In a recent result with D. Aretz, we proved that the complete bornological convolution algebras of Lie groupoids and convolution bimodules of groupoid bibundles define a symmetric monoidal functor from the 2-category of differentiable stacks to the Morita 2-category of complete bornological algebras. (This is not quite true for $C^*$-algebras.) The convolution algebras can be thought of as the smooth noncommutative geometry of the differentiable stacks. I will motivate and explain all the ingredients of the theorem: differentiable stacks, 2-categories, the Morita 2-category, and bornological completion. As an application, I revisit the noncommutative torus which acquires the additional structure of a Hopf monoid.
海报.pdf
