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#Euclidean Spaces

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University of Chicago Department of Mathematics

Symmetries of Manifolds - Lecture 3

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Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
University of Chicago Department of Mathematics

Symmetries of Manifolds - Lecture 2

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Delve into symmetries of manifolds, exploring classical and recent results on spaces of symmetries for simple manifolds like spheres and discs, with insights into emerging conjectural perspectives.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
University of Chicago Department of Mathematics

Symmetries of Manifolds - Lecture 1

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Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
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1 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Floating Bodies and Duality in Spaces of Constant Curvature

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Explores p-affine surface area and floating bodies in curved spaces, extending Meyer & Werner's Euclidean results to spherical and hyperbolic geometries. Examines limiting behavior as curvature approaches zero.
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1 Lesons
30 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

An Intrinsic Persistent Homology Transform

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Explores an intrinsic persistent homology transform for metric spaces, focusing on metric graphs. Discusses injectivity results and compares to related constructs in topological data analysis.
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1 Lesons
51 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Entropy and C^0 Stability of Hypersurfaces - IPAM at UCLA

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Explore entropy's role in hypersurface complexity, focusing on sphere rigidity, stability properties, and generalizations in higher dimensions. Gain insights into cutting-edge research in geometric analysis.
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10 Lesons
24 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Convex Sunflower Theorems and Neural Codes

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Explore convex sunflower theorems and neural codes, connecting neuroscience with discrete geometry to understand place cell encoding and cognitive mapping in rat hippocampus.
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19 Lesons
58 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Borsuk-Ulam Theorems into Higher-Dimensional Codomains

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Exploration of Borsuk-Ulam theorems in higher dimensions, generalizing results and discussing open questions related to optimal diameters and Schur polynomials.
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9 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Johnathan Bush - Maps of Čech and Vietoris–Rips Complexes into Euclidean Spaces

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Explore simplex-preserving maps in Čech and Vietoris–Rips complexes, their applications, and the challenge of finding such maps from various domains to Euclidean spaces.
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11 Lesons
45 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vanessa Robins - The Extended Persistent Homology Transform for Manifolds with Boundary

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Explore extended persistent homology transform for shape analysis, offering finite distances between shapes with different Betti numbers and applications in shape clustering.
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9 Lesons
59 minutes
On-Demand
Free-Video
IMSA

Coassociative Fibrations in G2 Geometry

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Explore G2 geometry in 7D spaces, focusing on coassociative submanifolds. Learn about their properties, deformation theory, and constructions forming fibrations with singular fibers in 7-manifolds.
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1 Lesons
58 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Some Comments on the Fundamental Gap of the Dirichlet Laplacian in Hyperbolic Space

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Explore the fundamental gap of convex domains in hyperbolic space, comparing it with Euclidean space and examining different types of convexity in this advanced mathematical analysis.
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1 Lesons
40 minutes
On-Demand
Free-Video
ICTP Mathematics

A Survey of Volume Inequalities - Basic Notions Seminar - 2019

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Explores volume inequalities in Euclidean space, discussing identities and inequalities for convex sets and star-bodies. Covers Gromov's conjecture and is accessible to a general mathematical audience.
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1 Lesons
59 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Reconstructing Hidden Geometric Structures in Data From Distance Matrices

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Explore techniques for reconstructing metric spaces and embeddings from distance matrices, covering theoretical foundations, practical applications, and open problems in geometric data analysis.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Simons Institute

Localization Schemes

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Explore innovative localization schemes for analyzing Markov chain mixing times in continuous and discrete spaces, with applications to Ising models and Glauber dynamics.
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1 Lesons
1 hour
On-Demand
Free-Video
Joint Mathematics Meetings

Differential Operators and the Geometry of Domains in Euclidean Space

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Explore the interplay between differential operators and domain geometry in Euclidean space with Tatiana Toro's insightful lecture, the inaugural AMS Maryam Mirzakhani Lecture at JMM 2020.
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1 Lesons
51 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Homeomorphisms of Euclidean Space

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Explore recent advances in understanding the topological group of homeomorphisms of Euclidean space, including methods and emerging conjectures in geometric topology.
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1 Lesons
42 minutes
On-Demand
Free-Video
Wrath of Math

General Linear Transformations on Vector Spaces

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Explore general linear transformations on vector spaces, their properties, and examples. Learn to distinguish between linear and non-linear transformations in this comprehensive overview.
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13 Lesons
17 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Looking for p-Energy Forms in Cheeger Spaces

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Explore p-energy forms in Cheeger spaces without relying on gradients. Learn about constructing these forms using characteristic features of Cheeger metric measure spaces.
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1 Lesons
47 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Schoen's Conjecture for Limits of Isoperimetric Surfaces

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Explore Schoen's conjecture for asymptotically flat Riemannian manifolds, focusing on area-minimizing hypersurfaces and recent developments in mathematical relativity.
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1 Lesons
57 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

De Rham Algebras of Closed Quasiregularly Elliptic Manifolds are Euclidean

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Explore quasiregular mappings and de Rham cohomology in closed manifolds, leading to a homeomorphic classification of certain 4-manifolds.
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1 Lesons
35 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Polynomially Convex Embeddings of Real Manifolds in C^n

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Explore geometric embeddings of real manifolds in complex spaces, focusing on polynomial convexity and its connections to approximation theory and diverse mathematical areas.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
International Centre for Theoretical Sciences

Nash's C^1 Isometric Embedding Theorem and the Borisov-Gromov Problem - Lecture 3

