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

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. To appear.

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

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 5ου 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. NEW appl-lin-alg2.pdf

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

5) Εισαγωγή στην Αλγεβρική Τοπολογία (An introduction to Algebraic Topology). Σημειώσεις μεταπτυχιακού μαθήματος (Notes for a graduate course), Σελίδες 95. 2001. SimiosisAlgTop011.pdf ,  SimiosisAlgTop11.pdf , SimiosisAlgTop21.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

Papers in preparation

1)     Self maps of spaces generated by wreath products.

2)     Self maps between quotients of Dickson Algebras.

3)     Applications of modular invariants on finite loop spaces.

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

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

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

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

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

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

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

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

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

9) 924th A.M.S. Meeting, Invariant Theory session. Université de Montréal, September 26-28, 1997, Canada.

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

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

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

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

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

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

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

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

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

ORGANIZER INTERNATIONAL SUMMER SCHOOL

A SATELLITE CONFERENCE OF THE THIRD EUROPEAN CONGRESS OF MATHEMATICS

“INTERACTIONS BETWEEN ALGEBRAIC TOPOLOGY AND INVARIANT THEORY”

Speakers: H. E. A. Campbell, F. R. Cohen, L. Smith, R. M. W. Woods

IOANNINA, 26-30 JUNE 2000

Proceedings (technical), Technical Report, 3, Special Volume, December 2000, University of Ioannina.  Photo jpeg-file

Supported by: The General Secretary of Research and Technology, University of Ioannina, Prefecture of Ioannina.

of the Hellenic mathematical society

Επαγγελματικές ευκαιρίες για μαθηματικούς. Employment opportunities for mathematicians

IMPORTANT PEOPLE IN THE FIELD

# POINCARE CONJECTURE

http://www.newyorker.com/magazine/2006/08/28/manifold-destiny

Ricci flow and the Poincare conjecture” J. Morgan and G. Tian, AMS – Clay Mathematics Institute.

Geometry & Topology Publications