MC 6460 and Zoom (Please email amgrad@uwaterloo.ca for the meeting link)
Candidate
Peter Tsimiklis | Applied Mathematics, University of Waterloo
Title
Higher Gauge Theory and Discrete Geometry
Abstract
In four dimensions, gravity can be seen as a constrained topological model. This provides a natural way to construct quantum gravity models, since topological models are relatively straightforward to quantize. The difficulty arises in implementing the constraints to get gravity at the quantum level. Different procedures have generated the so-called Barrett-Crane and EPRL-FK spin foam models.
Following the dimensional/categorical ladder, the natural structures to quantize 4d topological models are 2-categories which augment the gauge group symmetries of the model into 2-group symmetries. These augmented 2-group models are natural since they can accommodate nonabelian decorations on the faces in the discrete picture.
In this talk, I will discuss the discretization and the quantization of topological theories with 2-group symmetries. In particular, I will construct a classical phase space for a given class of 2-symmetries. At the quantum level I will outline how to recover their partition function from the Feynman diagrams of a (2-group) field theory.