PIRSA:17120020

Fully extended functorial field theories and dualizability in the higher Morita category

Scheimbauer, C. (2017). Fully extended functorial field theories and dualizability in the higher Morita category. Perimeter Institute. https://pirsa.org/17120020

Scheimbauer, Claudia. Fully extended functorial field theories and dualizability in the higher Morita category. Perimeter Institute, Dec. 11, 2017, https://pirsa.org/17120020 

          @misc{ pirsa_PIRSA:17120020,
            doi = {10.48660/17120020},
            url = {https://pirsa.org/17120020},
            author = {Scheimbauer, Claudia},
            keywords = {Mathematical physics},
            language = {en},
            title = {Fully extended functorial field theories and dualizability in the higher Morita category},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {dec},
            note = {PIRSA:17120020 see, \url{https://pirsa.org}}
          }

Claudia Scheimbauer Technical University of Munich (TUM)

DOI 10.48660/17120020
Collection
Talk Type Scientific Series
Subject

Abstract

Atiyah and Segal's axiomatic approach to topological and conformal quantum field theories provided a beautiful link between the geometry of "spacetimes" (cobordisms) and algebraic structures. Combining this with the physical notion of "locality" led to the introduction of the language of higher categories into the topic.
Natural targets for extended topological field theories are higher Morita categories: generalizations of the bicategory of algebras, bimodules, and homomorphisms.

After giving an introduction to topological field theories, I will explain how one can use geometric arguments to obtain results on dualizablity in a ``factorization version’’ of the Morita category and using this, examples of low-dimensional field theories “relative” to their observables. An example will be given by polynomial differential operators, i.e. the Weyl algebra, in positive characteristic and its center. This is joint work with Owen Gwilliam.