Giorgos Kapetanakis

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Me in Hagia Sophia

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
Office 211, Building B
(+30) 22310 60164
4th GNTM GANT Seminar

Αcademic employment

Education

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. Translates of completely normal elements and the Morgan-Mullen conjecture
    T. Garefalakis and G. Kapetanakis
    Canad. Math. Bull., to appear, 2026
  2. An estimate for incomplete mixed character sums and applications
    A.C. Mazumder, G. Kapetanakis, S. Kala and D.K. Basnet
    Finite Fields Appl., 117(102874): 17pp., 2027
  3. Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields
    A.C. Mazumder, G. Kapetanakis and D.K. Basnet
    Finite Fields Appl.,110(102745): 14pp., 2026
  4. Existence of special types of primitive pairs in finite fields avoiding affine hyperplanes
    H. Hazarika, G. Kapetanakis and D.K. Basnet
    Appl. Algebra Engrg. Comm. Comput., 37:879-894, 2026
  5. Normal points on Artin-Schreier curves over finite fields
    G. Kapetanakis and L. Reis
    Comptes Rendus Math., 365:541-554, 2025
  6. Fq-primitive points on varieties over finite fields
    S. Takshak, G. Kapetanakis and R.K. Sharma
    Finite Fields Appl., 103(102582): 8pp., 2025
  7. The trace of primitive and 2-primitive elements in finite fields, revisited
    S.D. Cohen and G. Kapetanakis
    Southeast Asian Bull. Math., 48(2): 161-184, 2024
  8. The existence of Fq-primitive points on curves using freeness
    S.D. Cohen, G. Kapetanakis and L. Reis
    Comptes Rendus Math., 360:641-652, 2022
  9. On the existence of primitive normal elements of rational form over finite fields of even characteristic
    H. Hazarika, D.K. Basnet and G. Kapetanakis
    Internat. J. Algebra Comput., 32(2):357-382, 2022
  10. Finite field extensions with the line or translate property for r-primitive elements
    S.D. Cohen and G. Kapetanakis
    J. Aust. Math. Soc., 111(3):313-319, 2021
  11. The translate and line properties for 2-primitive elements in quadratic extensions
    S.D. Cohen and G. Kapetanakis
    Int. J. Number Theory, 16(9):2029-2040, 2020
  12. The trace of 2-primitive elements of finite fields
    S.D. Cohen and G. Kapetanakis
    Acta Arith., 192(4):397-419, 2020
  13. Further results on the Morgan-Mullen conjecture
    T. Garefalakis and G. Kapetanakis
    Des. Codes Cryptogr., 87(11):2639-2654, 2019
  14. A Swan-like note for a family of binary pentanomials
    G. Kapetanakis
    Appl. Algebra Engrg. Comm. Comput., 30(5):361-372, 2019
  15. Variations of the primitive normal basis theorem
    G. Kapetanakis and L. Reis
    Des. Codes Cryptogr., 87(7):1459-1480, 2019
  16. On the existence of primitive completely normal bases of finite fields
    T. Garefalakis and G. Kapetanakis
    J. Pure Appl. Algebra, 223(3):909-921, 2019
  17. Prescribing coefficients of invariant irreducible polynomials
    G. Kapetanakis
    J. Number Theory, 180:615-628, 2017
  18. Enumerating permutation polynomials
    T. Garefalakis and G. Kapetanakis
    Finite Fields Appl., 47:85-93, 2017
  19. A note on the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials
    T. Garefalakis and G. Kapetanakis
    Finite Fields Appl., 35:61-63, 2015
  20. Normal bases and primitive elements over finite fields
    G. Kapetanakis
    Finite Fields Appl., 26:123-143, 2014
  21. An extension of the (strong) primitive normal basis theorem
    G. Kapetanakis
    Appl. Algebra Engrg. Comm. Comput., 25(5):311-337, 2014
  22. On the Hansen-Mullen conjecture for self-reciprocal irreducible polynomials
    T. Garefalakis and G. Kapetanakis
    Finite Fields Appl., 18(4):832-841, 2012

Other journal publications

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

Preprints

  1. Existence of primitive normal pairs over finite fields with prescribed subtrace
    K. Chatterjee, G. Kapetanakis, S.K. Tiwari and H. Sharma
    arXiv:2405.11463 [math.NT], 2024
  2. An inductive proof of the Frobenius coin problem of two denominators
    G. Kapetanakis and I. Rizos
    arXiv:2308.03050 [math.NT], 2023
  3. Primitive normal pairs of elements with one prescribed trace
    A.C. Mazumder, H. Hazarika, D.K. Basnet and G. Kapetanakis
    arXiv:2306.03426 [math.NT], 2023

Theses

Talks

Teaching

Faculty Member (2021-today)

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

  1. Algebra
    Spring 2025-26, Spring 2024-25, Spring 2022-23, Spring 2021-22, Spring 2020-21
  2. Algebraic Coding Theory
    Spring 2025-26
  3. Operations Research
    Fall 2025-26, Fall 2024-25, Fall 2023-24, Fall 2021-22
  4. Introduction to Number Theory
    Spring 2023-24, Spring 2022-23, Spring 2021-22
  5. Group Theory
    Fall 2023-24
  6. Linear Algebra II
    Fall 2023-24, Fall 2021-22
  7. Ring and Module Theory
    Fall 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
    Fall 2020-21
  2. Discrete Mathematics
    Fall 2020-21, Spring 2018-19
  3. Number Theory
    Spring 2019-20
  4. Applied Algebra
    Fall 2019-20, Fall 2018-19
  5. Coding Theory
    Fall 2019-20
  6. Analytic Geometry and Complex Numbers
    Fall 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
    Spring 2019-20
  2. Financial Mathematics
    Fall 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
    Fall 2014-15
  2. Foundations of Mathematics
    Fall 2013-14
  3. General Mathematics II (at the Dept. of Materials Science and Engineering)
    Spring 2012-13
  4. Problem Laboratory
    Fall 2012-13
  5. Linear Algebra II
    Spring 2011-12
  6. Algebra
    Fall 2011-12, Spring 2007-08, Spring 2006-07

Activities

4th GNTM GANT Seminar ACA2025

Current and future activities

Past Activities

Editorial

Posters

ACA2025 Poster