Seminar in Real and Complex Geometry

Thursday, June 20, 2024, 16:15-17:45, online via zoom

Vladimir Fock
(Université de Strasbourg)

Singularities, Stokes data and clusters


In the talk we will suggest an explantation of a correspondence between singularities and quivers stated first by S.Fomin, P.Pylyavsky, E.Shustin, and D.Thurston. The observation is that a singularity in two variables as well as its versal deformations can (non-canonically) be transformed into a differential operators of one complex variable. The Stokes data of these operator amounts to be a flag configuration. The space of such configurations admits a cluster coordinates corresponding to FPST quiver. Amazingly, different differential operators corresponding to a given singularities give apparently different but birationally canonically isomorphic varieties.
We will discuss tropical limit of this construction making it more canonical and its relation to the combinatorics of FPST.