Integrable systems from Calabi-Yau categories


Rozenblyum, N. (2023). Integrable systems from Calabi-Yau categories. Perimeter Institute. https://pirsa.org/23040087


Rozenblyum, Nikita. Integrable systems from Calabi-Yau categories. Perimeter Institute, Apr. 06, 2023, https://pirsa.org/23040087


          @misc{ pirsa_PIRSA:23040087,
            doi = {10.48660/23040087},
            url = {https://pirsa.org/23040087},
            author = {Rozenblyum, Nikita},
            keywords = {Mathematical physics},
            language = {en},
            title = {Integrable systems from Calabi-Yau categories},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {apr},
            note = {PIRSA:23040087 see, \url{https://pirsa.org}}

Nick Rozenblyum University of Chicago


I will describe a general categorical approach to constructing Hamiltonian actions on moduli spaces. In particular cases, this specializes to give a ``universal" Hitchin integrable system as well as the Calogero-Moser system.  Moreover, I will describe a generalization to higher dimensions of a classical result of Goldman which says that the Goldman Lie algebra of free loops on a surface acts by Hamiltonian vector fields on the character variety of the surface.  A key input is a description of deformations of Calabi-Yau structures, which is of independent interest. This is joint work with Chris Brav.

Zoom link:  https://pitp.zoom.us/j/92929253744?pwd=WGFNQmRJck5NdzFFdU8xcXRlN3RRQT09