Picture of Egor Pifagorov
Ezra Getzler (Northwestern University), "Higher Lie Groupoids"
by Egor Pifagorov - Thursday, 20 June 2019, 11:20 AM

Лаборатория Чебышева, аудитория 105 (14-я линия В. О., 29)
ср. 26 июня 17:15

Ezra Getzler (Northwestern University)

Higher Lie Groupoids

Lie groupoids are one of the basic ideas in geometry: they include manifolds, of course, but also the actions of Lie groups on manifolds, foliations, and are also important in the study of Poisson manifolds. (The analogous concept in algebraic geometry, Artin stacks, is also of great important in that subject, especially in the study of moduli.) In the last few decades, higher analogues of Lie groupoids have appeared in various mathematical problems, especially in physics. In this talk, I give an introduction to “what is a higher Lie groupoid?” and give a construction, due to myself and Kai Behrend, which associates to any differential graded Banach algebra (for example, finite dimensional
differential graded algebra) a higher Lie groupoid. This construction
generalizes the Lie group of invertible elements in a Banach algebra.