Giorgos Kapetanakis

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I am an assistant professor at the Department of Mathematics of the University of Thessaly. You may be interested in taking a look at my CV .

Contact details

	gnkapet@gmail.com
	Department of Mathematics, University of Thessaly, 3rd km Old National Road Lamia-Athens, 35100 Lamia, Greece
	211, Building B
	(+30) 22310 60164

Events and seminars

• Algebra and Number Theory Session of the Third Congress of Greek Mathematicians - TCGM 2026, Athens, Greece, 2026.
• Greek Algebra & Number Theory Seminar (G.A.N.T.), online.

Prior academic employment

• 10/2018-01/2021: Adjunct Faculty Member, Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece.
• 09/2016-09/2018: Postdoctoral Researcher, Algebra and Number Theory Group, Sabanci University, Istanbul, Turkey.
• 02/2016-05/2016: Postdoctoral Researcher, LabSEC, Federal University of Santa Catarina, Florianopolis, SC, Brazil.

Education

• PhD in Mathematics, Department of Mathematics and Applied Mathematics, University of Crete, Greece.
• MSc in Pure Mathematics, Department of Mathematics, University of Crete, Greece.
• BSc in Mathematics, Department of Mathematics, University of Athens, Greece.

Research

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

Mathematical journal publications

1. T. Garefalakis and G. Kapetanakis. Translates of completely normal elements and the Morgan-Mullen conjecture. Canad. Math. Bull., to appear, 2026.
2. A.C. Mazumder, G. Kapetanakis, S. Kala and D.K. Basnet. An estimate for incomplete mixed character sums and applications. Finite Fields Appl., to appear, 2026.
3. A.C. Mazumder, G. Kapetanakis and D.K. Basnet. Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields. Finite Fields Appl.,110(102745): 14pp., 2026.
4. H. Hazarika, G. Kapetanakis and D.K. Basnet. Existence of special types of primitive pairs in finite fields avoiding affine hyperplanes. Appl. Algebra Engrg. Comm. Comput., 37:879-894, 2026.
5. G. Kapetanakis and L. Reis. Normal points on Artin-Schreier curves over finite fields. Comptes Rendus Math., 365:541-554, 2025.
6. S. Takshak, G. Kapetanakis and R.K. Sharma. F_q-primitive points on varieties over finite fields. Finite Fields Appl., 103(102582): 8pp., 2025.
7. S.D. Cohen and G. Kapetanakis. The trace of primitive and 2-primitive elements in finite fields, revisited. Southeast Asian Bull. Math., 48(2): 161-184, 2024.
8. S.D. Cohen, G. Kapetanakis and L. Reis. The existence of F_q-primitive points on curves using freeness. Comptes Rendus Math., 360:641-652, 2022.
9. H. Hazarika, D.K. Basnet and G. Kapetanakis. On the existence of primitive normal elements of rational form over finite fields of even characteristic. Internat. J. Algebra Comput., 32(2):357-382, 2022.
10. S.D. Cohen and G. Kapetanakis. Finite field extensions with the line or translate property for r-primitive elements. J. Aust. Math. Soc., 111(3):313-319, 2021.
11. S.D. Cohen and G. Kapetanakis. The translate and line properties for 2-primitive elements in quadratic extensions. Int. J. Number Theory, 16(9):2029-2040, 2020.
12. S.D. Cohen and G. Kapetanakis. The trace of 2-primitive elements of finite fields. Acta Arith., 192(4):397-419, 2020.
13. T. Garefalakis and G. Kapetanakis. Further results on the Morgan-Mullen conjecture. Des. Codes Cryptogr., 87(11):2639-2654, 2019.
14. G. Kapetanakis. A Swan-like note for a family of binary pentanomials. Appl. Algebra Engrg. Comm. Comput., 30(5):361-372, 2019.
15. G. Kapetanakis and L. Reis. Variations of the primitive normal basis theorem. Des. Codes Cryptogr., 87(7):1459-1480, 2019.
16. T. Garefalakis and G. Kapetanakis. On the existence of primitive completely normal bases of finite fields. J. Pure Appl. Algebra, 223(3):909-921, 2019.
17. G. Kapetanakis. Prescribing coefficients of invariant irreducible polynomials. J. Number Theory, 180:615-628, 2017.
18. T. Garefalakis and G. Kapetanakis. Enumerating permutation polynomials. Finite Fields Appl., 47:85-93, 2017.
19. T. Garefalakis and G. Kapetanakis. A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials. Finite Fields Appl., 35:61-63, 2015.
20. G. Kapetanakis. Normal bases and primitive elements over finite fields. Finite Fields Appl., 26:123-143, 2014.
21. G. Kapetanakis. An extension of the (strong) primitive normal basis theorem. Appl. Algebra Engrg. Comm. Comput., 25(5):311-337, 2014.
22. T. Garefalakis and G. Kapetanakis. On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials. Finite Fields Appl., 18(4):832-841, 2012.

