PIRSA:20050050

Projective elliptic genera and applications

Han, F. (2020). Projective elliptic genera and applications. Perimeter Institute. https://pirsa.org/20050050

Han, Fei. Projective elliptic genera and applications. Perimeter Institute, May. 25, 2020, https://pirsa.org/20050050 

          @misc{ pirsa_PIRSA:20050050,
            doi = {10.48660/20050050},
            url = {https://pirsa.org/20050050},
            author = {Han, Fei},
            keywords = {Mathematical physics},
            language = {en},
            title = {Projective elliptic genera and applications},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {may},
            note = {PIRSA:20050050 see, \url{https://pirsa.org}}
          }

Fei Han

National University of Singapore

Talk number
PIRSA:20050050
Collection
Talk Type
Subject
Abstract
Projective vector bundles (or gerbe modules) are generalizations of vector bundles in the presence of a gerbe on manifolds. Given a projective vector bundle, we will first show how to use it to twist the Witten genus to get modular invariants, which we call projective elliptic genera. Then we will give two applications: (1) given any pseudodifferential operator, we will construct modular invariants generalizing the Witten genus, which corresponds to the Dirac operator; (2) we will enhance the Hori map in T-duality to the graded Hori map and show that it sends Jacobi forms to Jacobi forms. This represents our joint works with Mathai.