Metric Geometry Courses and Certifications

Banach Center

Distance, Curvature and Symmetry - A Haphazard Tour Through Metric Geometry

Explorez les concepts fondamentaux de la géométrie métrique, y compris la distance, la courbure et la symétrie, dans ce tour d'horizon captivant présenté par Alexandru Chirvasitu.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Society for Industrial and Applied Mathematics

Packing Points in Projective Spaces

Explore optimal point arrangements in projective spaces, surveying current research and open problems in this fundamental area of metric geometry with applications in digital communication.

• YouTube
• 47 minutes
• On-Demand
• Conference Talk

Applied Algebraic Topology Network

Urysohn Width

Explore the 100-year history and applications of Urysohn width, a metric invariant quantifying space approximation by simplicial complexes. Discover its role in dimension theory and modern geometric challenges.

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

Applied Algebraic Topology Network

Vietoris-Rips Thickenings - Problems for Birds and Frogs

Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Macroscopic Scalar Curvature and Local Collapsing

Exploration of macroscopic scalar curvature in Riemannian geometry, focusing on volume bounds for manifolds with hyperbolic metrics and collapsing techniques in metric geometry.

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

Applied Algebraic Topology Network

The Gromov-Hausdorff Distance Between Spheres

Explore upper and lower bounds for Gromov-Hausdorff distances between spheres, including optimal correspondences and topological concepts related to the Borsuk-Ulam theorem.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Failure of the Curvature-Dimension Condition in Sub-Finsler Manifolds

Explore the failure of curvature-dimension conditions in sub-Finsler manifolds, examining smooth norms, Heisenberg groups, and measure contraction properties in non-smooth spaces.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Metric Geometry of Spaces of Persistence Diagrams

Explora la geometría métrica de espacios de diagramas de persistencia, examinando sus propiedades y aplicaciones en el análisis topológico de datos.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Non-Regular Spacetime Geometry via Metric Measure Geometry

Explore non-regular spacetime geometry using metric geometry, extending Lorentzian geometry beyond smooth manifolds to study curvature in low-regularity spaces and general relativity.

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

Hausdorff Center for Mathematics

Vector-Valued Concentration on the Symmetric Group

Presentación de una nueva desigualdad de concentración vectorial para la medida uniforme en el grupo simétrico, con implicaciones para la geometría métrica de espacios de Banach.

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

Hausdorff Center for Mathematics

Functional Inequalities in Metric Geometry - Lecture 4

Présentation des inégalités fonctionnelles discrètes comme invariants pour les plongements bi-Lipschitz de graphes finis dans des espaces de Banach et métriques, avec applications aux résultats de non-plongement.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The Space of Causal Diamonds as a Lorentzian Pre-Length Space

Exploración de la geometría y estructura geodésica del hiperespacio de diamantes causales en Relatividad Matemática, estableciendo una estructura de espacio pre-longitud lorentziano y analizando sus propiedades.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Alexandrov's Patchwork and the Bonnet-Myers Theorem for Lorentzian Length Spaces

Exploración de límites de curvatura temporal en espacios de longitud lorentzianos, incluyendo el análogo del Patchwork de Alexandrov y un resultado tipo Bonnet-Myers para cotas inferiores negativas.

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

Hausdorff Center for Mathematics

Functional Inequalities in Metric Geometry - Lecture 3

Explore discrete functional inequalities as invariants for bi-Lipschitz embeddings of finite graphs, leading to nonembeddability results for various graph structures in Banach and metric spaces.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Functional Inequalities in Metric Geometry - Part I

Explore discrete functional inequalities as invariants for bi-Lipschitz embeddings of finite graphs, leading to nonembeddability results for various graph structures in Banach and metric spaces.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video