Seminar in Real and Complex Geometry
Thursday, February 1, 2018, 11:00-12:00,
Schreiber building, room 209
Michael Polyak (Technion)
Pseudo-tropical curves
Abstract
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.
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