settings.
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1 Lesons
50 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Intrinsic Volumes on Pseudo-Riemannian Manifolds

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Explore intrinsic volumes in pseudo-Riemannian geometry, covering Hadwiger's theorem, Weyl's principle, and Crofton formulas. Learn about recent developments in this advanced mathematical field.
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1 Lesons
30 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Gaussian Isoperimetry and Related Topics III

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Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.
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1 Lesons
49 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Gaussian Isoperimetry and Related Topics II

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Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.
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1 Lesons
47 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems - Lecture IV

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Explore advanced concepts in free boundary problems, focusing on regularity in obstacle problems. Learn key results, current research, and open challenges in this mathematical field.
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1 Lesons
54 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems - Lecture II

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Explore free boundary problems in PDE, focusing on regularity in obstacle problems. Learn key results, current research, and open questions in this mathematical field.
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1 Lesons
56 minutes
On-Demand
Free-Video
ICTP Mathematics

Regularity Theory for Area-Minimizing Currents - Lecture 5

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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.
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1 Lesons
1 hour 49 minutes
On-Demand
Free-Video
ICTP Mathematics

Existence and Regularity Theories of Brakke Flow - Lecture 4

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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.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Gaussian Isoperimetry and Related Topics I

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Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof techniques using geometric measure theory.
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1 Lesons
50 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 1

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Explore advanced harmonic analysis concepts: Nikodym sets and maximal functions associated with spheres. Gain insights from expert Jongchon Kim in this comprehensive lecture.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 2

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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.
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1 Lesons
37 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Distance Problems and Their Many Variants - Lecture 2

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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.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 2

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Explores advanced concepts in harmonic analysis, focusing on Nikodym sets and maximal functions related to spheres. Builds on recent developments in the field.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Hausdorff Center for Mathematics

Complex Monge-Ampère Operators and Functional Hermitian Intrinsic Volumes

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Explore geometric construction of Monge-Ampère operators on finite convex functions, examining their properties and related valuations as functional versions of Hermitian intrinsic volumes.
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1 Lesons
24 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Around the Nash Problem for Smooth Valuations

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Explore smooth valuations on manifolds, their relation to translation-invariant valuations, and Crofton formulas. Discover surprising flexibility properties in finite subspace families.
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1 Lesons
39 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Geometric Functionals of Polyconvex Excursion Sets of Poisson Shot Noise Processes

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Explore geometric functionals of polyconvex excursion sets in Poisson shot noise processes, including asymptotics, variance bounds, and central limit theorems for intrinsic volumes.
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1 Lesons
21 minutes
On-Demand
Free-Video
Fields Institute

Boundary Regularity of Minimal Surfaces

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Explore boundary regularity of minimal surfaces with Camillo De Lellis. Gain insights into advanced mathematical concepts and their applications in geometric analysis.
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1 Lesons
42 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Rigidity of Mass-Preserving 1-Lipschitz Maps from Integral Current Spaces into Euclidean Spaces

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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.
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1 Lesons
42 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Curvature Tensors and Measures of Singular Spaces - Lecture 3

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Explore advanced concepts in geometry, focusing on curvature tensors and measures of singular spaces in this in-depth mathematical lecture.
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1 Lesons
55 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Curvature Tensors and Measures of Singular Spaces - Part I

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Explore curvature tensors and measures of singular spaces in advanced geometry, focusing on concepts beyond Riemannian geometry.
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1 Lesons
50 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

On the Radon-Carleman Problem in Uniformly Rectifiable Domains

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Explore the Radon-Carleman Problem in uniformly rectifiable domains with mathematician Irina Mitrea. Gain insights into advanced mathematical concepts and their applications in analysis.
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1 Lesons
36 minutes
On-Demand
Free-Video
Big Ideas In Dynamics

Length Functions on Currents

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Explore length functions on currents, delving into advanced concepts in dynamics and geometric measure theory.
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1 Lesons
53 minutes
On-Demand
Free-Video
Conference GSI

On the Entropy of Rectifiable and Stratified Measures

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Explore entropy concepts for rectifiable and stratified measures, delving into mathematical intricacies and theoretical foundations.
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1 Lesons
23 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Recent Developments in Constant Mean Curvature Hypersurfaces - Part I

