Enumerative geometry in the extended tropical vertex group

Abstract: The extended tropical vertex group is a pro-nilptotent Lie group, which has been introduced in [arxiv:1912.09956] studying the relationship between scattering diagrams and infinitesimal deformations of holomorphic pairs. Scattering diagrams were introduced by Kontsevich and Soibelman in the context of mirror symmetry. They are defined algebraically, in terms of pro-nilpotent Lie groups, but in many applications they have a combinatorial structure which encodes enumerative geometric data (as Donaldson--Thomas invariants, Gromov--Witten invariants,...). In particular, Gross, Pandharipande and Siebert showed how to compute genus zero log Gromov--Witten invariants for P^2 via scattering diagrams in the so called tropical vertex group. In this talk, I will discuss a possible generalization regarding how to compute genus zero relative Gromov--Witten invariants for toric P^2 using scattering diagrams in the extended tropical vertex group.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html