Welcome to my home page! I am a postdoc researcher at the Algebra and Number Theory Group of Sabanci University, under the supervision of Cem Güneri. You *are* interested in taking a look at **my CV** [pdf, Dropbox].

Email: | gnkapet@gmail.com |
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Address: | Sabanci University, Faculty of Engineering and Natural Sciences, Orhanli-Tuzla, 34956 Istanbul, Turkey. |

Office: | FENS 1001 |

**09/2016-02/2018:**Postdoctoral Researcher, Algebra and Number Theory Group, Sabanci University, Istanbul, Turkey (supervisors: Henning Stichtenoth and Alev Topuzoğlu).**02/2016-05/2016:**Postdoctoral Researcher, LabSEC, Federal University of Santa Catarina, Florianopolis, SC, Brazil (supervisor: Daniel Panario, short visit).

**PhD in Mathematics,**Department of Mathematics and Applied Mathematics, University of Crete, Greece (advisor: Theodoulos Garefalakis, thesis:*Polynomials with special properties over finite fields*). [pdf, slides]**MSc in Pure Mathematics,**Department of Mathematics, University of Crete, Greece (advisor: Theodoulos Garefalakis, thesis:*The Prime Number Theorem in Function Fields*, in greek). [pdf, slides]**BSc in Applied Mathematics**, Department of Mathematics, Univesrity of Athens, Greece (specialization: Computational Mathematics).

Research interests: I am interested in all aspects of finite fields and their applications including: polynomials, normal bases, primitive elements, permutation polynomials, coding theory and cryptography.

- G. Kapetanakis and L. Reis. Variations of the primitive normal basis theorem.
*Des. Codes Cryptogr.*, to appear. [pdf, arXiv, DOI] - T. Garefalakis and G. Kapetanakis. On the existence of primitive completely normal bases of finite fields.
*J. Pure Appl. Algebra*, to appear. [pdf, arXiv, DOI] - G. Kapetanakis. Prescribing coefficients of invariant irreducible polynomials.
*J. Number Theory*, 180:615-628, 2017. [pdf, DOI] - T. Garefalakis and G. Kapetanakis. Enumerating permutation polynomials.
*Finite Fields Appl.*, 47:85-93, 2017. [pdf, DOI] - T. Garefalakis and G. Kapetanakis. A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials.
*Finite Fields Appl.*, 35:61-63, 2015. [pdf, DOI] - G. Kapetanakis. Normal bases and primitive elements over finite fields.
*Finite Fields Appl.*, 26:123-143, 2014. [pdf, DOI] - G. Kapetanakis. An extension of the (strong) primitive normal basis theorem.
*Appl. Algebra Engrg. Comm. Comput.*, 25(5):311-337, 2014. [pdf, DOI, ShareIt] - T. Garefalakis and G. Kapetanakis. On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials.
*Finite Fields Appl.*, 18(4):832-841, 2012. [pdf, DOI]

- T. Garefalakis and G. Kapetanakis. Further results on the Morgan-Mullen conjecture. Submitted for publication.
- G. Kapetanakis. A Swan-like note for a family of binary pentanomials. Submitted for publication.

**Jun 2018:**On the existence of primitive completely normal bases of finite fields. First Congress of Greek Mathematicians, Department of Mathematics, University of Athens, Athens, Greece. [slides]**May 2018:**Variations of the primitive normal basis theorem. Antalya Algebra Days XX, Nesin Mathematics Village, Sirince, Izmir, Turkey. [slides]**Nov 2017:**Prescribing coefficients of invariant irreducible polynomials. FENS, Sabanci University, Istanbul, Turkey. (seminar)**Nov 2017:**Prescribing coefficients of invariant irreducible polynomials. Department of Mathematics, Bogazici University, Istanbul, Turkey. [slides]**Jun 2017:**On a conjecture of Morgan and Mullen. 13th International Conference on Finite Fields and their Applications (Fq13), Gaeta, Italy. [slides]**May 2017:**Prescribing coefficients of invariant irreducible polynomials. Antalya Algebra Days XIX, Nesin Mathematics Village, Sirince, Izmir, Turkey. [slides]**May 2017:**On a Conjecture of Morgan and Mullen. Department of Mathematics, Mimar Sinan Fine Arts University, Istanbul, Turkey. [slides]**Apr 2017:**On a Conjecture of Morgan and Mullen. Department of Mathematics, Bilkent University, Ankara, Turkey. [slides]**Oct 2016:**Details of the proof of the Hansen-Mullen conjecture for self-reciprocal polynomials. FENS, Sabanci University, Istanbul, Turkey. (seminar)**Oct 2016:**The Hansen-Mullen Conjecture. FENS, Sabanci University, Istanbul, Turkey. [slides]**Feb 2016:**Polynomials with Special Properties over Finite Fields. LabSEC, UFSC, Florianopolis, Brazil. [slides]**Jul 2013:**Normal Bases and Primitive Elements over Finite Fields. 11th International Conference on Finite Fields and their Applications (Fq11), Magdeburg, Germany. [slides]**Sep 2012:**An Extension of the Strong Primitive Normal Basis Theorem. RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials, Strobl, Austria. [slides]**Jul 2011:**On the Hansen-Mullen Conjecture for Self-Reciprocal Irreducible Polynomials. 10th International Conference on Finite Fields and their Applications (Fq10), Ghent, Belgium. [slides]

*Applicable Algebra in Engineering, Communication and Computing*, Referee.*Asian-European Journal of Mathematics*, Referee.*Communications in Algebra*, Referee.*Designs, Codes and Cryptography*, Referee.*Finite Fields and Their Applications*, Referee.*Journal of Number Theory*, Referee.*Linear Algebra and its Applications*, Referee.*Mathematical Reviews (MathSciNet)*, Reviewer*Open Mathematics*, Assistant Editor. [profile]

**Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece.** During my PhD and MSc studies, I served as a Teaching Assistant at the following undergraduate courses of the department (in Greek):

*Geometry and Linear Algebra*(fall 2014-2015).*Foundations of Mathematics*(spring 2013-2014).*General Mathematics II*(spring 2012-2013, at the Dept. of Materials Science and Technology).*Problem Laboratory*(fall 2012-2013).*Linear Algebra II*(spring 2011-2012).*Algebra*(fall 2011-2012, spring 2007-2008 and spring 2006-2007).