Smooth 2-Groups and Their Principal Bundles

Explore the concept of smooth 2-groups and their principal bundles in this 46-minute lecture by Emily Cliff at the Centre de recherches mathématiques (CRM). Delve into the categorical generalization of groups, where 2-groups are introduced as categories with multiplication operations satisfying group axioms up to coherent isomorphisms. Discover the category of Lie groupoids and bibundles, which forms the foundation for defining smooth 2-groups. Learn about principal bundles for smooth 2-groups and examine classification results that compare them to principal bundles for ordinary groups. No prior knowledge of 2-groups or Lie groupoids is required for this talk, which is based on collaborative work with Dan Berwick-Evans, Laura Murray, Apurva Nakade, and Emma Phillips. This lecture is part of the Workshop on Quantum symmetries: Tensor Categories, Topological quantum field theories, and Vertex algebras held in October-November.