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Tom Sutherland
Tom Sutherland, Group of Mathematical Physics, University of Lisbon

Mirror symmetry for Painlevé surfaces

This talk will survey aspects of mirror symmetry for ten families of non-compact hyperkähler manifolds on which the dynamics of one of the Painlevé equations is naturally defined. They each have a pair of natural realisations: one as the complement of a singular fibre of a rational elliptic surface and another as the complement of a triangle of lines in a (singular) cubic surface. The two realisations relate closely to a space of stability conditions and a cluster variety of a quiver respectively, providing a perspective on SYZ mirror symmetry for these manifolds. I will discuss joint work in progress with Helge Ruddat studying the canonical basis of theta functions on these cubic surfaces.

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Projecto FCT UIDB/04459/2020.