Algebraic Geometry Seminar

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Skeletons, Degenerations, and Gromov-Witten Theory

Speaker: Dhruv Ranganathan, Yale University

Location: Warren Weaver Hall 1314

Date: Tuesday, September 22, 2015, 3:30 p.m.

Synopsis:

Non-archimedean analytic geometry provides a precise geometric connection between tropical enumerative geometry and logarithmic Gromov--Witten theory. This framework leads to a simple new description of the algebraic moduli space of rational curves in toric varieties with prescribed contact orders. Applications include a new proof of Nishinou and Siebert's classical/tropical correspondence theorem and a new result on the structure of the tropical rational double Hurwitz cycle. Time permitting, I will explain how these ideas lead to a new perspective on the realization problem for embedded tropical curves in higher genus.