[Turkmath:6202] FGC-IPM-HRI online number theory seminars

[Özlem Ejder]

Dear all,

We would like to announce that in 6 days (from now) the new semester of the
"FGC-IPM Number Theory Webinars" will start. Our first speaker is Türkü
Özlüm Çelik from Koç University.

*Date and Time*: Wednesday October 11, 2022,  at *17:00.*

Zoom link: https://kocun.zoom.us/j/99715471656
Meeting ID: 997 1547 1656
passcode: 848084

*Title: *Algebraic Curves from Polygons

*Abstract: *
We study constructing an algebraic curve from a Riemann surface given via a
translation surface, which is a collection of finitely many polygons in the
plane with sides identified by translation. We use the theory of discrete
Riemann 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 side of the transcendental divide between Riemann
surfaces and algebraic curves. Using Riemann theta functions, we give
numerical experiments and resulting conjectures up to genus 5.


You can find the upcoming talks at
https://researchseminars.org/seminar/FGC-IPM.

Sevgiler
Özlem
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