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October 07, 2020
Wednesday, October 07
Geometry and Topology
Time: 11:30
Speaker: Joel Villatoro (KU Leuven)
Title: "Diffeological Vector Bundles vs Sheaves of Modules"
Room: Zoom Meeting ID: 958 6908 4555

Abstract: In this talk I will give a quick overview on both diffeology, and sheaves of modules on smooth manifolds. Both diffeological vector bundles and sheaves of modules, can be thought of as generalizations of the notion of a vector bundle on a manifold. At first glance, the two approaches seem quite different, but I will show that one can construct a natural functor from the category of sheaves of modules to the category of diffeological vector bundles. We will then see that, under some fairly mild assumptions, this functor is actually an equivalence of categories. In the last part of the talk I will give some examples where understanding this correspondence has proven to be useful.