Session S31 - Mathematical-Physical Aspects of Toric and Tropical Geometry

Tuesday, July 13, 12:15 ~ 13:15 UTC-3

Topological SYZ fibrations with discriminant in codimension two.

Ilia Zharkov

Kansas State University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

To date only for K3 surfaces (trivial) and the quintic threefold (due to M. Gross) the discriminant can be made to be in codimension two. I will outline the source of the problem and how to resolve it in much more general situations using phase and over-tropical pairs-of-pants. Joint project with Helge Ruddat. If time permits, I'll explain an application to lifting tropical cycles from the SYZ base to "holomorphic" and "Lagrangian" type objects in the torus fibrations.

Joint work with Helge Ruddat (University of Mainz, Germany), Grigory Mikhalkin (University of Geneva, Switzerland), Gabe Kerr (Kansas State University, USA) and Ludmil Katzarkov (University of Miami, USA & Higher School for Economics, Russia).

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