Lie Groupoids Courses and Certifications

Fields Institute

Differentiating Higher Lie Groupoids and Generalized van Est Theory

Explore the mathematical concepts of higher Lie groupoids and generalized van Est theory in this advanced lecture by Alejandro Cabrera from Universidade Federal do Rio de Janeiro.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Principal Bundle Groupoids versus Vector Bundle Groupoids in Differential Geometry

Delve into the mathematical correspondence between vector bundle groupoids and principal bundle groupoids, exploring frame bundles, Lie groupoids, and their geometric applications.

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

Fields Institute

A Fixed-Point Formula for Dirac Operators on Lie Groupoids

Explore fixed-point formulas for Dirac operators on Lie groupoids, delving into advanced mathematical concepts and their applications in geometric analysis.

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

IMSA

Fundamentals of Lie Groupoids and Algebroids - Lecture Series

Introducción a la teoría de Lie de grupoides y algebroides, explorando sus definiciones, propiedades y aplicaciones en diversas estructuras geométricas.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Fields Institute

Lie Groupoids Determined by Their Orbit Spaces

Explore how Lie groupoids are uniquely determined by their orbit spaces, delving into advanced concepts in Hamiltonian geometry and mathematical physics.

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

Global Noncommutative Geometry Seminar

Equivariant Local Index Theory for Lie Groupoids

Explore equivariant local index theory for Lie groupoids, covering motivation, key concepts, and advanced mathematical techniques in noncommutative geometry.

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

Fields Institute

Derived Higher Lie Groupoids

Explore advanced concepts in algebraic topology and differential geometry, focusing on derived higher Lie groupoids and their applications in Hamiltonian geometry.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Banach-Lie Groupoids in Infinite-dimensional Geometry - Part 2

Delve into advanced mathematical concepts of Banach-Lie groupoids, exploring theoretical frameworks and applications in infinite-dimensional geometry.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Banach-Lie Groupoids in Infinite-dimensional Geometry - Part 1

Dive into the mathematical foundations of Banach-Lie groupoids, exploring their theoretical framework and applications in infinite-dimensional geometry.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Banach-Lie Groupoids - Part 3

Delve into advanced mathematical concepts of Banach-Lie groupoids, exploring theoretical frameworks and applications in infinite-dimensional geometry through expert analysis.

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

IMSA

An Introductory Mini Course into Quantum Toric Geometry Lecture I - Day 1

Explore quantum toric geometry, a non-commutative generalization of toric geometry. Learn about stacks, quantum tori, and quantum toric varieties, building on foundations of traditional toric geometry.

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

Centre de recherches mathématiques - CRM

Smooth 2-Groups and Their Principal Bundles

Explore smooth 2-groups and principal bundles in Lie groupoids. Learn about categorical generalizations of groups and their applications in mathematics.

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

Dublin Institute for Advanced Studies DIAS

Frame PB-Groupoid of a VB-Groupoid

Explore properties of special principal bundles, focusing on frames of VB-groupoids and their relation to geometric connections and structures on Lie groupoids.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

Vortex Sheets and Groupoids in Ideal Hydrodynamics

Explore Arnold's group-theoretic approach to ideal hydrodynamics and its applications to vortex sheets, fluids with moving boundaries, and multiphase fluids using Lie groupoid symmetries.

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

Stony Brook Mathematics

Geodesic Framework for Vortex Sheets and Generalized Fluid Flows

Explore geodesic frameworks for vortex sheets and generalized fluid flows, examining group-theoretic approaches to ideal hydrodynamics and Lie groupoid symmetries in mathematical physics.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video