Seminar in Real and Complex Geometry

Thursday, November 10, 2022, 16:15-17:45, Orenstein 111 (and online via zoom)

Grigory Mikhalkin
(University of Geneve)

Tropical, real and symplectic geometry


This lecture will focus on the way how tropical curves appear in symplectic geometry settings. On one hand, tropical curves can be lifted as Lagrangian submanifolds in the ambient toric variety. On the other hand, they can be lifted as holomorphic curves. The two lifts use two different tropical structures on the same space, related by a certain potential function. We pay special attention to correspondence theorems between tropical curves and real curves, i.e. holomorphic curves invariant with respect to an antiholomorphic involution. The resulting real curves produce, in their turn, holomorphic membranes for tropical Lagrangian submanifolds.