CURRICULUM VITAE

Nondas E. Kechagias

Professor, Department of Mathematics, University of Ioannina, Ioannina 45110, Greece

Office: 302651008276 FAX: 302651008203

E-mail: nkechag @ uoi.gr

EDUCATION

Doctoral: Mathematics 1990, Queen's University, Ontario, Canada

Title: Homology operations and modular invariant theory

Supervisor: Professor H. E. A. Campbell

Genealogy math: Lefschetz Solomon, Steenrod Norman Earl, Hsiang, Wu Chung, Sharpe Richard W., Campbell H. Edward Alexander.

Master's: Mathematics 1986, York University, Ontario, Canada

Bachelor: Mathematics 1983, University of Athens, Greece

Academic and Professional Appointments

Head, 11/2015---11/2017

Professor, Ioannina, 5/2015

Vice Chairman, Ioannina 9/2011---9/2014

Associate Professor, Ioannina, 8/2009---5/2015

Assistant Prof (tenure), Ioannina, 9/1996---8/2009

Visiting Assistant Prof., Aegean, 9/1993---8/1996

Visiting Assistant Prof., York, 8/1992---12/1992

Visiting Assistant Prof., Crete, 9/1990---7/1992 &1/1993---8/1993

Papers in refereed journals

1) The Steenrod algebra action on generators of rings of invariants of subgroups of $GL(n,Z/pZ)$, Proceedings of the A.M.S.., 118, No 3, (1993), pp. 943-952, MR1152986 (93i:55023).

2) Mod odd modular coinvariants, homology operations, and limit spaces, Canada. J. Math., 45, No 4, (1993),pp. 803-819, MR1227660 (94i:55026).

3) Extended Dyer-Lashof algebras and modular coinvariants, Manuscripta Math., 84, (1994), pp. 261-290, MR1291121 (95g:55007).

4) A note on $U_nxU_m$ modular invariants, Canada. Math. Bull., 40, No 1, (1997), pp. 54-59, MR1443725 (98c:13009).

5) The transfer between rings of modular invariants of subgroups of $GL(n,Z/pZ)$}, The Fields Institute Communications of the A.M.S.., Editors S. Kochman and P. Selick, 19,(1998), pp. 165-180, MR1622345 (99f:13003).

6) Modular Invariant Theory, Homology Operations, and the Transfer between Rings of Invariants of Parabolic Subgroups, The Greek Bulletin of Mathematical Society, 38,(1996), pp. 79-88, MR1617511 (99b:55035).

7) H. E. A. Campbell and N. Kechagias, Arnon completion of the Dyer-Lashof algebra, Israel Journal of Math.,114, (1999), pp. 189-202. MR1738679 (2001c:55011)

8) An invariant theoretic description of the primitive elements of the mod-p cohomology of a finite loop space which are annihilated by Steenrod Operations, "Proceedings of a Workshop on Invariant Theory, April 2002, Queen's University". C.R.M.- A.M.S. Proceedings and Lecture Notes Volume 35 (2003),159-174. MR2066463 (2005b:55014)

9) Adem relations in the Dyer-Lashof algebra and Dickson invariants, Algebraic and Geometric Topology 4 (2004), paper no. 13, pages 219-241. MR2059190 (2005c:55031) http://www.maths.warwick.ac.uk/agt/ dvi-file

10) I. P. Hughes and N. Kechagias, Rings of Invariants of modular p-groups which are hypersurfaces, Journal of Algebra, Volume 291, Issue 1, Pages 72-89. MR2158511 (2006d:13005)

11) A note on parabolic subgroups and the Steenrod Algebra action, pages 12. Algebra Colloquium, Volume 15 (2008), Number 4, 689-698. MR2452001 (2009h:13004)

12) Even dimensional submanifolds of spheres with nonnegative curvature, Soochow J. Math. 33 (2007), no. 4, 939-948. MR2404615 (2009b:53051)

13) The transfer in mod-p group cohomology between $\Sigma_P\int\Sigma_{P^{N-1}}, \Sigma_{P^{N-1}}\int\Sigma_P$ and $\Sigma_{P^N}$ , J. Homotopy Relat. Struct. 4 (2009), no. 1, 153--179. MR2520991 (2010h:20117)

14) Dickson invariants and a new description of H ∗ (Q 0 S 0 ,Z/pZ) via H ∗ (BΣ ∞ ,Z/pZ) , Journal of Homotopy and Related Structures, Volume 8, Issue 2 (2013), Page 201-229. MR3095325

15) The component Dyer-Lashof coalgebras as subcoalgebras of free unstable coalgebras, 34 pages. J. Pure Appl. Algebra 219 (2015), no. 4, 839-863. MR3282113

16) Infinite Loop Spaces, Dyer-Lashof Algebra, Cohomology of the Infinite Symmetric Group and Modular Invariants. 29 pages. Springer Proceedings in Mathematics & Statistics, Vol. 219, 2017, 204-234. MR3748897

17) The mod2 Steenrod and Dyer-Lashof coalgebras as quotients of a free algebra, Topology and its Applications, Topology Appl. 275 (2020), 107008, 18 pp. 55S10 (13A50 16T05 55P10).

