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SUMMARY:Alexander Solynin (Texas Tech University\, USA)
DTSTART:20230502T130000Z
DTEND:20230502T140000Z
DTSTAMP:20260422T201242Z
UID:CAvid/103
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/103/">
 Quadratic differentials in complex analysis and beyond</a>\nby Alexander S
 olynin (Texas Tech University\, USA) as part of CAvid: Complex Analysis vi
 deo seminar\n\nLecture held in N/A.\n\nAbstract\nI will discuss the role o
 f quadratic differentials in the extremal\nproblems in Complex Analysis an
 d beyond. We start with main\ndefinitions\, then discuss \nJenkins' theory
  of extremal partitioning\, and then I will\nmention main results of the d
 ifferentiation theory for the\nJenkins' weighted sum of moduli suggested b
 y this speaker in\n1985-2000.\n\nTurning to applications\, I show first ho
 w quadratic differentials\ncan be used to study fingerprints of (complex) 
 polynomial\nlemniscates. The main result here includes\, as special cases\
 ,\nEbenfelt-Khavinson-Shapiro characterization of fingerprints of\npolynom
 ial lemniscates as well as Younsi characterization of\nrational lemniscate
 s. Then I will show that every real algebraic\ncurve can be treated as a t
 rajectory of a quadratic differential\ndefined on a certain Riemann surfac
 e.\n\n\nAfter that\, we will discuss how quadratic differentials on\n$\\ov
 erline{\\mathbf{C}}$ with the minimal possible number of poles\n(that is $
 4$) can be used to solve the problem on the canonical\nembeddings of pairs
  of arcs\, studied recently by M. Bonk and\nA. Eremenko\, and in several o
 ther extremal problems on ring\ndomains.\n
LOCATION:https://researchseminars.org/talk/CAvid/103/
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