Other journal publications

1. G. Kapetanakis and I. Rizos. Teaching perspectives of the Frobenius coin problem of two denominators. Teach. Math., XXVI(2):57-67, 2023.

Preprints

1. K. Chatterjee, G. Kapetanakis, S.K. Tiwari and H. Sharma. Existence of primitive normal pairs over finite fields with prescribed subtrace. Submitted for publication, 2024.
2. G. Kapetanakis and I. Rizos. An inductive proof of the Frobenius coin problem of two denominators. Submitted for publication, 2023.
3. A.C. Mazumder, H. Hazarika, D.K. Basnet and G. Kapetanakis. Primitive normal pairs of elements with one prescribed trace. Submitted for publication, 2023.

Theses

• PhD: Polynomials with special properties over finite fields. Department of Mathematics and Applied Mathematics, University of Crete, Greece.
• MSc: The prime number theorem in function fields (in greek). Department of Mathematics, University of Crete, Greece.

Talks

• Jul 2026: Translates of completely normal elements and the Morgan-Mullen conjecture, 3rd Congress of Greek Mathematicians, Athens, Greece.
• May 2026: Translates of completely normal elements and the Morgan-Mullen conjecture, Department of Mathematics, University of Western Macedonia, Kastoria, Greece.
• Dec 2025: Translates of completely normal elements and the Morgan-Mullen conjecture, 3rd Greek Number Theory Meeting, Patras, Greece.
• Jul 2025: Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields. 30th Conference on Applications of Computer Algebra (ACA 2025), Heraklion, Greece.
• May 2025: An estimate for incomplete mixed character sums and applications. 10th Greek Algebra and Number Theory Conference, Heraklion, Greece.
• Dec 2023: The existence of Fq-primitive points on curves using freeness. 1st Greek Number Theory Meeting, Athens, Greece.
• Jun 2023: The line and the translate properties for r-primitive elements. 15th International Conference on Finite Fields and Their Applications (Fq15), Paris, France.
• May 2023: The line and the translate properties for r-primitive elements. 9th Greek Algebra and Number Theory Conference, Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece.
• Apr 2023: Towards the primitive completely normal basis theorem. Greek Algebra & Number Theory Seminar (GANT).
• Dec 2021: The existence of Fq-primitive points on curves using freeness. Carleton Finite Fields eSeminar, School of Mathematics and Statistics, Carleton University, Ottawa, Canada.
• Nov 2021: The existence of Fq-primitive points on curves using freeness. Post-graduate program workshop, Department of Mathematics, University of the Aegean, Karlovasi, Samos, Greece.
• May 2021: Towards the primitive completely normal basis theorem. Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece.
• Apr 2019: The line and the translate problem for r-primitive elements. FENS, Sabanci University, Istanbul, Turkey.
• Nov 2018: (Almost) normal and (almost) primitive elements of finite fields. Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece.
• Jun 2018: On the existence of primitive completely normal bases of finite fields. 1st Congress of Greek Mathematicians, Department of Mathematics, University of Athens, Athens, Greece.
• May 2018: Variations of the primitive normal basis theorem. Antalya Algebra Days XX, Nesin Mathematics Village, Sirince, Izmir, Turkey.
• Nov 2017: Prescribing coefficients of invariant irreducible polynomials. FENS, Sabanci University, Istanbul, Turkey.
• Nov 2017: Prescribing coefficients of invariant irreducible polynomials. Department of Mathematics, Bogazici University, Istanbul, Turkey.
• Jun 2017: On a conjecture of Morgan and Mullen. 13th International Conference on Finite Fields and their Applications (Fq13), Gaeta, Italy.
• May 2017: Prescribing coefficients of invariant irreducible polynomials. Antalya Algebra Days XIX, Nesin Mathematics Village, Sirince, Izmir, Turkey.
• May 2017: On a Conjecture of Morgan and Mullen. Department of Mathematics, Mimar Sinan Fine Arts University, Istanbul, Turkey.
• Apr 2017: On a Conjecture of Morgan and Mullen. Department of Mathematics, Bilkent University, Ankara, Turkey.
• Oct 2016: Details of the proof of the Hansen-Mullen conjecture for self-reciprocal polynomials. FENS, Sabanci University, Istanbul, Turkey.
• Oct 2016: The Hansen-Mullen Conjecture. FENS, Sabanci University, Istanbul, Turkey.
• Feb 2016: Polynomials with Special Properties over Finite Fields. LabSEC, UFSC, Florianopolis, Brazil.
• Jul 2013: Normal Bases and Primitive Elements over Finite Fields. 11th International Conference on Finite Fields and their Applications (Fq11), Magdeburg, Germany.
• 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.
• Jul 2011: On the Hansen-Mullen Conjecture for Self-Reciprocal Irreducible Polynomials. 10th International Conference on Finite Fields and their Applications (Fq10), Ghent, Belgium.

