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Severin Bunk
Severin Bunk, Universität Hamburg

Universal Symmetries of Gerbes and Smooth Higher Group Extensions

Gerbes are geometric objects describing the third integer cohomology group of a manifold and the B-field in string theory; they can essentially be understood as bundles of categories whose fibre is equivalent to the category of vector spaces. Starting from a hands-on example, I will explain gerbes and their categorical features. The main topic of this talk will then be the study of symmetries of gerbes in a universal manner. We will see that these symmetries are completely encoded in an extension of smooth 2-groups. In the last part, I will survey how this construction can be used to provide a new smooth model for the string group, via a theory of group extensions in $\infty$-topoi.

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