Sub-Riemannian Geometry Courses and Certifications

Hausdorff Center for Mathematics

Emanuel Milman: Functional Inequalities on Sub-Riemannian Manifolds via QCD

Explores functional inequalities on sub-Riemannian manifolds using QCD, offering novel quantitative estimates for Poincaré and log-Sobolev inequalities with applications to Heisenberg groups.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Finding Solitons in Differential Geometry

Explore solitons in differential geometry, their role in discovering distinguished geometric structures, and applications in various mathematical contexts including Lie groups and algebras.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Isoperimetric Inequality for Hausdorff Contents and Its Applications

Explore isoperimetric inequality for Hausdorff contents, its applications in systolic geometry, and new systolic inequalities for non-simply connected Riemannian manifolds.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Geometry and Topology of Data

Explore hyperconvexity and generalized curvature in metric spaces, linking topological data analysis with geometric concepts for a deeper understanding of data structures.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Curvature Bounds and the Length of the Shortest Closed Geodesic

Explore upper bounds for shortest periodic geodesics on Riemannian manifolds, examining curvature's impact on closed geodesic length in various geometric contexts.

• YouTube
• 47 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature

Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Metric Reconstruction via Optimal Transport

Explores metric reconstruction using optimal transport theory, introducing Vietoris-Rips thickening to recover metric information from point samples in metric spaces, with applications to Riemannian manifolds.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Hyperkähler Manifolds: An Introduction - Part 4.1

Explore advanced concepts in complex geometry, focusing on Hyperkähler manifolds and their properties in this comprehensive mathematical lecture.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Perverse Sheaves and Schobers on Riemann Surfaces - Tobias Dyckerhoff

Explore derived constructible categories on stratified Riemann surfaces, t-structures, Verdier duality, and categorified perverse sheaves with applications in algebraic geometry and topology.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Stochastic Ricci Flow on Surfaces

Explores stochastic Ricci flow in 2D, introducing its formulation, symmetry properties, and construction of weak solutions. Discusses implications for compact surfaces and open questions.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

International Mathematical Union

Laurent Saloff-Coste - Breaking Heat Kernel Estimates Into Pieces

Breaking heat kernel estimates on Riemannian manifolds by analyzing pieces separately and reconstructing the whole. Explores Brownian motion within segments and transitions between them.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Towards a Theory of Non-commutative Optimization - Geodesic First and Second Order Methods for Moment Maps and Polytopes

Explore non-commutative optimization theory for geodesically convex problems, unifying diverse applications in computer science, mathematics, and physics through innovative first and second-order methods.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

IMSA

Bifurcation Phenomena in Geometric Variational Problems

Explore classical Bifurcation Theory and its modern applications in Riemannian Geometry, covering minimal and constant mean curvature surfaces and the Yamabe problem.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Fields Institute

Riemannian Manifolds, Isometries, and Geodesics - Lecture 3

Explore Riemannian manifolds, isometries, and geodesics, with a focus on the upper half-plane and hyperbolic metric in this advanced geometry lecture.

• YouTube
• 55 minutes
• Self-Paced
• Free Video