Preprints

1) Relations between parabolic and Dickson algebra generators and applications, pages 11.

2) Arithmetic between sequences of natural numbers and cyclotomic polynomials, pages 8. Sequ11.dvi

3) The structure of the endomorphism ring End{F_{q}[End(V)]}F_{q}[End(V)/GL(V)] of a finite vector space, pages 12, endom.dvi

4) A Steenrod-Milnor action ordering on Dickson invariants, 2008, pages 16. Steen-Mil.pdf

From Review: Hung Annalen

5) Dickson algebras are atomic at $p$, 15 pages. http://arxiv.org/abs/1108.3685

6) Fiber bundles-Hopf Fibration.Hopf.pdf

ΔΙΔΑΣΚΑΛΙΑ 2023-2024

1) ΧΕΙΜΕΡΙΝΟ ΕΞΑΜΗΝΟ. 123 ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ. Φυλλάδια 123-FYLLADIO1-2

2) ΧΕΙΜΕΡΙΝΟ ΕΞΑΜΗΝΟ. 525 ΘΕΩΡΙΑ ΟΜΑΔΩΝ. GroupsNotes.pdf

3) ΕΑΡΙΝΟ ΕΞΑΜΗΝΟ. 828 ΤΟΠΟΛΟΓΙΚΕΣ ΟΜΑΔΕΣ ΠΙΝΑΚΩΝ. Topological-Groups.pdf

4) ΕΑΡΙΝΟ ΕΞΑΜΗΝΟ. ΓΕ5 ΑΛΓΕΒΡΙΚΗ ΤΟΠΟΛΟΓΙΑ Ι. . NotesAlgTop1.pdf

5) ΕΑΡΙΝΟ ΕΞΑΜΗΝΟ 629 ΕΦΑΡΜΟΓΕΣ ΓΡΑΜΜΙΚΗΣ ΑΛΓΕΒΡΑΣ. MS-Teams code

p1wf5su

efarmoges_ths_grammikhs_algebras.pdf

Non-Refereed papers, University Notes and Teaching material (in Greek)

1) Γενικευμένες Θεωρίες Συνομολογίας (Generalized Cohomology Theories). Greek Mathematical Reviews, 46, 1998, pages 15. Survey article. Γ1

2) Ευκλείδεια Γεωμετρία και πεπερασμένες υποομάδες ισομετριών (Euclidian Geometry and finite subgroups of isometries). Ομάδες και Εφαρμογές, Πρακτικά 5^ου Θερινού Σχολείου (Summer School), Πανεπιστήμιο Αιγαίου (University of Aegean), Σελίδες (pages) 23. 2000. Εκδόσεις Ζήτη. Γ2

3) Εφαρμογές της Γραμμικής Άλγεβρας στις Επιστήμες (Applications of Linear Algebra in Sciences). Πανεπιστήμιο Ιωαννίνων (University of Ioannina press), Σελίδες (pages 198). 2008. efarmoges_ths_grammikhs_algebras.pdf

4) Εφαρμοσμένη Γραμμική Άλγεβρα (Applied Linear Algebra). Σημειώσεις (Notes), Σελίδες 93. 2002.

5) Στοιχεία Κλασικής Αλγεβρικής Τοπολογίας (Notes on Algebraic Topology). Σημειώσεις μεταπτυχιακού μαθήματος (Notes for a graduate course), Σελίδες 311. 2022. NotesAlgTop1.pdf

6) Σημειώσεις στη Θεωρία Ομάδων (Notes for an introductory course in Group Theory). 2010. GroupsNotes.pdf

7) Poincaré Conjecture, Τοπολογία-Γεωμετρία-Ανάλυση. Poincare Conjecture.pdf

8) Τοπολογικές ομάδες πινάκων (Notes for an introductory course in Matrix Lie Groups) 2019. Topological-Groups.pdf

