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SUMMARY:Bernat Espigulé (Universitat de Girona)
DTSTART:20260616T120000Z
DTEND:20260616T130000Z
DTSTAMP:20260513T203848Z
UID:OWNS/168
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/168/">R
 estricted polynomial roots\, reciprocal power series\, and finite capture 
 for collinear affine IFS</a>\nby Bernat Espigulé (Universitat de Girona) 
 as part of One World Numeration seminar\n\n\nAbstract\nI will discuss how 
 roots of polynomials with coefficients in a finite symmetric integer digit
  set can be studied through a family of affine iterated function systems w
 hose first-level pieces are centered on a line\, evenly spaced\, and symme
 tric with respect to the origin. After passing to reciprocal power series\
 , the closure of the relevant root sets outside the unit disk can be inter
 preted as a connectedness locus: zeros of such power series describe overl
 aps in the attractor. This viewpoint is related to the theory of planar se
 lf-affine tiles with collinear digit sets\, as studied by Akiyama\, Lorida
 nt\, Thuswaldner\, and the broader self-affine-tile and number-system lite
 rature.\n\nThe main part of the talk will explain a finite-capture procedu
 re for the non-real part of the locus\, based on successive geometric encl
 osures. In a precise parameter range\, this turns an infinite analytic pro
 blem into a finite geometric one. I will emphasize examples and pictures\,
  with only minimal formulas.\n\nThis is based on joint work with David Juh
 er\, building on earlier joint work with David Juher and Joan Saldaña.\n
LOCATION:https://researchseminars.org/talk/OWNS/168/
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