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Isoperiodic confocal families of conics and Painleve VI equations

  • 主讲人:Vladimir Dragovic (University of Texas at Dallas)
  • 举办方: Beijing-Novosibirsk Seminar on Geometry and Mathematical Physics
  • 时间: 2022-05-26 13:00 - 2022-05-26 14:00
  • 地点: online

Recording: https://disk.pku.edu.cn:443/link/E5B7644DC430D723D286320314989157
Valid Until: 2026-06-30 23:59

 

Abstract: We study Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal family, which is a question that naturally arose in the analysis of the numerical range and Blaschke products. We examine the behaviour of the rotation numbers and discover confocal families of conics with the property that each conic from the family is inscribed in k-Poncelet polygons inscribed in the circle, with the same k. Characterization of all such families is given and it is proved that they always correspond to k = 4. Relationship to the solutions to Painleve VI equations is established. This is based on joint work with Milena Radnovic.

 

Bio: Vladimir Dragovic is a Professor and Head of the Mathematical Sciences Department at the University of Texas at Dallas. Prior to this he was a Full Research Professor at Serbian Academy of Sciences and Arts, the founder and president of the Dynamical Systems group and co-president of The Centre for Dynamical Systems, Geometry and Combinatorics of the Mathematical Institute of the Serbian Academy of Sciences and Arts. Prof. Dragović graduated and received his Doctor of Sciences in Mathematics degree at the Faculty of Mathematics, University of Belgrade. His research interests include integrable dynamical systems with applications to classical and statistical mechanics, extremal polynomials, isomonodromy deformations, Painleve and Schlesinger equations, algebraic geometry and analysis on Riemann surfaces.

 

 

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