Dmitri Pavlov, Texas Tech University

**Title**: The geometric cobordism hypothesis

**Abstract**: I will explain my recent joint work with Daniel Grady on 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 structures,

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, and a construction of power operations on the level of field theories (extending the recent work of Barthel-Berwick-Evans-Stapleton).

I will illustrate the general theory by constructing the prequantum Chern-Simons theory as a fully extended nontopological functorial field theory.

If time permits, I will discuss the ongoing work on defining quantization of field theories in the setting of the geometric cobordism hypothesis.