**Contact:**

E-mail: pnkoumantos[at]gmail.com

Welcome to my homepage!

I am a Mathematician working in the field of Mathematical Physics, differential equations, ergodic theorems and dynamical systems, and integral equations.

**Education**

· PhD in Mathematical Physics, Department of Physics, University of Athens, Greece (2019).

· MSc Basic Physics diploma with specialization in Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Greece (2010).

· Ptychion (BSc) in Mathematics (towards theoretical mathematics), Department of Mathematics, University of Athens, Greece (2006).

**Research Interests**

Mathematical Physics, Differential equations, Ergodic theory, Dynamical Systems, Integral equations.

**S****cientific Services**

Zentralblatt für Mathematik (zbMATH) zbMATH

Mathematical Reviews (MR) mathscinet-MR

**Publications**

*Dissertations**:*

[1] P. N. Koumantos, Differential *Evolution Equations in Theoretical Mechanics*, PhD Dissertation, University of Athens, Athens 2019. pergamos.lib.uoa.gr/uoa/dl/object/2866624 ; thesis.ekt.gr/thesisBookReader/id/45354#page/1/mode/2up

Advisor: Associate Professor Panaiotis Pavlakos (Department of Mathematics).

[2] P.N. Koumantos, *Ergodic Theorems in Classical and Quantum Mechanics*, MSc Dissertation, University of Athens, Athens 2010. opac.seab.gr/record=b1535079~S6*gre

Advisor: Associate Professor Panaiotis Pavlakos (Department of Mathematics).

*Book Chapters: *

[1] E. S. Athanasiadou, V. F. Dionysatos, P. N. Koumantos, and P. K. Pavlakos,* Almost periodic solutions of Navier-Stokes-Ohm type equations in Magneto-hydrodynamics*, In: Applications of Mathematics and Informatics to Science and Engineering, Daras, Nicholas J. (Ed.), Springer Optimization and Its Applications Vol. 91, pp. 43-57, Springer 2014. MR 3329748; Zbl 1302.35354 doi.org/10.1007/978-3-319-04720-1_3

*Articles:*

[1] P. N. Koumantos, *Order topology** in Minkowski space and applications*, Rep. Math. Phys. 87 (2) (2021), 209-223. doi.org/10.1016/S0034-4877(21)00026-4

[2] P. N. Koumantos, *Uniqueness of the solution of a nonlinear algebraic system* *(*to appear).

[3] P. N. Koumantos, *Nonlinear evolution equations in Minkowski space-time*, Rep. Math. Phys. 84 (2) (2019), 187-199. MR 4026502; Zbl 07239556 doi.org/10.1016/S0034-4877(19)30082-5

[4] C. L. Asimomytis, P. N. Koumantos and P. K. Pavlakos,* Nonlinear Volterra-type diffusion equations and theory of quantum fields*, Math. Methods Appl. Sci. 41 (3) (2018), 1107-1113. MR 3762337; Zbl 06857705 doi.org/10.1002/mma.4486

[5] P. N. Koumantos, *On the structure of space-time and linear evolution equations*, J. Appl. Math. Bioinf. 8 (2) (2018), 1-15. www.scienpress.com/journal_focus.asp?main_id=57&Sub_id=IV&volid=358

[6] P. N. Koumantos, *Mean ergodic theorems for Lorentz operators*, Rep. Math. Phys. 80 (2) (2017), 153-159. MR 3721903; Zbl 06861678 doi.org/10.1016/S0034-4877(17)30073-3

[7] P. N. Koumantos and M. E. Makraki,* On Carathéodory formula in triangle geometry*, Octogon 24 (2) (2016), 469-480. www.uni-miskolc.hu/~matsefi/Octogon/index.php?menu=archive&volume=2016_2

[8] P. N. Koumantos, O. R. Katsikas, E. S. Athanasiadou and P. K. Pavlakos,* On commutative and non-commutative quantum stochastic diffusion flows*, J. Appl. Math. Bioinf. 5 (3) (2015), 97-112. Zbl 1356.34076 www.scienpress.com/journal_focus.asp?main_id=57&Sub_id=IV&volid=208

[9] E. S. Athanasiadou, V. F. Dionysatos, P. N. Koumantos and P. K. Pavlakos, *A semigroup approach to functional differential evolution equations*, Math. Methods Appl. Sci. 37 (2) (2014), 217-222. MR 3153097; Zbl 1321.34098 doi.org/10.1002/mma.2891

[10] P. N. Koumantos, P. K. Pavlakos and X. D. Moussas, *On solutions in the hydrodynamic approximation of solar and stellar winds with viscosity*, Physics Inter. 5 (2) (2014), 136-139. doi.org/10.3844/pisp.2014.136.139

[11] P. N. Koumantos, *On the exponential equation **x^{x^{a}}=b*, Octogon 22 (1) (2014), 267-271. www.uni-miskolc.hu/~matsefi/Octogon/index.php?menu=archive&volume=2014_1

[12] P. N. Koumantos and P. K. Pavlakos, *Mean* *ergodic theorems in Jordan Banach weak algebras*, J. Math. Syst. Sci. 3 (3) (2013), 146-149.

