Euclidean Spaces Courses and Certifications

Applied Algebraic Topology Network

Reconstructing Hidden Geometric Structures in Data From Distance Matrices

Explore techniques for reconstructing metric spaces and embeddings from distance matrices, covering theoretical foundations, practical applications, and open problems in geometric data analysis.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Wrath of Math

General Linear Transformations on Vector Spaces

Explore general linear transformations on vector spaces, their properties, and examples. Learn to distinguish between linear and non-linear transformations in this comprehensive overview.

• YouTube
• 17 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Homeomorphisms of Euclidean Space

Explore recent advances in understanding the topological group of homeomorphisms of Euclidean space, including methods and emerging conjectures in geometric topology.

• YouTube
• 42 minutes
• On-Demand
• Free Video

HyperComplex Seminar

On Weak 1-Semiconvexity of Open Sets in Euclidean Spaces

Explore weak 1-semiconvexity in Euclidean spaces, examining its properties, connections to linearly accessible domains, and implications for set disconnectedness in higher dimensions.

• YouTube
• 19 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

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

Explore density of test functions in Sobolev spaces on Euclidean space, advancing understanding of mathematical analysis.

• YouTube
• 15 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

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

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.

• YouTube
• 1 hour 53 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

Polynomially Convex Embeddings of Real Manifolds in C^n

Explore geometric embeddings of real manifolds in complex spaces, focusing on polynomial convexity and its connections to approximation theory and diverse mathematical areas.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

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

Explore a 1.55-approximation algorithm for Euclidean capacitated vehicle routing in random settings, presented by Zipei Nie.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

De Rham Algebras of Closed Quasiregularly Elliptic Manifolds are Euclidean

Explore quasiregular mappings and de Rham cohomology in closed manifolds, leading to a homeomorphic classification of certain 4-manifolds.

• YouTube
• 35 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

On the Uniqueness Problem for Spacetime Extensions

Explore uniqueness conditions for Lorentzian manifold extensions, analyzing boundary agreement and presenting recent findings on necessary conditions and non-uniqueness mechanisms.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Looking for p-Energy Forms in Cheeger Spaces

Explore p-energy forms in Cheeger spaces without relying on gradients. Learn about constructing these forms using characteristic features of Cheeger metric measure spaces.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Schoen's Conjecture for Limits of Isoperimetric Surfaces

Explore Schoen's conjecture for asymptotically flat Riemannian manifolds, focusing on area-minimizing hypersurfaces and recent developments in mathematical relativity.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Schmid College, Chapman University

Geometric Inequalities Between Intrinsic and Extrinsic Curvature Invariants

Explore geometric inequalities between intrinsic and extrinsic curvature invariants in Riemannian manifolds, focusing on Nash's Theorem and recent developments in the field.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Recent Developments in Constant Mean Curvature Hypersurfaces - Part II

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.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Capacity in Low Regularity with Connections to General Relativity

Explore capacity in metric spaces, its behavior under convergence, and connections to general relativity's total mass concept.

• YouTube
• 59 minutes
• On-Demand
• Free Video