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Refined curve counting and the tropical vertex group

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Sara Filippini (Universität Zürich)

  • Emmy Noether Kolloquium
When Nov 17, 2015
from 12:00 pm to 12:50 pm
Where Hilbertraum
Contact Name
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  • Emmy Noether Kolloquium
Wann 17.12.2015 
von 12:00 bis 12:50
Wo 05-432 (Hilbertraum)
Termin übernehmen  vCal

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-Goettsche 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.