Dan Burghelea: Difference between revisions

Add links
From Wikipedia, the free encyclopedia
Next edit →
Content deleted Content added
VisualWikitext
←Created page with '{{Infobox academic | name = Dan Burghelea | image = | birth_date = {{birth date and age|1943|07|30}} | birth_place =...'
(No difference)

Revision as of 10:09, 26 January 2021

Dan Burghelea
Born (1943-07-30) July 30, 1943 (age 80)
Ramnicu Valcea, Romania
NationalityRomanian-American
Occupation(s)Mathematician, academic and researcher
AwardsDoctor Honoris-Causa, University of Timisoara
Knight of the order Faithful Service (Romania)
Distinction Academic Merit, Romanian Academy of Sciences
Medal of Honor, the Romanian mathematical Society
Academic background
EducationUniversity Degree in Mathematics
Ph.D., Mathematics
Alma materUniversity of Bucharest
Mathematical Institute of the Romanian Academy
ThesisHilbert manifolds
Doctoral advisorMiron Nicolescu
Academic work
InstitutionsOhio State University

Dan Burghelea is a Romanian-American mathematician, academic and researcher. He is an Emeritus Professor of Mathematics at Ohio State University.[1]

Burghelea has contributed to a number of mathematical domains such as geometric and algebraic topology (including differential topology, algebraic K-theory, cyclic homology), global and geometric analysis (including topology of infinite dimensional manifolds, spectral geometry, dynamics), applied topology (including computational topology).[2]

Early life and education

Burghelea was born in Ramnicu Valcea, Romania, in 1943. He attended University of Bucharest and graduated in Mathematics in 1965, with a diploma-thesis in algebraic topology. He obtained his Ph.D. in 1968 from Institute of Mathematics of the Romanian Academy (IMAR) with a thesis on Hilbert manifolds.[1]

In 1972, Burghelea was awarded the title of Doctor Docent in sciences by the University of Bucharest, making him the youngest recipient of the highest academic degree in Romania.[3]

Career

After a brief military service, Burghelea started his career in 1966 as a junior researcher at IMAR. He was promoted to Researcher in 1968, and to Senior Researcher in 1970. After the dissolution of IMAR, he was employed by Institute of Nuclear Physics (IFA-Bucharest) and National Institute for Scientific Creation (INCREST) from 1975 till 1977. Burghelea left Romania for USA in 1977 and in 1979 joined the Ohio State University as a Professor of Mathematics. He retired in 2015, and remained associated with this University as an Emeritus Professor.[4]

Research

Burghelea has worked in algebraic, differential, geometrical topology, differential and complex geometry, commutative algebra, global and geometric analysis, and applied topology.[5]

Burghelea's most significant contributions are Topology of infinite dimensional manifolds;[6] Homotopy type of the space of homeomorphisms and diffeomorphisms of compact smooth manifolds;[7][8] Algebraic K-theory and cyclic homology of topological spaces, differentia graded group rings and commutative algebras;[9][10][11] Zeta-regularized determinants of elliptic operators and implications to torsion invariant, for Riemannian manifolds.[12][13][14][15]

He has also proposed and studied a computer friendly alternative to Morse-Novikov theory which makes the results of the Morse-Novikov theory, a powerful tool in topology, applicable outside topology in situations of interest in fields like physics and data analysis.[16]

He has authored several books including Groups of Automorphisms of Manifolds and New Topological Invariants for Real- and Angle-valued Maps: An Alternative to Morse-Novikov Theory.

He has advised several Ph.D. students.[17]

Awards and honors

  • 1966 - Simion Stoilow Prize, the Romanian Academy
  • 1995 - Doctor Honoris-Causa, University of Timisoara[18]
  • 2003 - Knight of the order Faithful Service, rank (commander)
  • 2005 - Honorary membership, IMAR, Romania[19]
  • 2009 - Distinction Academic Merit, Romanian Academy of Sciences
  • 2019 - Medal of Honor, the Romanian mathematical Society

Bibliography

Selected Books

  • Introducere in Topologia Differentiala
  • The concordance-homotopy groups of geometric automorphism groups (1971) ISBN 978-0387055602
  • Groups of Automorphisms of Manifolds' (1975) ISBN 978-3540071822
  • New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-Novikov Theory (2017) ISBN 978-9814618267

