**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:**

Begüm Gülşah Çaktı, ongoing Ersin Süer, ongoing 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

Jan. 16, 2018

L'examen final de Math 201 : Analyse a Plusieurs Varibles est diponible ici .

Jan. 16, 2018

Resume de notes de Math 201 : Analyse a Plusieurs Varibles est diponible ici .

Jan. 08, 2019

The final exam of Math 504 : Advanced Algebra is available here.

Jan. 08, 2019

The summary of the grades of Math 504 : Advanced Algebra is available here.

Oct. 29, 2016

Journees Arithmetiques will take place in Istanbul in 2019.

Jan. 16, 2018

L'examen final de Math 201 : Analyse a Plusieurs Varibles est diponible ici .

Jan. 16, 2018

Resume de notes de Math 201 : Analyse a Plusieurs Varibles est diponible ici .

Jan. 08, 2019

The final exam of Math 504 : Advanced Algebra is available here.

Jan. 08, 2019

The summary of the grades of Math 504 : Advanced Algebra is available here.

Oct. 29, 2016

Journees Arithmetiques will take place in Istanbul in 2019.