Geometri- och topologiseminarium: Refined curve counting and the tropical vertex group
- Plats: Ångströmlaboratoriet 3419
- Föreläsare: Sara Angela Filippini (Cambridge University)
- Kontaktperson: Maksim Maydanskiy
Abstract: The tropical vertex group of Kontsevich and Soibelman is generated by formal symplectomorphisms of the 2-dimensional algebraic torus. It plays a role in many problems in algebraic geometry and mathematical physics. Based on the tropical vertex group, Gross, Pandharipande and Siebert introduced an interesting Gromov-Witten theory on weighted projective planes which admits a very special expansion in terms of tropical counts. I will describe a refinement or "q-deformation" of this expansion, motivated by wall-crossing ideas, using Block-Göttsche invariants. This leads naturally to the definition of a class of putative q-deformed curve counts. We prove that this coincides with another natural q-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined. This is joint work with Jacopo Stoppa.