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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. |