**Ayberk Zeytin**

Galatasaray Universitesi

Matematik Bolumu

Ciragan Cad. No.36, Besiktas, 34349

Istanbul / Turkey

Research

**Research Interests:**

action of the absolute Galois group on algebraic curves and surfaces,

subgroups of the modular group,

Teichmueller theory,

Weber's class number problems

and a bit of continued fractions

**Publications & Preprints:**

Comments, corrections and suggestions are always welcome.

(Please take into account that published versions may differ from the ones below!)

**Hecke continued fractions and Higman-Thompson groups**, submitted

**InfoMod: A visual and computational approach to Gauss’ binary quadratic forms , to appear in Applicable Algebra in Engineering, Communication and Computing**(DOI: 10.1007/s00200-020-00460-w)

**Multivariate Lucas Polynomials and Ideal Classes in Quadratic Number Fields , in Turk J Math, 42: 1543 – 1555, 2018**(DOI: 10.3906/mat-1608-65)

**Binary Forms and Euclidean Bianchi Groups , in progress**(with M.H. Sengun)

**A panorama of the fundamental group of the modular orbifold**, in

**Handbook of Teichmueller Theory, vol. VI**, pp: 501-519, (DOI: 10.4171/161-1/16) (with M. Uludag)

**Class number problems and Lang conjectures,**in Algebraic Geometry and Number Theory: Lecture Notes of a CIMPA-CMI-TUBITAK Summer School held at Galatasaray University Istanbul, 2014(Birkhauser-Progress in Mathematics), available online as an IHES preprint here

**The Cark Groupoid and Thompson's Groups, in progress**(with M. Uludag)

**On Reduction Theory of Binary Quadratic Forms,**Publ. Math. Debrecen, 89/1-2 (2016), 203–221. (DOI: 10.5486/PMD.2016.7470)

**Binary Quadratic Forms as Dessins**, J. Theor. Nombres Bordeaux 29/2 (2017), pp:445-469 (DOI: 10.5802/jtnb.987) (with M. Uludag and M. Durmus)

**Polygonal Belyi morphisms, has evolved and became Belyi Lattes maps, to appear in Kyushu Journal of Mathematics.**

**Quadrangulations of sphere and ball quotients , Math. Nachr.**287, No. 1, 105 - 121 (2014)(DOI: 10.1002/mana.201200174) (with M. Uludag)

The web-page of the software, called InfoMod, that is developed by H. Ayral, C. C. Sarioglu, A. M. Uludag and myself is here.

The PARI/gp code to do computations with carks is here (updated on 08.08.2016 with some more routines).

The PARI/gp code to do computations with complex continued fractions is here. At the moment, the algorithm works only for the fields Q(\sqrt(-1)) and Q(\sqrt(-2)). The algorithms are in progress, and do not have any claim of being optimal.

The above packages come WITHOUT ANY WARRANTY. Use at your own risk.

Recently, with my 11 year old laptop I've calculated a Belyi map (in fact a what I call Belyi-Lattes map) of degree 841, which took just above 5 minutes. You can see the map here.

With this PARI/gp code, you can compute much more complicated ones.

**Editorial:**

Number Theory: Proceedings of the Journées Arithmétiques, 2019, XXXI, Held at Istanbul University , De Gruyter, 2021 (with Kağan Kurşungöz)

Algebraic Geometry and Number Theory: Lecture Notes of a CIMPA-CMI-TUBITAK Summer School held at Galatasaray University

**MSc. Students:**

Ege Serdar, On the cohomology of Thompson's groups, ongoing (expected January 2024)

Begüm Gülşah Çaktı, On the Picard group of real quadratic number fields, now PhD candidate at Bogazici University

Şahan İzgi (Theta functions of indefinite binary quadratic forms), now math teacher at St. Pulchérie

Melike Efe (Classification of Lattes maps), obtained her PhD from Sabancı University

**Popular Math:**

(with B.G. Cakti)

**Spiraller, Asal Sayilar ve Polinomlar**, Matematik Dunyasi, 106

(with Ibrahim Emir Cicekli)

**Ikinci Kuvvette Karsiliklilik**, submitted to Matematik Dunyasi

News

Jul 22, 2023

Je vais enseigner Math 301 - Topologie ce semestre. Syllabus du cours est disponible ici.

Jul 22, 2023

Je vais enseigner Math 301 - Topologie ce semestre. Syllabus du cours est disponible ici.