Topology Seminar (Main Talk): Extended topological field theories in low dimensions

Seminar | March 15 | 4:10-5 p.m. | 3 Evans Hall

 Chris Schommer-Pries, Notre Dame

 Department of Mathematics

Our current understanding of the classification of (various kinds of) extended 3-dimensional topological field theories is fairly complete. I will survey aspects of this classification, which reveal connections between 3-dimensional topology and areas outside of topology such as fusion tensor categories (e.g. from subfactors of Von Neumann algebras), modular tensor categories (e.g. from quantum groups at roots of unity), and general non-semisimple tensor categories (e.g. from representations of hopf algebras). The underlying methods use techniques arising from Lurie's cobordism hypothesis combined with parametrized Morse theory. I hope to highlight more recent developments involving non-semisimple categories and partially defined topological field theories which might yield new avenues to explore in dimension four. This talk is based on various joint work with B. Bartlett, C. Douglas, N. Snyder, and J. Vicary.