Wall-crossing structures and Chern-Simons theory.


Soibelman, Y. (2023). Wall-crossing structures and Chern-Simons theory.. Perimeter Institute. https://pirsa.org/23020047


Soibelman, Yan. Wall-crossing structures and Chern-Simons theory.. Perimeter Institute, Feb. 10, 2023, https://pirsa.org/23020047


          @misc{ pirsa_PIRSA:23020047,
            doi = {10.48660/23020047},
            url = {https://pirsa.org/23020047},
            author = {Soibelman, Yan},
            keywords = {Mathematical physics},
            language = {en},
            title = {Wall-crossing structures and Chern-Simons theory.},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {feb},
            note = {PIRSA:23020047 see, \url{https://pirsa.org}}

Yan Soibelman Kansas State University


In 2008 jointly with Maxim Kontsevich we introduced the notion of stability data on graded Lie algebras. In the case of the Lie algebra of vector fields on a symplectic torus it underlies the wall-crossing formulas for Donaldson-Thomas invariants of 3-dimensional Calabi-Yau categories. In 2013 we introduced the notion of wall-crossing structure, which is a locally-constant sheaf of stability data. Wall-crossing structures naturally appear in complex integrable systems, Homological Mirror Symmetry and many other topics not necessarily related to Donaldson-Thomas theory. Recently, in 2020 we introduced a sublass of analytic wall-crossing structures. We formulated a general conjecture that analytic wall-crossing structure gives rise to resurgent (i.e. Borel resummable) series.

Many wall-crossing structures have geometric origin, and moreover they naturally appear in our Holomorphic Floer Theory program. Aim of my talk is to discuss wall-crossing structures associated with a pair of holomorphic Lagrangian submanifolds of a complex symplectic manifold (in most cases it will be the cotangent bundle). These wall-crossing structures underly Cecotti-Vafa wall-crossing formulas, and as such they appear naturally in the study of exponential integrals in finite and infinite dimensions. I am going to explain our conjectural approach to Chern-Simons theory  which is based on the idea of wall-crossing structure. In some aspects this approach is related to the work of Witten on analytic continuation of Chern-Simons theory.

Zoom link:  https://pitp.zoom.us/j/99446428842?pwd=aDRzbFJoNytDNURDUVFMNGQzNjBFQT09