I am a faculty member at Groningen University.
Office: Groningen University, Bernoulli Institute, Bernoulliborg 356, Groningen, Netherlands
e-mail: e.ozman[at] rug [dot] nl
Research Interests: Arithmetic Geometry, Algebraic Number Theory, Rational Points on Curves, Brauer- Manin obstruction, Modular Curves, Q-Curves, Prym Varieties, Invariants of Curves over Algebraically Closed Fields of Characteristic p and Galois Towers of Curves.
Previous Employment: Before coming to Groningen University, I was a faculty memeber at Bogazici University, Istanbul, a post-doc at University of Texas-Austin and an EPDI Laureate.
Publications
Iterated Monodromy Group of a PCF Quadratic Non-polynomial Map, with Ö. Ejder and Y. Kara, submitted.
Computing Quadratic Points on Modular Curves X_0(N), with N. Adžaga, T. Keller, P. Michaud-Jacobs, F. Najman, and B. Vukorepa, to appear in Mathematics of Computation.
On Ternary Diophantine Equations of Signature (p,p,3) over Number Fields, with Isik and Kara, Canadian Journal of Mathematics, 75(4), 1293-1313, 2022.
The boundary of the p-rank 0 stratum of the moduli space of cyclic covers of the projective line, with Pries and Weir, Nagoya Math. J. 248, 865–887, 2022.
The Hasse Norm Principle in Global Function Fields, with A. Mânzăţeanu, R. Newton, N. Sutherland, R.G. Uysal, Research Directions in Number Theory, AWM Series, Springer,2021
S -Unit Equations and the Asymptotic Fermat Conjecture over Number Fields, with S. Siksek, Proceedings of the Journees Arithmetiques XXXI, 2021
On Ternary Diophantine Equations of Signature (p, p, 2) over Number Fields, with E. Isik and Y. Kara, Turkish Journal of Mathematics, 2020
A bound on the primes of bad reduction for CM curves of genus 3, with Kilicer, Lauter, Garcia,Newton and Streng, Proceedings of AMS, 2020
Asymptotic Generalized Fermat's Last Theorem over Number Fields, with Kara, International Journal of Number Theory, 2020
Rational Points On Twisted Modular Curves, in Automorphic Forms and Related Topics edited by Anni et al, Contemporary Mathematics, AMS, 2019
Quadratic Points on Modular Curves, with S. Siksek in Mathematics of Computation, 2019
On the existence of ordinary and almost ordinary Prym varieties, with R. Pries, in Asian Journal of Mathematics, 2019
Non-ordinary curves with a Prym variety of low p -rank, with Celik,Elias,Gunes,Newton, Pries and Thomas in Research Directions in Number Theory, AWM Series Vol. 11, 2018
RLWE Cryptography for the Number Theorist, with Elias,Lauter and Stange, Directions in Number Theory, AWM Series, Vol. 3, 2016
The distribution of Fq-Points on cyclic l-Covers of genus g, with Bucur,David,Feigon,Kaplan, Lalin and Wood in IMRN, 2016
Provably weak instances of Ring-LWE , with Elias,Lauter and Stange, Advances in Cryptology- CRYPTO2015, 2015
Bad reduction of genus-3 curves with complex multiplication, with Bouw,Cooley,Lauter, Garcia,Manes,Newton, in Research Directions in Number Theory, AWM Series, Vol. 2, 2015
Local-global trace questions, with Ciperiani, Proc. American Mathematical Society, 2015
Unramifed Brauer classes on cyclic covers of the projective plane, with Ingalls,Obus and Viray with an appendix by Thomas, Proc. of Brauer groups and obstruction problems, Birkhauser, 2016
On Polyquadratic Twists of X0(N), Journal of Number Theory, 2013
Newton and Hodge polygons for a variant of the Kloosterman family, with Bellovin, Garthwaite, Pries, Williams and Zhu. AMS/CRM Contemp. Research Directions in Number Theory, 2013
Points on Quadratic Twists of Modular Curves, Acta Arithmetica, 2012
Semi-direct product Galois covers of curves in characteristic p, with Gruendken, Hall-Seelig, Im, Pries and Stevenson, Fields Inst. Commun., 60, Amer. Math. Soc., 2011.
Books Edited
Women in Numbers Europe 2, Research Directions in Number Theory, AWM Series, Volume 11, Springer, 2018 with Bouw, Johnson-Leung and Newton
Popular Mathematics
Keşiflere Açılan Kapı: Hatalar, Matematik Dünyası 2014-I (A. Bassa, E. Özman)
Düzgün Asallar, Matematik Dünyası 2021-I
A4 kağıt, Pentagon ve Arşimet'in Sığırları, Matematik Dünyası 2014-II (A. Bassa, E. Özman)
Sır Vermeden Kanıtlamak, Matematik Dünyası (A. Bassa, E. Özman)
Students
Kubra Kaytanci(MSc), 2017
Ilkiz Bildik, (MSc), 2017
Eda Kirimli, (MSc), 2018
Erman Isik, (MSc), 2019
Tugce Koc (MSc), 2019
Harun Kir (MSc), 2019
Pinar Degirmenci (Msc), 2022 (co-advised with Beyarslan)
Omer Avci (Msc), 2024
Begum Gulsah Cakti (PhD)
Postdoctoral Researchers
Yasemin Kara, 2018-2020, PhD Cornell University
Özlem Ejder, 2020-2022, PhD, Southern California University