– Europe/Lisbon
Room P3.10, Mathematics Building — Online
The geometric cobordism hypothesis
I will explain my recent work with Daniel Grady on the locality of functorial field theories (arXiv:2011.01208) and the geometric cobordism hypothesis (arXiv:2111.01095). The latter generalizes the Baez–Dolan cobordism hypothesis to nontopological field theories, in which bordisms can be equipped with geometric structure, such as smooth maps to a fixed target manifold, Riemannian metrics, conformal structures, principal bundles with connection, or geometric string structures.
Applications include
- a generalization of the Galatius–Madsen–Tillmann–Weiss theorem;
- a solution to a conjecture of Stolz and Teichner on representability of concordance classes of functorial field theories;
- a construction of power operations on the level of field theories (extending the recent work of Barthel–Berwick-Evans–Stapleton);
- and a recent solution by Grady of a conjecture by Freed and Hopkins on deformation classes of reflection positive invertible field theories.
If time permits, I will talk about planned work on the nonperturbative quantization of functorial field theories and generalized Atiyah–Singer-style index theorems.
Additional file
Local participants are invited to join us in room 3.10 (3rd floor, Mathematics Department, Instituto Superior Técnico).