Riemannian Geometry Courses and Certifications

Hausdorff Center for Mathematics

Brunn-Minkowski Inequalities for Sprays on Riemannian Surfaces

Generalization of Minkowski average on Riemannian manifolds, characterizing curve families on surfaces satisfying Brunn-Minkowski inequality. Explores conditions for constant-speed curves and geodesic curvature.

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

Dublin Institute for Advanced Studies DIAS

Multigap Topological Insulators: Non-Abelian Bands, Riemannian Geometry, Quantised Optical Responses

Explore the physics of multigap topological insulators, covering non-Abelian bands, homotopy classification, momentum-space Riemannian geometry, and quantized optical responses in condensed matter systems.

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

BIMSA

Noncommutative Geometry and Semiclassical Analysis - Applications in Contact and Sub-Riemannian Geometry

Explore bridges between semiclassical analysis and noncommutative geometry, with applications to contact and sub-Riemannian geometry including Weyl's laws.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Sub-Riemannian Geometry of Osculating Curves - From Tangent Lines to Algebraic Curves

Delve into nonholonomic constraints and sub-Riemannian structures through geometric models of osculating curves, exploring tangent lines, conics, and cubics in plane curve movements.

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

Institute for Pure & Applied Mathematics (IPAM)

Sub-Riemannian Geometry of Optimal Transport: Mostly Classical and a Bit of Quantum

Delve into the sub-Riemannian geometry of Monge-Kantorovich transport, exploring controllability issues, structure groups, and related quantum theory concepts in this mathematical presentation.

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

The Royal Institution

The Extraordinary Theorems of John Nash

Explore John Nash's revolutionary contributions to game theory and geometric analysis with Fields Medal winner Cédric Villani, delving into the world of mathematical genius and groundbreaking theorems.

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

ICTP Mathematics

Differential Geometry

Master differential geometry through comprehensive lectures covering manifolds, curvature, and geometric structures in this ICTP diploma program by Claudio Arezzo.

• YouTube
• 1 day 2 hours 13 minutes
• On-Demand
• Free Video

Mathemaniac

Exponentiating Vectors, Derivatives, and Vector Fields - Mathematical Concepts Explained

Explore the concept of exponentiation applied to vectors, derivatives, and vector fields, uncovering connections between seemingly different mathematical ideas and their practical applications.

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

Fields Institute

Optimal Transportation, Geometry and Dynamics

Explore advanced mathematical theory connecting optimal transport problems with geometric structures and dynamical systems through 24 comprehensive lectures from Fields Institute.

• YouTube
• 1 day 9 hours 39 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Introduction to General Relativity

Dive into Einstein's theory of spacetime, gravity, and the universe through comprehensive lectures by renowned physicist Ashoke Sen from ICTS.

• YouTube
• 2 days 17 hours 50 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Calculus of Variations in Probability and Geometry

Explore advanced mathematical techniques connecting calculus of variations, probability theory, and geometric inequalities through expert lectures on isoperimetric problems and applications.

• YouTube
• 11 hours 14 minutes
• On-Demand
• Free Video

ICTP Mathematics

Geometric Measure Theory and Optimal Transport

Explore advanced mathematical concepts connecting geometric measure theory with optimal transport through expert lectures on regularity theory, Monge-Ampère equations, and stability results.

• YouTube
• 1 day 7 hours 45 minutes
• On-Demand
• Free Video

ICTP Mathematics

Dynamics of the Geodesic Flow on Surfaces Without Conjugate Points - Lecture 2

Explore geodesic flow dynamics, maximal entropy measures, and Patterson-Sullivan measures on ideal boundaries in surfaces without conjugate points.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

ICTP Mathematics

Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 1

Explore optimal transportation, Monge-Ampère equations, and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio from Scuola Normale Superiore di Pisa.

• YouTube
• 1 hour 48 minutes
• On-Demand
• Free Video

ICTP Mathematics

Differential Geometry - Lecture 19

Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture by Claudio Arezzo.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video