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.
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.
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.
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.
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.
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.
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.
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.
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.
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.