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 conformal field theory

Publications & Preprints:
Comments, corrections and suggestions are always welcome.
(Please take into account that published versions may differ from the ones below!)

(with M. Uludag and H. Ayral) InfoMod: A visual and computational approach to Gauss’ binary quadratic forms , submitted

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

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

(with M. Uludag) 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)

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

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

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

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

Polygonal Belyi morphisms, has evolved and became Belyi Lattes maps, submitted.

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

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:
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:
(with B.G. Cakti) Spiraller, Asal Sayilar ve Polinomlar, Matematik Dunyasi, 106

News

Nov. 11, 2018
Resultats de l'exament partiel 1 de Math 201: Analyse a Plusieurs Variables est disponible ici.

Nov. 11, 2018
The first mid-term exam of Math 504 : Advanced Algebra will take place on 21 Nov. 2018 Wednesday.

Oct. 27, 2018
Troisieme feuille d'exercices de Math 201: Analyse a Plusieurs Variables est disponible ici.

Oct. 27, 2018
The second exercise sheet of Math 504: Advanced Algebra is available here.

Oct. 29, 2016
Journees Arithmetiques will take place in Istanbul in 2019.