Topology and Geometry Seminar
Location: Live Stream
Speaker: Elliot Cheung, University of British Columbia
Title: Towards a Discretization of Chern-Simons Theory
Zoom Link: https://uregina-ca.zoom.us/j/97896109097?pwd=RkI2UkZsMlYyZTBzejhEY1R4RCt4Zz09
Abstract:
We will describe a discretization of Chern-Simons theory using Whitney forms. Derived moduli spaces are often described using L∞ algebras and it is interesting to explore how a derived moduli space varies as we modify the 'governing L∞ algebra' by a homotopy. In this example, we utilize the well-known Dupont homotopy operator to define a discretization of the infinite-dimensional DGLA controlling the moduli problem relevant to Chern-Simons theory. In doing so, we can describe an ( ind-) finite-dimensional model for a derived enhancement of the moduli space of flat connections on an oriented closed 3-manifold M equipped with a triangulation KM. This derived moduli space has a -1-shifted symplectic structure which also comes with 'geometric quantization data'. This can be used to define a 3-manifold invariant, which can be viewed as a discretization of Witten's Chern-Simons partition function invariant for 3-manifolds.