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SUMMARY:Alexander Kiselev (Duke University)
DTSTART:20220602T153000Z
DTEND:20220602T163000Z
DTSTAMP:20260423T035905Z
UID:SIAM-PDE/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/21/
 ">The flow of polynomial roots under differentiation</a>\nby Alexander Kis
 elev (Duke University) as part of Seminar In the Analysis and Methods of P
 DE (SIAM PDE)\n\n\nAbstract\nFeatured Article:   "Global regularity for a 
 nonlocal PDE describing evolution of polynomial roots under differentiatio
 n"\, to appear\, SIAM J Math Analysis \n\nFeatured Article Authors: A. Kis
 elev\, Changhui Tan \n\nThe question of how roots of polynomials move unde
 r differentiation is classical. Contributions to this subject have been ma
 de by Gauss\, Lucas\, Marcel Riesz\, Polya and many others. In 2018\, Stef
 an Steinerberger derived formally a PDE that should describe the dynamics 
 of roots under differentiation in certain situations. The PDE in question 
 is of hydrodynamic type and bears a striking resemblance to the models use
 d in mathematical biology to describe collective behavior and flocking of 
 various species - such as fish\, birds or ants. The equation is critical\,
  but due to strongly nonlinear form of its coefficients\, proving global r
 egularity for its solutions is harder than for equations such as Burgers\,
  SQG or Euler alignment model. I will discuss joint work with Changhui Tan
  in which we establish global regularity of Steinerberger's equation and m
 ake a rigorous connection between its solutions and evolution of roots und
 er differentiation for a class of trigonometric polynomials.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/21/
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