We want to announce the new IMSA's Frontiers in Mathematics Lecture Series. This lecture series aims to highlight outstanding recent achievements in mathematics, with a particular emphasis on those of female mathematicians from Latin America or working in Latin America.
The lectures consist of a week-long visit to IMSA during which the awardee will deliver two in-person lectures. There will be a live broadcast at IMSAC institutions and other universities worldwide. The lectures should give a general mathematical audience explanation of the speaker's oeuvre.
General Audience Seminar
Maria Amelia Salazar Pinzon, Assistant Professor at the Departamento de Matematica Aplicada of the Universidade Federal Fluminense, Brazil
University of Miami & IMSA
Fundamentals of Lie Groupoids and Algebroids
Monday, January 23, 2023, 5:00pm
Lakeside Village, Auditorium
Click here for Video
Abstract: In recent years, Lie groupoids and algebroids have come to the fore because of their versatility in describing seemingly distinct geometric structures, ranging from foliations and group actions, to Poisson bivectors and generalized complex structures. Intuitively, Lie groupoids and algebroids can be thought of as finite-dimensional geometric objects that encode certain infinite dimensional Lie groups and Lie algebras. The aim of this talk is to provide a gentle introduction to the Lie theory of these objects, illustrating the various definitions and properties with examples. Time permitting, we will state a few fundamental questions for Lie groupoids and algebroids that are the analogs of the corresponding ones for finite dimensional Lie groups and Lie algebras.
Research Seminar
Maria Amelia Salazar Pinzon, Assistant Professor at the Departamento de Matematica Aplicada of the Universidade Federal Fluminense, Brazil
University of Miami & IMSA
On Local Integration of Lie Brackets
Tuesday, January 24, 2023, 5:00pm
Lakeside Village, Auditorium
Click here for Video
Abstract: The foundation of Lie theory is Lie's three theorems that provide a construction of the Lie algebra associated to any Lie group; the converses of Lie's theorems provide an integration, i.e. a mechanism for constructing a Lie group out of a Lie algebra. The Lie theory for groupoids and algebroids has many analogous results to those for Lie groups and Lie algebras, however, it differs in important respects: one of these aspects is that there are Lie algebroids which do not admit any integration by a Lie groupoid. In joint work with Cabrera and Marcut, we showed that the non-integrability issue can be overcome by considering local Lie groupoids instead. In this talk I will explain a construction of a local Lie groupoid integrating a given Lie algebroid and I will point out the similarities with the classical theory for Lie groups and Lie algebras.
