Functoriality of Lie groupoid convolution algebrasMPIM

by David Aretz (MPIM)

Wednesday Oct 22, 2025, 10:30 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Higher Differential Geometry Seminar

I will discuss the following guiding slogan: The noncommutative differential geometry of a differentiable stack is encoded in the convolution algebra of smooth functions on a Lie groupoid presentation. I will introduce the bornological convolution algebra associated to a Lie groupoid and show how this construction assembles into a 2-functor. In particular, this functorial perspective implies Morita invariance. I will also describe several examples illustrating how aspects of the transverse geometry of a Lie groupoid manifest algebraically in the convolution algebra. This is joint work with Christian Blohmann.