Editorial

• Proceedings of the 30tʰ Applications of Computer Algebra (ACA 2025), Springer Proceedings in Mathematics & Statistics, Springer (to appear). Editor with Z. Zafeirakopoulos, I. Kotsireas and M. Wester.

Service (journals)

• Acta Arithmetica, Referee.
• Advances in Mathematics of Communications, Referee.
• Applicable Algebra in Engineering, Communication and Computing, Referee.
• Asian-European Journal of Mathematics, Referee.
• Bulletin of the Brazilian Mathematical Society, New Series, Referee.
• Bulletin of the London Mathematical Society, Referee.
• Chinese Annals of Mathematics, Series B, Referee.
• Communications in Algebra, Referee.
• Cryptography and Communications, Referee.
• Designs, Codes and Cryptography, Referee.
• Discrete Mathematics, Referee.
• Finite Fields and Their Applications, Referee.
• Forum Mathematicum, Referee.
• IEEE Open Journal of Circuits and Systems, Referee.
• IEEE Transactions on Information Theory, Referee.
• Indian Journal of Pure and Applied Mathematics, Referee.
• Journal of Algebra, Referee.
• Journal of Algebra and Its Applications, Referee.
• Journal of Mathematical Research with Applications, Referee.
• Journal of Number Theory, Referee.
• Journal of Pure and Applied Algebra, Referee.
• La Matematica: Official Journal of the Association for Women in Mathematics, Referee.
• Linear Algebra and its Applications, Referee.
• Mathematical Reviews (MathSciNet), Reviewer.
• Mathematics of Computation, Reviewer.
• Open Mathematics, Assistant Editor and Referee.
• The Ramanujan Journal, Referee.

Service (conferences)

• 30th Conference on Applications of Computer Algebra (ACA 2025), Heraklion, Greece, 2025, Chair.
• International Workshop on the Arithmetic of Finite Fields (WAIFI 2024), Ottawa, Canada, 2024, Reviewer.
• 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022), Philadelphia, PA, USA, 2022, Reviewer.
• International Workshop on the Arithmetic of Finite Fields (WAIFI 2020), Rennes, France, 2020, Reviewer.
• 14th International Conference on Finite Fields and their Applications (Fq14), Vancouver, Canada, 2019, Reviewer.
• Mathematical Aspects of Computer and Information Sciences, Gebze/Istanbul, Turkey, 2019, Program Comittee.
• The Tenth International Workshop on Coding and Cryptography, Saint-Petersburg, Russia, 2017, Reviewer.
• Workshop on Mathematics in Communications, Santander, Spain, 2016, Reviewer.

Teaching

Assistant Professor (2021-today)

Department of Mathematics, University of Thessaly, Greece. I have taught the following courses of the department:

1. Algebra, SS 2025-26, SS 2024-25, SS 2022-23, SS 2021-22, SS 2020-21.
2. Algebraic Coding Theory, SS 2025-26.
3. Operations Research, FS 2025-26, FS 2024-25, FS 2023-24, FS 2021-22.
4. Introduction to Number Theory, SS 2023-24, SS 2022-23, SS 2021-22.
5. Group Theory, FS 2023-24.
6. Linear Algebra II, FS 2023-24, FS 2021-22.
7. Ring and Module Theory, FS 2022-23.

Adjunct Faculty Member (2018-2021)

Department of Mathematics and Applied Mathematics, University of Crete, Greece. I have taught the following courses of the department:

1. Introduction to Linear Algebra, FS 2020-21.
2. Discrete Mathematics, FS 2020-21, SS 2018-19.
3. Number Theory, SS 2019-20.
4. Applied Algebra, FS 2019-20, FS 2018-19.
5. Coding Theory, FS 2019-20.
6. Analytic Geometry and Complex Numbers, FS 2018-19.

Scientific Collaborator (2019-2020)

Higher School of Tourism Education of Crete (ASTEK), Greece. I have taught the following courses of the school:

1. Business Statistics, SS 2019-20.
2. Financial Mathematics, FS 2019-20.

Teaching Assistant (2006-2015)

Department of Mathematics and Applied Mathematics, University of Crete, Greece. During my PhD and MSc studies, I served as a Teaching Assistant at the following courses of the department:

1. Geometry and Linear Algebra, FS 2014-15.
2. Foundations of Mathematics, FS 2013-14.
3. General Mathematics II (at the Dept. of Materials Science and Engineering), SS 2012-13.
4. Problem Laboratory, FS 2012-13.
5. Linear Algebra II, SS 2011-12.
6. Algebra, FS 2011-12, SS 2007-08, SS 2006-07.

Legend: FS=Fall Semester; SS=Spring Semester.

Giorgos Kapetanakis.