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Colliding holes in Riemann surfaces

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we will show that on the level of monodromy manifolds the confluence of the Painleve differential equations corresponds to colliding two holes or two sides of the same hole in a Riemann sphere. This procedure gives rise to the notion of bordered cusp in a Riemann surface. We will introduce the concept of "SL2 decorated character variety" of a Riemann surface with bordered cusps and we will show that such decorated character varieties are endowed with a generalised cluster algebra structure. We will also provide a very explicit quantisation procedure.

Mathematics; Ordinary differential equations; Dynamical systems and ergodic theory; Dynamical systems

video/mp4

Author affiliation: University of Loughborough

2017-04-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61107

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/