Workshop on geometric structures, Lie groupoids and symmetries

This is a workshop on geometric structures, Lie groupoids and symmetries, supported by Universiteit Utrecht, which will be held on February 27th 2020 in Utrecht (The Netherlands), in occasion of the PhD defence of Francesco Cattafi.

Speakers:

Christian Blohmann (Max-Planck-Institut für Mathematik)
Bas Janssens (Technische Universiteit Delft)
María Amelia Salazar (Universidade Federal Fluminense)

Registration:

Registration is free but compulsory, in order to arrange lecture rooms and catering. Please contact f.cattafi[at]uu.nl AS SOON AS POSSIBLE if you are interested to participate.

Schedule:

10.30-11.00	Arrival	MIN 2.06
11.00-12.00	Talk Salazar	MIN 2.06
12.00-14.00	Lunch	Educatorium
14.00-15.00	Talk Blohmann	MIN 0.16
15.00-15.30	Coffee break	MIN 0.16
15.30-16.30	Talk Janssens	MIN 0.16

Titles and abstracts:

Local actions of bisection groups (Christian Blohmann) Abstract TBA
Pin groups and diffeomorphism invariance (Bas Janssens) A Pin group is a double cover of O(3,1) in much the same way as a Spin group is a double cover of SO(3,1). There are no less than eight different Pin groups. We argue that only two of these can be used to describe fermionic fields coupled to gravity in a diffeomorphism invariant way. Perhaps surprisingly, these are *not* the two Pin groups that are naturally associated to the Clifford algebras Cl(3,1) and Cl(1,3).
Van Est differentiation and integration (María Amelia Salazar)

The classical Van Est theory relates the smooth cohomology of Lie groups with the cohomology of the associated Lie algebra, or its relative versions. Some aspects of this theory generalize to Lie groupoids and their Lie algebroids. Continuing an idea from Li-Bland and Meinrenken, we revisit the van Est theory using the Perturbation Lemma from homological algebra. Using this technique, we obtain precise results for the van Est differentiation and integrations maps at the level of cochains. Specifically, we construct homotopy inverses to the van Est differentiation maps that are right inverses at the cochain level. This is joint work with E. Meinrenken.

Venue:

All activities will take place at Utrecht Science Park de Uithof. The talks will be in the Minnaert building (MIN): in room 2.06 (second floor) in the morning, and in room 0.16 (ground floor) in the afternoon. Both lecture rooms will be equipped with blackboards and a beamer. Lunch will be provided for free to all participants in the Educatorium canteen; please tell us in advance if you have any food allergies and/or other dietary requirements.

How to get there:

From Utrecht central station (Perron B2) you can get to the campus in 10 minutes by taking the new fast tram 22 (Direction Science Park P+R via Galgenwaard) and getting off at the stop Padualaan. Pay attention: unlike for buses, you have to check-in with your OV-chipkaart at the tram platform before boarding the tram (similarly for check-out). If for some reasons the tram does not run, or you are nostalgic of the slower route, another option is bus 28 (Direction Science Park P+R via Rijnsweerd), getting off at the stop Botanische Tuinen. There is also an OV-fiets service (bikes for rent, using the OV-chipkaart) available at the station, open from Monday to Friday, from 7.00 to 20.00. An invaluable source for travel information within the Netherlands is the route planner. For any further questions, please contact f.cattafi[at]uu.nl