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SUMMARY:Faouzi Thabet (University of Gabès)
DTSTART:20231212T140000Z
DTEND:20231212T150000Z
DTSTAMP:20260422T201809Z
UID:CAvid/116
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/116/">
 Trajectories of Particular Quadratic Differentials on the Riemann Sphere</
 a>\nby Faouzi Thabet (University of Gabès) as part of CAvid: Complex Anal
 ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn this lecture\, 
 we give some basics of the theory of Quadratic\nDifferentials on the Riema
 nn Sphere. In the first part\, the focus will be on\nthe investigation of 
 the existence of finite critical trajectories\, and the\ndescription of th
 e critical graph of some quadratic differentials related to\nsolutions as 
 Cauchy transform of a signed measure of an algebraic quadratic\nequation a
 s the form : $p\\left( z\\right) \\mathcal{C}^{2}\\left( z\\right)\n+q\\le
 ft( z\\right) \\mathcal{C}\\left( z\\right) +r=0\,$ for some polynomials $
 p\,$\n$q$ and $r.$ As an example\, we study the large-degree analysis of t
 he\nbehaviour of the generalized Laguerre polynomials $L_{n}^{(\\alpha )}$
  when\nthe parameters are complex and depend on the degree $n$ linearly.\n
 \nIn the second part\, we describe the critical graph of a polynomial quad
 ratic\ndifferential related to the Schr\\"{o}dinger equation with cubic po
 tential.\n
LOCATION:https://researchseminars.org/talk/CAvid/116/
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