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Explore Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem in Riemannian geometry. Delve into surprising constructions and open questions linked to the Onsager conjecture.
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1 Lesons
1 hour 53 minutes
On-Demand
Free-Video
HyperComplex Seminar

On Weak 1-Semiconvexity of Open Sets in Euclidean Spaces

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Explore weak 1-semiconvexity in Euclidean spaces, examining its properties, connections to linearly accessible domains, and implications for set disconnectedness in higher dimensions.
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1 Lesons
19 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Sobolev Spaces: Density of Test Functions in Euclidean Space - Part 2

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Explore density of test functions in Sobolev spaces on Euclidean space, advancing understanding of mathematical analysis.
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1 Lesons
15 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Recent Developments in Constant Mean Curvature Hypersurfaces - Part II

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Explore recent developments in constant mean curvature hypersurfaces, focusing on min-max theorems and the half-volume spectrum. Gain insights into advanced geometric analysis concepts.
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14 Lesons
51 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Intrinsic Flat Stability of the Positive Mass Theorem for Graphical Manifolds

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Explore intrinsic flat stability of positive mass theorem for graphical manifolds, focusing on asymptotically flat and hyperbolic cases. Gain insights into rigidity, stability, and ongoing research.
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1 Lesons
53 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Geometric Inequalities Between Intrinsic and Extrinsic Curvature Invariants

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Explore geometric inequalities between intrinsic and extrinsic curvature invariants in Riemannian manifolds, focusing on Nash's Theorem and recent developments in the field.
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1 Lesons
57 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Sticky Kakeya Sets and the Sticky Kakeya Conjecture

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Explore the intriguing world of Kakeya sets and delve into the sticky Kakeya conjecture. Uncover groundbreaking insights on this fundamental problem in harmonic analysis and Fourier transform behavior.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Complexity of Submanifolds and Colding-Minicozzi Entropy

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Explore Colding-Minicozzi entropy's role in analyzing submanifold complexity and its applications to mean curvature flow singularities and hypersurface simplicity.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Finite Point Configurations in Euclidean, Discrete, and Arithmetic Settings

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Explore finite point configurations across Euclidean, discrete, and arithmetic spaces. Discover size requirements for subsets containing congruent copies of given configurations, with connections to learning theory.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Minimal Surfaces and the Isoperimetric Inequality

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Explore the generalization of the isoperimetric inequality to submanifolds in Euclidean space, focusing on minimal submanifolds and their sharp isoperimetric properties.
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1 Lesons
55 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
Centre de recherches mathématiques - CRM

Large Steklov Eigenvalues Under Geometric Constraints

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Explore large Steklov eigenvalues in compact Riemannian manifolds, examining geometric constraints and constructing metrics with fixed volume and boundary conditions.
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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

Generic Dynamics of the Mean Curvature Flows

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Explore generic dynamics of mean curvature flows, including perturbation of shrinkers and isolatedness of cylindrical singularities in hypersurface evolution.
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1 Lesons
47 minutes
On-Demand
Free-Video
BIMSA

Optimal Immersions in the Calculus of Variations of Surfaces

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Explore innovative minmax techniques for optimal surface immersions, including recent progress on Yau, Willmore, and 16π conjectures in calculus of variations.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Capacity in Low Regularity with Connections to General Relativity

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Explore capacity in metric spaces, its behavior under convergence, and connections to general relativity's total mass concept.
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1 Lesons
59 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

On the Uniqueness Problem for Spacetime Extensions

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Explore uniqueness conditions for Lorentzian manifold extensions, analyzing boundary agreement and presenting recent findings on necessary conditions and non-uniqueness mechanisms.
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1 Lesons
47 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

The Brownian Transport Map - IPAM at UCLA

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Explore Lipschitz transport maps between probability measures, focusing on the Brownian transport map's construction, properties, and applications to Euclidean functional inequalities.
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10 Lesons
24 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Skeletonization Algorithms With Theoretical Guarantees for Point Clouds

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Explore skeletonization algorithms for point clouds, including Mapper, alpha-Reeb graphs, and Homologically Persistent Skeleton. Compare their performance on synthetic and real data sets.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Sphere Packings with Forbidden Distances

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Delve into the mathematical exploration of sphere packing configurations, examining forbidden distances and their implications in geometric number theory through advanced analytical approaches.
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1 Lesons
25 minutes
On-Demand
Free-Video
Simons Institute

Fast Streaming Euclidean Clustering with Constant Space

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Explore streaming algorithms for k-median and k-means clustering, achieving constant space complexity independent of data size and aspect ratio. Improve space and update time for approximate subspace embeddings.
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1 Lesons
31 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Euclidean Capacitated Vehicle Routing in Random Setting - A 1.55-Approximation Algorithm

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Explore a 1.55-approximation algorithm for Euclidean capacitated vehicle routing in random settings, presented by Zipei Nie.
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1 Lesons
47 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On Gilles Pisier's Approach to Gaussian Concentration, Isoperimetry, and Poincare-Type Inequalities

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Explore advanced mathematical concepts in measure concentration, isoperimetry, and Poincaré-type inequalities through Pisier's approach and its extensions to rotationally invariant distributions.
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1 Lesons
54 minutes
On-Demand
Free-Video
Institute for Advanced Study

Quadratic Stability of the Brunn-Minkowski Inequality

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Delve into advanced mathematical concepts exploring the quadratic stability of Brunn-Minkowski inequality, its geometric implications, and connections to related inequalities in convex geometry.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video