Frontiers in Mathematics Lecture Series - Research Talk

Explore the foundations of Lie theory and its extensions to groupoids and algebroids in this research seminar by Maria Amelia Salazar Pinzon, Assistant Professor at the Universidade Federal Fluminense, Brazil. Delve into the intricacies of Lie's three theorems and their converses, examining the construction of Lie algebras from Lie groups and vice versa. Investigate the differences between classical Lie theory and its groupoid-algebroid counterparts, focusing on the challenges of integrating Lie algebroids into Lie groupoids. Discover a novel approach to overcoming non-integrability issues through the use of local Lie groupoids, as presented in Pinzon's joint work with Cabrera and Marcut. Learn about the construction of local Lie groupoids that integrate given Lie algebroids, drawing parallels with classical theory. The seminar covers topics such as infinitesimals, local integration, tubular structures, algebraic integration, relaxation forms, and geometric instructions, providing a comprehensive overview of this advanced mathematical research.

Introduction
Objects
Infinites
Local Integration
More Reperto Form
Tubular Structures
morphisms
algebraic integration
relaxation form
real consequences
Geometric instructions
Synthetic realization