Families of singular connections and the Painlevé equations
AbstractThe theme of this talk is a systematic construction of the ten isomonodromic families of connections of rank two on the projective line inducing Painlevé equations and some families of connections living above elliptic curves. These are obtained by considering the complex analytic Riemann--Hilbert morphism from a moduli space of connections to a categorical moduli space of analytic data (i.e., ordinary monodromy, Stokes matrices and links), here called the monodromy space. Our method extends the work of Jimbo, Miwa and Ueno.
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