ΕΚΛΑΪΚΕΥΜΕΝΕΣ ΟΜΙΛΙΕΣ

1) ΕΞΕΛΙΞΗ ΤΗΣ ΑΛΓΕΒΡΙΚΗΣ ΤΟΠΟΛΟΓΙΑΣ Algebraic-Topol-Evolution

2) ΕΞΕΛΙΞΗ ΤΗΣ ΑΛΓΕΒΡΑΣ Evolution-Algebra

3) ΡΟΜΠΟΤΙΚΗ ΚΑΙ ΑΛΓΕΒΡΙΚΗ ΤΟΠΟΛΟΓΙΑ ΡΟΜΠΟΤΙΚΗ

4) ΙΣΤΟΡΙΑ ΚΡΥΠΤΟΓΡΑΦΙΑΣ CRYPTOGRAPHY

5) ΠΡΩΤΟΙ ΑΡΙΘΜΟΙ ΚΑΙ Η ΕΙΚΑΣΙΑ ΤΟΥ RIEMANN

Riemann-Hypothesis

Students

1) Κλεάνθης Ξενιτίδης, Master Thesis, Ιούλιος 2009. «Δυϊκότητα Poincare και Alexander». "Poincare and Alexander duality". Xenitidis.pdf

2) Χρήστος Σαρακασίδης, Master Thesis, Ιούλιος 2014. «Χώροι διαμόρφωσης και οι ομάδες πλεξίδων του Artin». "Configuration spaces and the Artin braid group".Sarakasidis.pdf

3) Γεωργία Κουτσάφτη. Master Thesis, Μάιος 2020, «Τοπολογικός Βαθμός Απεικόνισης και το Θεώρημα Σταθερού Σημείου». "Topological Degree and Fixed Point Theorem". Koutsafti.pdf

4) Γεώργιος Δημητριάδης. Master Thesis, Απρίλιος 2021. «Tate Cohomology of Finite Groups». Dimitriadis.pdf

SELECTED INVITED ADDRESSES

1) Hellenic Mathematical Society, Annual meeting. Lefkada 3-5 Nov. 2017. HMS-4-11-17

2) University of Rochester, Department of Mathematics. 21 Nov. 2014.

3) University of Chicago, Department of Mathematics. 13 Nov. & 18 Nov. 2014.

4) University of Chicago, Department of Mathematics. Sep. - Dec. 2014. U.S.A. Sabbatical.

5) University of the Aegean, Geometry and Topology in Samos. 11-15 June 2012. Greece.

6) Queen's University, Workshop on Invariant Theory, April 2002. Canada.

7) Queen's University, Department of Mathematics. September 7 - November 28, 2000. Canada. Sabbatical.

8) University of Rochester, Department of Mathematics. October 25-28, 2000. U.S.A.

9) Mathematisches Institute, Universität Göttingen, June 14-20, 1999. Germany.

10) 924th A.M.S. Meeting, Invariant Theory session. Université de Montréal, September 26-28, 1997, Canada.

11) Schloss Dachstuhl, Invariant Theory Conference, May 1996, Germany.

12) The Fields Institute, Workshop on Stable Homotopy Theory, University of Toronto, January 1-31, 1996, Canada.

13) Mathematisches Institute, Heidelberg Universität, June 12 - July 6, 1995. Germany.

14) Queen's University, Department of Mathematics. January 1 - February 23, 1995. Canada.

15) International conference in Algebraic Topology, Oaxtepec Mexico, July 1991.

16) University of Manchester, Adams Memorial Conference. July 1990. England.

INVITED ADDRESSES - TALKS

1) University of Murcia, Interactions between ring theory & representation of algebras. 12-17 January. 1998, Spain.

2) Centre de recerca Mathematica Barcelona, Advances in homotopy theory. 4-10 June 1998, Spain.

3) University of Samos, Summer School, Groups. 11-18 July 1999, Creece.

4) Institut Mathematique, Louvain-la-Neeuve, Algebraic Topology, 14-20 June 2004. Belgium.

5) National Technical University of Athens, 8 Greek Conference in Algebra, 28-31 May 2008. Greece.

6) University of Ioannina, Seminar, 23-11-2011 and 13-3-2013.

7) National Technical University of Athens, 14 July 2013. Greece.

8) University of Thessaloniki, Greek Conference in Algebra, 02-03 May 2014. Greece. Talk-Thes-05-14

9) International Conference on Topology and its Applications, Nafpaktos, July 2014.

10) National Technical University of Athens, 2 July 2015. Greece.

11) Workshop on Group Actions - Classical and Derived. June 13 - 17, 2016, The Fields Institute

12) University of Ioannina, Math club, 05-04-2016. History of Cryptography. Cryptography.pdf

13) First Congress of Greek Mathematicians, Hellenic Mathematical Society, Athens, June 2018.

14) International Conference on Topology and its Applications, Nafpaktos, July 2018.

15) University of the Aegean, 7 December 2019. Greece.

16) University of Patras. 11 December 2019. Greece.

THALES Research Program 2012-2015 Coordinator S. Lambropoulou N.T.U.A. Algebraic modeling of topological and computational structures and applications.