Research

In Preparation 

1. (w/ B.G. Catki, E. Ozman and Y. Kara) Modular Approach to the Diophantine Equation Ax^p + By^p = Cz^2 over Number Fields, (2025), in preparation.

2. Algebraic structure of fine Mordell-Weil groups and the growth of the plus-minus Tate-Shafarevich groups over anticyclotomic Zp-extensions of imaginary quadratic fields, (2025), in preparation.

Preprints

1. On Modular Approach to Diophantine Equation x^4-y^4=nz^p over Number Fields, (2023) arXiv.

Publications

1. (w/ Antonio Lei) On the growth of Tate-Shafarevich groups of p-supersingular abelian varieties of GL2-type over Zp-extensions of number fields, Journal of the Australian Mathematical Society (to appear), 2025, arXiv.

2. (w/ Antonio Lei) The growth of Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic Zp-extensions at inert primes, Mathematika, 2025, arXiv

3. On Anticyclotomic Iwasawa Theory of Hecke Characters at Ordinary Primes, Annales mathématiques du Québec (to appear), 2023, arXiv 

4. (w/ Ekin Ozman, Yasemin Kara) On Ternary Diophantine Equations of Signature (p, p, 3) over Number Fields, Canadian Journal of Mathematics, 2022,  Algorithms and results, arXiv

5. (w/ Ekin Ozman, Yasemin Kara) On Ternary Diophantine Equations of Signature (p, p, 2) Over Some Totally Real Number Fields, Turkish Journal of Mathematics, 2020, S-unit solution list, Number Fields list