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!)

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, submitted.

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.

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

MSc. Students:
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), now a PhD student at Sabancı University

Popular Math:
recently, with my 8 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. (with B.G. Cakti) Spiraller, Asal Sayilar ve Polinomlar, Matematik Dunyasi, 106

News

Aug 04, 2020
I will be teaching Math 504 - Advanced Algebra in Fall 2021. Course syllabus will be available here.

Aug 04, 2020
Je vais enseigner Math 201 - Analyse a Plusieurs Variables I ce semestre. Syllabus du cours va apparaitre ici.