Frame PB-Groupoid of a VB-Groupoid
Explore the concept of frame PB-groupoids derived from VB-groupoids in this advanced mathematics lecture. Delve into the world of principal bundles and their significance in gauge theories, with a focus on frames of vector bundles on manifolds. Examine how these principal bundles relate to geometric connections, reduction, and various structures on underlying manifolds. Investigate the properties of a specialized principal bundle, specifically the set of frames on the tangent vector bundle TG, where G represents the space of arrows in a Lie groupoid. Discover how this configuration results in TG becoming a VB-groupoid and the corresponding principal bundle forming a PB-groupoid. Presented by Alfonso Garmendia from I'Institut d'Estudis Catalans, Barcelona, this 70-minute talk offers a deep dive into advanced mathematical concepts at the intersection of differential geometry and category theory.