Seminar in Real and Complex Geometry

Thursday, January 5, 2023, 16:15-17:45, online via zoom




Uriel Sinichkin
(Tel Aviv University)

Floor diagrams in tropical geometry


Abstract
             

This is the third talk in the introductory series, following "Introduction to tropical geometry" and "Refined tropical enumerative invariants". Floor diagrams is a combinatorial tool introduced by Brugalle and Mikhalkin to solve tropical enumerative questions and thus, by the correspondence theorem, classical questions in enumerative algebraic geometry. We will describe Mikhalkin's so-called "lattice path algorithm" and show how floor diagrams arise naturally from it. We then will show how floor diagrams can be used to compute and analyze complex, real, and refined invariants we saw in previous talks of the series. If time permits we will explore connections to relative Gromov-Witten invariants and generalizations to the enumeration of tropical hypersurfaces in higher dimensions.