Seminar in Real and Complex Geometry

Thursday, February 1, 2018, 11:00-12:00, Schreiber building, room 209

Michael Polyak (Technion)

Pseudo-tropical curves


I will describe joint work with Sergei Lanzat. We consider a generalization of tropical curves, removing requirements of rationality of slopes and integrality and discuss the resulting theory and its interrelations with other areas. Balancing conditions are interpreted as criticality of a certain action functional. A generalized Bezout-Bernstein theorem involves Minkowsky sum and mixed areas. A problem of counting curves passing through an appropriate collection of points turns out to be related to quadratic Plücker relations in Gr(2,4) and some nice Lie algebra. I will also discuss a new recursive relation for this count.