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SUMMARY:Türkü Özlüm Çelik (Koc University)
DTSTART:20231011T140000Z
DTEND:20231011T150000Z
DTSTAMP:20260424T095144Z
UID:FGC-IPM/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/40/"
 >Algebraic Curves from Polygons</a>\nby Türkü Özlüm Çelik (Koc Univer
 sity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nWe stud
 y constructing an algebraic curve from a Riemann surface given via a trans
 lation surface\, which is a collection of finitely many polygons in the pl
 ane with sides identified by translation. We use the theory of discrete Ri
 emann surfaces to give an algorithm for approximating the Jacobian variety
  of a translation surface whose polygon can be decomposed into squares. We
  first implement the algorithm in the case of L-shaped polygons where the 
 algebraic curve is already known. The algorithm is also implemented in any
  genus for specific examples of Jenkins-Strebel representatives\, a dense 
 family of translation surfaces that\, until now\, lived on the analytic si
 de of the transcendental divide between Riemann surfaces and algebraic cur
 ves. Using Riemann theta functions\, we give numerical experiments and res
 ulting conjectures up to genus 5.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/40/
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