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Explore recent developments in constant mean curvature hypersurfaces, focusing on existence theory using min-max methods and discussing open problems in the field.
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23 Lesons
47 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Currents on Metric Spaces and Intrinsic Flat Convergence

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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.
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1 Lesons
55 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Self-Similar Solutions to Extension and Approximation Problems - Lecture

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Explore self-similar solutions in extension and approximation problems, focusing on Lipschitz and Hölder maps with unique properties in higher dimensions.
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12 Lesons
58 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Area-Minimizing Integral Currents: Singularities and Structure - Lecture

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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.
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10 Lesons
1 hour 1 minute
On-Demand
Free-Video
BIMSA

The David-Semmes Problem, Rectifiability, and Harmonic Measure - ICBS 2024

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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.
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1 Lesons
47 minutes
On-Demand
Free-Video
BIMSA

Hausdorff Dimension of Three-Dimensional Kakeya Sets

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Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
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1 Lesons
1 hour
On-Demand
Free-Video
BIMSA

Exponential Decay of Intersection Volume and Applications

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Explore exponential decay of intersection volume and its applications in extremal and probabilistic combinatorics with distinguished researcher Hong Liu.
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1 Lesons
50 minutes
On-Demand
Free-Video
BIMSA

Hausdorff Dimension of Three-Dimensional Kakeya Sets

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Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.
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1 Lesons
1 hour
On-Demand
Free-Video
BIMSA

Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps

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Explore sharp rectifiability results for singular sets of minimizing harmonic maps, with uniform Minkowski bounds and integrability. Analyze quantitative stratification and dimension-reduction techniques.
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1 Lesons
49 minutes
On-Demand
Free-Video
Banach Center

Bourgain's Proof of the Circular Maximal Function Theorem - Part 3

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Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into advanced mathematical concepts and techniques.
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1 Lesons
48 minutes
On-Demand
Free-Video
Banach Center

Bourgain's Proof of the Circular Maximal Function Theorem - Part 4

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Explore Bourgain's groundbreaking proof of the circular maximal function theorem in this advanced mathematical lecture by Jonathan Hickman.
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1 Lesons
53 minutes
On-Demand
Free-Video
Banach Center

Bourgain's Proof of the Circular Maximal Function Theorem - Part 2

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Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into advanced mathematical concepts and techniques.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Banach Center

Bourgain's Proof of the Circular Maximal Function Theorem - Part 1

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Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into its mathematical intricacies and significance in harmonic analysis.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Banach Center

Dynamically Defined Random Fractals

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Explore dynamically defined random fractals and their mathematical properties through expert insights from Karoly Simon of Budapest University of Technology and Economics.
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1 Lesons
51 minutes
On-Demand
Free-Video
Institute for Advanced Study

Regularity for Stationary Varifolds

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Explore advanced concepts in geometric measure theory, focusing on regularity properties of stationary varifolds and their applications in minimal surface theory.
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1 Lesons
20 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

面積0の集合と関連する問題 - 2021年4月

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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。
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3 Lesons
25 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

C^0 Convex Integration for Incompressible Euler - Lecture 4

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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.
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1 Lesons
2 hours 3 minutes
On-Demand
Free-Video
ICTP Mathematics

Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2

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Explore optimal transportation and Monge Ampère equations, covering key concepts like super differentials, isoperimetric problems, and probability measures in this advanced mathematics lecture.
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15 Lesons
1 hour 58 minutes
On-Demand
Free-Video
Joint Mathematics Meetings

The Kakeya Needle Problem for Rectifiable Sets

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Explore the Kakeya needle problem for rectifiable sets, covering basic theorems, discrete sets, differential structures, and dimensions, with insights from mathematician Marianna Csőrnyei.
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8 Lesons
54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Onsager Theorem and Beyond - Lecture Series

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Explore advanced topics in fluid dynamics and differential geometry with renowned mathematician Camillo De Lellis, covering Onsager's theorem, Euler equations, and isometric embeddings.
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5 Lesons
1 hour 37 minutes
On-Demand
Free-Video