Reading groupoid

The format is hybrid, with the possibility to attend in person either in Madrid (at ICMAT), in Warsaw (at IMPAN), or online. If you wish to attend online, please contact us.

You can download the latest version of the lecture notes. Moreover, the sessions are recorded. Video links are distributed via the mailing list or available upon request.

Next talks

• Lecture 9 (16 December 2025, 15:30 CEST), Oscar Carballal (UCM, Madrid, Spain).

Past talks

• Lecture 1 (7 October 2025, 15:30 CEST), Oscar Carballal (UCM, Madrid, Spain).
• Abstract: We illustrate the need for groupoids through a series of examples, primarily following R. Loja (2021) and Weinstein (1996), and discuss some of their recent applications in Mathematical Physics. We also outline potential directions for future topics of our Reading Groupoid.
• Lecture 2 (14 October 2025, 15:30 CEST), Bartosz Maciej Zawora (KMMF-UW, Warsaw, Poland).
• Abstract: We will talk about Lie groupoids, give some examples, and prove some fundamental results.
• Lecture 3 (21 October 2025, 15:30 CEST), Rubén Izquierdo López (ICMAT, Madrid, Spain).
• Abstract: We will talk about locally trivial Lie groupoids.
• Lecture 4 (4 November 2025, 15:30 CEST), Asier López Gordón (IMPAN, Warsaw, Poland).
• Abstract: We will introduce bisections and illustrate them with several examples.
• Lecture 5 (18 November 2025, 15:30 CEST), Juan Manuel López Medel (ICMAT, Madrid, Spain).
• Abstract: In this session we first record basic facts about local bisections and give an explicit formula for multiplication in the tangent groupoid. We continue with Section 1.5. Components and Transitivity. We show that the identity–component subgroupoid C is generated by symmetric neighbourhoods of the unit section, is open, and yields connected reductions of principal bundles by choosing components of the total space. Finally, orbits are shown to be submanifolds and transitive Lie groupoids are locally trivial.
• Lecture 6 (25 November 2025, 15:30 CEST), Paula Alba San Miguel (UNED, Madrid, Spain).
• Abstract: In this section we discuss Lie groupoid actions on smooth manifolds, the morphisms between such actions, and their intrinsic definition. We also apply results from previous sections to the study of actions.
• Lecture 7 (2 December 2025, 15:30 CEST), Tomasz Sobczak (KMMF-UW, Warsaw, Poland).
• Lecture 8 (9 December 2025, 15:30 CEST), Juan Manuel López Medel (ICMAT, Madrid, Spain).
• Abstract: We will mainly talk about linear actions, and the relation with representation. We study a proposition that gives us a lot of examples as Riemannian frame groupoid, complex frame groupoid... Lastly, we show how are the linear actions on the fundamental groupoid.