Traces and higher structures

Christoph Schweigert (U Hamburg)

Aug 17. 2022, 10:00 — 11:00

Quantum topologists are used to think about traces
in the framework of spherical fusion categories, i.e.
in a two-dimensional context to which a two-dimensional
graphical calculus can be associated. We explain that traces
are already naturally defined for twisted endomorphisms of
linear categories, i.e. in a one-dimensional context.

For monoidal categories, the endomorphisms are twisted
by the Nakayama functor which is a twisted module functor
and hence an inherently three-dimensional object. This
naturally leads to a three-dimensional graphical calculus
which has natural applications to Turaev-Viro topological
field theories with defects.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures and Field Theory (Thematic Programme)
Anton Alekseev (U Genève)
Stefan Fredenhagen (U of Vienna)
Nicolai Reshetikhin (UC, Berkeley)
Thomas Strobl (U Lyon)
Chenchang Zhu (U Göttingen)