Dynamics of extremal polynomials, isomonodromic and isoharmonic deformations

We establish a synergy of integrable billiards, extremal polynomials, Riemann surfaces, combinatorics, potential theory, and isomonodromic deformations. The cross-fertilization between ideas coming from these distinct fields lead to new results in each of them. We introduce a new notion of iso-harmonic deformations. We study their isomonodromic properties in the first nontrivial examples and indicate the genesis of a new class of isomonodromic deformations. The talk is based on the current research with Vasilisa Shramchenko and:

[1] Dragović V., Radnović M., Periodic ellipsoidal billiard trajectories and extremal polynomials, Comm. Math. Phys. 372 (2019), 183–211.
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