Selected Articles

  • Burghelea, D, Kuiper, N, Hilbert manifolds, Annals of Math. 1969, (371-417)
  • Burghelea, D, Lashof, R, Stability for concordances and the suspension homomorphism, Annals of mathematics 105(3), 1977, 449-472
  • Burghelea, D, The rational homotopy groups of Diff M and Homeo M in stability range, Aarhus 1978, 604-626
  • Burghelea, D , Lashof, R, The geometric transfer and the homotopy type of automorphisms group of a manifold Trans. of the AMS 269 (1) 1982, 1-38
  • Burghelea D, Cyclic homology and algebraic K-theory of spaces I. Proc. Summer Institute on algebraic K-theory, Boulder Colorado, 1983. followed by
  • Burghelea, D., Fiedorowicz, Z. Cyclic homology and algebraic K-theory of spaces II. Topology, 25(3), 1986 303-317.
  • Burghelea, D, The cyclic homology of the group rings. Commentarii Mathematici Helvetici, 60(1), 1985 354-365.
  • Burghelea, D, Vique Poirrier, M. Cyclic homology of commutative algebras. I, Algebraic topology–rational homotopy (Louvain-la-Neuve, 1986), Lecture Notes in Math., Vol 1318, Springer-Verlag,Berlin-New York, 1988, 51–72.
  • Burghelea, D., Friedlander, L., Kappeler, T. (1992). Meyer-Vietoris type formula for determinants of elliptic differential operators. Journal of functional analysis, 107(1), 34-65.
  • Burghelea, D., Kappeler, T., McDonald, P., Friedlander, L. (1996). Analytic and Reidemeister torsion for representations in finite type Hilbert modules. Geometric and Functional Analysis GAFA, 6(5), (1996), 751-859.
  • Burghelea, D, Haller, S, Complex valued Ray-Singer Torsion, Journal of Functional Analysis, 248 (1), 2007 27-78
  • Burghelea, D, Haller, S, Torsion as a function on the space of representations, C*-algebras and elliptic theory, II, 2008, (41-66)
  • Burghelea, D, Haller,S,Topology of angle valued maps, bar codes and Jordan blocks (with Stefan Haller ), J Appl. and Comput. Topology (2017) Vol 1, issue 1. (on line) (pages 1-77)
  • D Burghelea, A Verona, Local homological properties of analytic sets, 
Manuscripta mathematica 7 (1), 55-66

References

  1. ^ a b "Dan Burghelea".
  2. ^ "Dan Burghelea - Google Scholar".
  3. ^ "Dan Burghelea - Dumitru Vatamaniuc".
  4. ^ "Dan Burghelea CV" (PDF).
  5. ^ "Dan Burghelea - Publications" (PDF).
  6. ^ "Hilbert Manifolds".
  7. ^ "The rational homotopy groups of Diff (M) and Homeo (Mn) in the stability range".
  8. ^ "Geometric transfer and the homotopy type of the automorphism groups of a manifold".
  9. ^ "Cyclic homology and algebraic K-theory of spaces—II".
  10. ^ "The cyclic homology of the group rings".
  11. ^ {{Cite web|url=https://link.springer.com/chapter/10.1007/BFb0077794%7Ctitle=Cyclic homology of commutative algebras I
  12. ^ "Meyer-vietoris type formula for determinants of elliptic differential operators".
  13. ^ {{cite web|url=https://link.springer.com/article/10.1007/BF02246786%7Ctitle=Analytic and Reidemeister torsion for representations in finite type Hilbert modules
  14. ^ "Complex-valued Ray–Singer torsion".
  15. ^ "Torsion, as a Function on the Space of Representations".
  16. ^ "Topology of angle valued maps, bar codes and Jordan blocks".
  17. ^ "Dan Burghelea - The Mathematics Genealogy Project".
  18. ^ "Professor DAN BURGHELEA" (PDF).
  19. ^ "Honorary members of the "Simion Stoilow" Institute of Mathematics of the Romanian Academy".

External links

Retrieved from "https://en.wikipedia.org/w/index.php?title=Dan_Burghelea&oldid=1002856664"