Geometry of isomonodromic deformations and other directions of my scientific activity

  • Konstantin Kalinin (St. Petersburg State University)
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Let us consider a linear system on the Riemann sphere and assume that the coefficients of the system additionally depend on some parameter t (time). The following question is interesting: what can one say about the dependence of the coefficients on t, if monodromy is fixed? For a system with only simple poles, deformation equations have a very rich geometrical structure: it is a Hamiltonian system on a Lie algebra and the simplest non-trivial case corresponds to Painlev\'{e}~VI equation. I am going to talk about the simplest non-trivial case of a system with an irregular singular point. This system has the same structure and leads to Painlev\'{e}~V equation.