Begüm Gülşah Çaktı

I am a visiting PhD student at the University of Groningen and a final-year PhD student at Boğaziçi University. My advisor is Ekin Özman. Moreover,

• I am a research fellow funded by the Scientific and Technological Research Council of Türkiye (TÜBİTAK) through the 2214-A International Research Fellowship Programme for PhD Students.

• I am a research assistant at Galatasaray University.

• I was a part-time lecturer at İstanbul Bilgi University.

• I did my MSc at Koç University under the supervision of Ayberk Zeytin.

• I did my BSc at Galatasaray University.

My research interest is centered around solving Diophantine equations using the modular method. I am particularly interested in identifying generalized Fermat equations for which the Asymptotic Generalized Fermat Conjecture holds with an explicit and effectively computable bound over number fields. I also have a soft spot for elliptic curves!

Preprints:

1. Solving Fermat-type equations over quadratic fields, to appear in the International Journal of Number Theory. arXiv code paper

2. Solving equations of signature (p,p,2) with coefficients over number fields, submitted. arXiv code. (with Erman Işık, Yasemin Kara, Ekin Özman)

3. Twisted L-values for elliptic curves over function fields, submitted. (with Jessica Alessandrì, Céline Maistret, Miriam Ní Chobhthaigh, Thu-Hà Triệu, Hanneke Wiersema)

Theses:

1. On the Picard group of real quadratic number fields, MSc thesis

2. Corps de nombres cyclotomiques, Senior project

Expository Writing:

1. Asallar, Spiraller ve Polinomlar, Matematik Dünyası, 106 (with Ayberk Zeytin)