Title： Diffeology and Lie's third theorem
Speaker：David Miyamoto
Institution： Max Planck Institute for Mathematics, in Bonn, Germany
Location：Zoom Id: 904 645 6677，Password: 2024
Meeting link：
https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
Abstract : Lie's third theorem is the result that every finite-dimensional Lie algebra integrates to a Lie group. Its two possible generalizations fail: not every Lie algebroid integrates to a Lie groupoid, and not every Banach Lie algebra integrates to a Banach Lie group. In this series of talks, we will show how diffeology, a category of generalized smooth spaces introduced by Souriau in the 1980s, can address this shortcoming.
In the first talk, we will introduce diffeology, with a focus on examples and relations to other smooth structures (orbifolds, infinite-dimensional manifolds, manifolds with boundary). This introduction will extend to the second talk, where we will discuss diffeology's role in the theory of Lie groupoids and singular foliations. Finally, in the third talk, we will present the machinery needed to diffeologically integrate certain Banach Lie algebras which admit no classical integration, and remark on the case for Lie algebroids.
Lecture 1: Diffeology and Lie's third theorem I, 20:00-21:00, May 13, 2025
Lecture 2: Diffeology and Lie's third theorem II, 20:00-21:00, May 14, 2025
Lecture 3: Diffeology and Lie's third theorem III, 20:00-21:00, May 15, 2025
Biography of the Speaker ：David Miyamoto is a postdoctoral researcher at the Max Planck Institute for Mathematics, in Bonn, Germany. He received his PhD from the University of Toronto, Canada, in 2023. His research focuses on the interplay between higher structures in differential geometry and diffeology.