**Talks - Research Announcements**

[1] M3ST 2009 International Conference on Modern Mathematical Methods in Science and Technology (Poros, Greece, September 3-5, 2009).

Research Announcement entitled: *On non-commutative and non-associative ergodic theorems* (jointly work: P. N. Koumantos and P. K. Pavlakos).

[2] Research Center for Astronomy and Applied Mathematics, Academy of Athens (Athens, Greece, February 22, 2011).

Invited Talk in RCAAM Seminar entitled: *Ergodic theorems with Applications in Classical and Quantum Mechanics* (jointly work: P. N. Koumantos and P. K. Pavlakos).

[3] M3ST 2012 International Conference on Modern Mathematical Methods in Science and Technology (Kalamata, Greece, 26-28 August 2012).

Research Announcement entitled: *A Semigroup approach to functional differential equations* (jointly work: E. Athanasiadou, V. Dionysatos, P. N. Koumantos and P. K. Pavlakos).

[4] 2nd International Conference on Applications of Mathematics and Informatics in Military Sciences, (Hellenic Military Academy, Vari, Greece, April 11-12, 2013).

Research Announcement entitled: *Almost periodic solutions of Navier-Stokes-Ohm type equations in Magneto-hydrodynamics* (jointly work: E. Athanasiadou, V. Dionysatos, P. N. Koumantos and P. K. Pavlakos).

[5] Research Center for Astronomy and Applied Mathematics, Academy of Athens (Athens, Greece, May 28, 2013).

Invited Talk in RCAAM Seminar entitled: *Dynamical Systems and Thermodynamics-Magneto-hydrodynamics* (jointly work: E. Athanasiadou, V. Dionysatos, P. N. Koumantos and P. K. Pavlakos).

[6] 2nd International Conference on Cryptography, Network Security and Applications in the Armed Forces (Hellenic Military Academy, Vari, Greece, April 2, 2014).

Research Announcement entitled: *Existence and uniqueness of quantum stochastic flows* (jointly work: E. Athanasiadou, O. Katsikas, P. N. Koumantos and P. K. Pavlakos).

[7] 2014 Intenational Conference on Topology and its Applications (Nafpaktos, Greece, July 3-7, 2014).

Research Announcement entitled: *The order topology in positivity preserving quantum stochastic integrals and monotone quantum stochastic dynamical systems* (jointly work: E. Athanasiadou, V. Dionysatos, O. Katsikas, P. N. Koumantos and P. K. Pavlakos).

[8] 3rd International Conference on Technology Trends and Scientific Applications in Artillery and other Military Science (TTSAAMS), Hellenic Artillery School (Nea Peramos Attikis, Greece, May 5-6, 2015).

Research Announcement entitled: *On the connection between the structure of space-time as ordered vector space and evolution equations* (independent work: P. N. Koumantos).

[9] 12th Hellenic Astronomical Conference (Thessaloniki, Greece, 28 June - 2 July, 2015).

Poster Presentation, in Session 1: Heliophysics and the Solar System, entitled: *On Solutions of the Navier-Stokes-Maxwell Equations in MHD* (independent work: P. N. Koumantos).

[10] M3ST 2015 International Conference on Modern Mathematical Methods in Science and Technology (Kalamata, Greece, 30 August - 1 September, 2015).

Research Announcement entitled: *Non-linear Volterra-type Diffusion Equations and Theory of Quantum Fields* (jointly work: C. Asimomytis, P. N. Koumantos and P. K. Pavlakos).

[11] M3ST 2015 International Conference on Modern Mathematical Methods in Science and Technology (Kalamata, Greece, 30 August - 1 September, 2015).

Research Announcement entitled: *Semigroup approach for the interaction of two fluids with the electromagnetic field* (independent work: P. N. Koumantos).

[12] 16th Pan-Hellenic Conference of Hellenic Physical Society (EEF) (Aegina, Greece, March 17-20, 2016).

