Lie groupoid and algebroid week in Coimbra II

School on modern aspects of the geometry and applications of Lie groupoids and Lie algebroids
Hybrid Format

This school will contain two mini-courses, aiming to introduce some modern advances  of the theory of Lie groupoids, Lie algebroids, and their applications. The goal is to have a leisurely schedule, allowing plenty of time for informal discussions.

It is geared toward PhD students, and other researchers interested in the topic, but previous exposure to Lie groupoids will not be assumed. 

The first day will contain a small crash-course on Lie groupoids and Lie algebroids, to introduce definitions, examples, and ideas used in the other courses.

We will record the (blackboard) lectures and transmit via Zoom to online participants.

Courses

• Sylvain Lavau : Some instances of graded geometry and homotopy algebra in Lie algebroid theory

The notion of Lie algebroid yields a natural generalization: that of Lie infinity-algebroid. This mathematical structure entails higher Lie brackets on a graded vector bundle, and finds applications in foliation theory. Another instance of higher geometry in Lie algebroid theory is that of representation up to homotopy. It turns out this notion is necessary to define the adjoint representation of a Lie algebroid, and forms the building block of the representation of Lie infinity algebroids. An example of a characteristic class in that context will be given. We will discuss all these notions, from the classical perspective as well as from the differential graded manifold perspective. If time permits, we would possibly discuss extra topics such as  BFV-BRST formalism.

• Žan Grad : Lie categories

Lie categories are categories with a compatible differentiable structure. In this short course, we will look at elementary notions and constructions which pertain to the interplay of a differentiable and a categorical structure. We will see how Lie groupoids fit into this theory and discuss some potential applications to physics.

• Crash-course on Lie groupoids and Lie algebroids 

Definitions, examples and some basic ideas useful for the other two courses.

Registration

Please register by sending an email to jnmestre@mat.uc.pt saying that you want to participate, and to receive the Zoom links.

Location

CMUC Seminar room (5.5), Department of Mathematics, University of Coimbra

Organizers

• Raquel Caseiro

• João Nuno Mestre

 The first Lie groupoid week in Coimbra was held in September 2022.