Mirror symmetry for Painlevé surfaces

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

03-Jul-2020, 16:00-17:00 (4 years ago)

Abstract: 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.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

( video )


Topological Quantum Field Theory Club (IST, Lisbon)

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