Alfonso Garmendia (KU Leuven University)
Quotients spaces present a problem in differential geometry, given that usually quotients of manifolds are not smooth. One way to deal with this problem is using Lie groupoids.
Nevertheless, a quotient space behaves different depending on which groupoid you decide to model it. Groupoids that are Morita equivalent give the same smooth behavior in their respective quotient space therefore the classes of Morita equivalent groupoids give the different models for the quotient space.
This talk uses the notions of quotient spaces and group actions to give an introduction on groupoids and Morita equivalence.