My Biography

Education

• Ph.D in Mathematics, Institute of Technology Tralee, 2010
• M.SC in Mathematics, University of Cyprus, 2004
• BSc (Hons) in Mathematics, University of Cyprus, 2001

Research

My main area of research is in Riemannian and pseudo-Riemannian geometry, submanifold theory and the spaces of oriented geodesics of certain manifolds.

Teaching

Waterford Institute of Technology, Waterford, Ireland - Lecturer (2015-present)

• Introductory Calculus,
• Advanced Engineering Maths, 
• Applied Calculus,
• Maths for Scientists, 
• Introductory Maths,
• Statistical Analysis,
• Mathematics Fundamentals,
• Applied Maths for Agriculture Scientists,
• Maths for Business.

 

 

Federal University of Manaus, Brazil - Assistant Lecturer (2014-2015)

• Undergraduate courses: Geometry I, Introduction in Analysis,
• Graduate courses: Analysis in R^n, Differential forms.

 

 

University of Cyprus - Visiting Assistant Lecturer (2011-2013)

• Engineering mathematics, Calculus I and Calculus II.

Publications and Talks

Peer-Reviewed Publications:

1. N.Georgiou and B. Guilfoyle, Almost Paracomplex Structures on 4-Manifolds, Differ. Geom. Appl., 82, 10.1016/j.difgeo.2022.101890 (2022)
2. N. Georgiou, M. Dussan and M. A. Magid, Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric, Kodai Math. J. 45, 117-142  (2022)
3. N.Georgiou and B. Guilfoyle, A new geometric structure on tangent bundles, Journal of Geometry and Physics, DOI: 10.1016/j.geomphys.2021.104415 (2022)
4. N. Georgiou and B. Guilfoyle, The causal topology of neutral 4-manifolds with null boundary, New York J. Math. 27, 477–507 (2021) 
5. N. Georgiou, A para-Kähler structure in the space of oriented geodesics in a real space form. Journal of Geometry 111, 41 (2020)
6. N. Georgiou, B. Guilfoyle, Hopf hypersurfaces in spaces of oriented geodesics, Journal of Geometry 108, 1129-1135 (2017)
7. N. Georgiou, B. Guilfoyle, W. Klingenberg, Totally null surfaces in neutral Kaehler 4-manifolds, Balkan Journal of Geometry and Its Applications 21, 27-41 (2016)
8. N. Georgiou, G. A. Lobos, On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms, Archiv der Mathematik 106, 285-293 (2016)
9. N. Georgiou, Lagrangian immersions in the product of Lorentzian two manifold, Geometriae Dedicata 178, 1-13 (2015)  
10. H. Anciaux, N. Georgiou, Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para- Kahler manifolds, Advances in Geometry 14, 587-612 (2014) 
11. N. Georgiou, B. Guilfoyle, Marginally trapped surfaces in spaces of oriented geodesics, Journal of Geometry and Physics 82, 1-12 (2014) 
12. N. Georgiou, On minimal Lagrangian surfaces in the product of Riemannian two manifolds, Tohoku Mathematical Journal 67, 137-152 (2013)
13. N. Georgiou, On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space, Mathematica Scandinavica 111, 187-209  (2012)
14. N. Georgiou, B. Guilfoyle, A characterization of Weingarten surfaces in hyperbolic 3-space, Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg 80, 233-253 (2010)
15. N. Georgiou, B. Guilfoyle, On the space of oriented geodesics of hyperbolic 3-space, Rocky Mountain Journal of Mathematics 40, 1183-1219 (2010)

 

Papers in Preprints:

1. The Blaschke-Lebesgue problem for constant width bodies of revolution, in collaboration with Henri Anciaux, arXiv:0903.4284 (2009).
2. Null hypersurfaces in 4-manifolds endowed with a product structure, arXiv:2212.10679 (2022)

 

Theses:

1. N. Georgiou, The geometry of the space of oriented geodesics of hyperbolic 3- space, PhD thesis,Institute of Technology Tralee, Ireland, 2009
2. N. Georgiou, Grassmann Manifolds and the Moduli Space of Metric 2-Step Nilpotent Lie Algebra, Master's thesis, University of Cyprus, 2003

 

 

Conference and seminar presentations:

 

1. April 2022 - Almost Paracomplex Structure on 4-manifolds, Irish Geometry Seminar, (Ireland)
2. June 2018 - The space of oriented geodesics in 3-dimensional real space forms, Geometric Computation and Applications workshop. Trinity College, Dublin, (Ireland)
3. May 2017 - Minimal Surfaces in the product of 2-mainfolds, Annual Irish Geometry Conference, Maynooth University, Maynooth (Ireland) 
4. February 2017 - Submanifolds in the space of oriented geodesics in 3-dimensional real space forms, Department of Mathematics & Statistics Colloquia, Maynooth University, Maynooth (Ireland)
5. May 2016, The space of oriented geodesics in three dimensional real space forms, Seminar Series in Mathematics & Physics, Waterford Institute of Technology (Ireland)
6. May 2015 - Minimal surfaces in the product of pseudo-Riemannian two manifolds, 12th Panhellenic Congress of Geometry, Salonica (Greece)
7. May 2014 - Minimal immersions in the product of two manifolds, Seminario Conjunto de Geometria Diferencial, Instituto de Matematica e Estatestica, Universidade de Sao Paulo (Brasil)
8. May 2014 - Lagrangian immersions in the product of two manifolds, Geometry Seminar at KU Leuven (Belgium)
9. March 2014 - Minimal Lagrangian surfaces in the product of Riemannian or Lorentzian surfaces, Geometry Seminar, University of Durham (United Kingdom)
10. October 2013 - Examples of neutral Kahler four manifolds, Seminario de Geometria y Topologia, the University of the Basque Country (Spain)
11. April 2013 - The space of oriented geodesics in three dimensional space forms, Geometric Seminar at Aristotle University, Thessaloniki (Greece)
12. February 2013 - The surface theory of a neutral, conformally at Kahler 4-manifold , Mathematic Seminar at EUC (Cyprus)
13. February 2012 - The Hamiltonian stability of H-minimal Lagrangian submanifolds in pseudo and para-Kahler manifolds , Mathematic Seminar, University of Cyprus (Cyprus)
14. March 2011 - The Hamiltonian stability of area-stationary Lagrangian surfaces in the space of oriented geodesics in hyperbolic 3-space , Coloquio de Matematica, Instituto de Matematica e Estatastica, Universidade Federal de Sao Carlos (Brasil)
15. March 2011 - The H-stability of H-minimal Lagrangian surfaces in pseudo-Riemannian Kahler manifolds , Seminario Conjunto de Geometria Diferencial, Instituto de Matematica e Estatestica, Universidade de Sao Paulo (Brasil) 
16. December 2010 - The spaces of oriented geodesics and applications to geometry, MathematicsSeminar, Frederick University (Cyprus)
17. December 2010 - On area-stationary surfaces in the space of oriented geodesics of hyperbolic 3-space, Geometry Seminar, University of Durham (United Kingdom)
18. April 2009 - The geometry of the space of oriented geodesics of hyperbolic 3-space and the submanifold theory, Geometry and Topology Splinter Group, BMC/IMS, National University of Ireland, Galway (Ireland)
19. December 2008 - The space of oriented geodesics of hyperbolic 3-space, Mathematic Seminar University of Cyprus (Cyprus)
20. June 2008 - The Geometry of the space of oriented geodesics of hyperbolic 3-space, Geometric Seminar, Humboldt University (Germany)
21. January 2008 - Hyperbolic geometry, Research Institute Seminar, Institute of Technology Tralee (Ireland)