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SUMMARY:Tamara Grava (University of Bristol and SISSA)
DTSTART:20220927T130000Z
DTEND:20220927T140000Z
DTSTAMP:20260422T201412Z
UID:CAvid/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/86/">T
 he Stieltjes-Fekete problem and degenerate orthogonal polynomials</a>\nby 
 Tamara Grava (University of Bristol and SISSA) as part of CAvid: Complex A
 nalysis video seminar\n\nLecture held in N/A.\n\nAbstract\nA result of Sti
 eltjes famously relates the zeroes of the classical orthogonal polynomials
  with the configurations of points on the line that minimize a suitable lo
 garithmic energy\, or equivalently the solutions\nof a suitable weighted F
 ekete problem. The optimal configuration satisfies an algebraic set of equ
 ations with the logarithmic derivative of the weight function as ``externa
 l field": we call this set of algebraic\nequations the Stieltjes-Fekete pr
 oblem. In this work we consider the\nStieltjes-Fekete problem with an arbi
 trary rational external field. We\nshow that its solutions are in one-to-o
 ne correspondence with the zeroes of certain non-hermitean orthogonal poly
 nomials that satisfy an excess of orthogonality conditions and are thus te
 rmed ``degenerate". This generalizes the above mentioned result of Stieltj
 es.\n
LOCATION:https://researchseminars.org/talk/CAvid/86/
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