Research Announcement entitled: *On hydrodynamic and magnetohydrodynamic evolution equations* (independent work: P. N. Koumantos).

[13] 3rd International Conference on Cryptography, Cyber-Security and Information Warfare (3rd CryCybIW) (Hellenic Military Academy, Vari, Greece, May 26-27, 2016).

Research Announcement entitled: *The Second Law of Thermodynamics and Stochastic Quantum-Thermodynamical Integrals* (jointly work: C. Asimomytis, P. N. Koumantos and P. K. Pavlakos).

[14] Institute of Applied & Computational Mathematics, Foundation of Technology and Research (IACM-FORTH) Heraklion, Crete, Greece (Heraklion, November 4, 2021).

Presentation of a special topic at the Seminar of IACM-FORTH (in the framework of the project with code 871) entitled: *Semi-groups of operators and evolution equations*.

[15] Department of Mathematics, Kuwait University (Kuwait, November 24, 2021).

Invited Colloquium Talk entitled: *On the action of the Lorentz operators and the topology in the Minkowski space* (independent work: P. N. Koumantos).

[16] Institute of Applied & Computational Mathematics, Foundation of Technology and Research (IACM-FORTH) Heraklion, Crete, Greece (Heraklion, February 10, 2022).

Presentation of a special topic at the Seminar of IACM-FORTH (in the framework of the project with code 871) entitled: *Basic concepts of algebraic topology*.

**Positions, Teaching**** and work experience**

•** ****1****/10/202****1**** - ****7/4/2022 ****:** Post-doctoral Researcher, in the context of the project entitled "Theoretical Understanding of static and dynamic properties of Skyrmions: towards a skyrmion-based technology. (ThunderSKY)" with code 871, Institute of Applied & Computational Mathematics, Foundation of Technology and Research (IACM-FORTH) Heraklion, Crete, Greece. https://thundersky.iacm.forth.gr/Home.html.

•** 7/10/2020 - 31/8/2021:** Adjunct Lecturer, NSRF Program - University Scholarship, Department of Mathematics & Applied Mathematics, University of Crete.

Independent teaching assignment for the following Undergraduate Semester Courses:

[1] Physics I (MEM109, Compulsory, winter semester 2020-2021) Physics1 (Class B),

[2] Physics II (MEM280, Elective, winter semester 2020-2021) Physics2,

[3] Methods of Applied Mathematics (MEM274, Elective, spring semester 2020-2021) MethApplMath.

· **2012-2013**: Teaching Assistant, University of Athens. Duties have included teaching sections of the courses, problem classes and office hours for the next compulsory six-month courses:

[1] Analysis I (Department of Physics, winter semester 2012-2013),

[2] Analysis II (Department of Informatics, spring semester 2012-2013).

Supervisor: Associate Professor Panaiotis Pavlakos (Department of Mathematics).

· **2011-2012:** Teaching Assistant, University of Athens. Duties have included teaching sections of the courses, problem classes and office hours for the next compulsory six-month courses:

[1] Analysis I (Department of Physics, winter semester 2011-2012),

[2] Analysis II (Department of Physics, spring semester 2011-2012),

Supervisor: Associate Professor Panaiotis Pavlakos (Department of Mathematics).

· **2010-2011:** Teaching Assistant, University of Athens. Duties have included teaching sections of the courses, problem classes and office hours for the next compulsory six-month courses:

[1] Mathematical Methods of Physics I (Department of Physics, winder semester 2010-2011),

[2] Complex Analysis I (Department of Mathematics, spring semester 2010-2011),

Supervisor: Associate Professor Panaiotis Pavlakos (Department of Mathematics).

· **2009-2010:** Teaching Assistant, University of Athens. Duties have included teaching sections of the courses, problem classes and office hours for the next compulsory six-month courses:

[1] Mathematical Methods of Physics I (Department of Physics, winter semester 2009-2010),

[2] Complex Analysis I (Department of Mathematics, spring semester 2009-2010).

Supervisor: Associate Professor Panaiotis Pavlakos (Department of Mathematics).

· **18/5/200****4 - 18/6/2004****:** Practical Exercise Program: ΕΠΕΑΕΚ ΙΙ for Undergraduate Students of Mathematics Department, University of Athens, Greece, 2004. Section of Astrophysics, Astronomy and Mechanics, and practiced at Gerostathopoulio University Observatory, Department of Physics, University of Athens.

Supervisor: Assistant Professor Theodoros Papayannopoulos (Department of Physics).