Dan Burghelea

Dan Burghelea (born July 30, 1943) is a Romanian-American mathematician, academic, and researcher. He is an Emeritus Professor of Mathematics at Ohio State University.

Dan Burghelea
Born	(1943-07-30) July 30, 1943 (age 80) Râmnicu Vâlcea, Kingdom of Romania
Nationality	Romanian-American
Occupation(s)	Mathematician, academic and researcher
Awards	Doctor Honoris-Causa, West University of Timișoara National Order of Faithful Service Distinction Academic Merit, Romanian Academy of Sciences Medal of Honor, the Romanian Mathematical Society
Academic background
Alma mater	University of Bucharest Institute of Mathematics of the Romanian Academy
Thesis	Hilbert manifolds (1968)
Doctoral advisor	Miron Nicolescu
Academic work
Institutions	Ohio State University

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, dynamical systems), and applied topology (including computational topology).

Early life and education

Burghelea was born in Râmnicu Vâlcea, Romania, in 1943, where he attended Alexandru Lahovari National College (at that time lyceum Nicolae Bălcescu).^[1] He attended the University of Bucharest and graduated in mathematics in 1965, with a diploma-thesis in algebraic topology. He obtained his Ph.D. in 1968 from the Institute of Mathematics of the Romanian Academy (IMAR) with a thesis on Hilbert manifolds.^[2]

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 the Institute of Nuclear Physics (IFA-Bucharest) and National Institute for Scientific Creation (INCREST) from 1975 until 1977. Burghelea left Romania for the United States in 1977, and in 1979 he joined the Ohio State University as a professor of mathematics. He retired in 2015, and remains associated with this university as an Emeritus Professor.

During his career he has been a visiting professor at numerous universities from Europe and the United States, including the University of Paris, the University of Bonn, ETH Zurich, the University of Chicago, and research institutions including the Institute for Advanced Study, Institut des Hautes Études Scientifiques, Max Planck Institute for Mathematics, Mathematical Sciences Research Institute; and invited speaker to many conferences in Europe, North and South America, and Asia and organized/co-organized workshops and conferences in Topology and Applications in Europe and the United States.^[4] He has significantly influenced the orientation of the geometry-topology research in Romania.^[5]

Research

Burghelea has worked in algebraic, differential, geometrical topology, differential and complex geometry, commutative algebra, global and geometric analysis, and applied topology.^[6]

His most significant contributions are on Topology of infinite dimensional manifolds;^[7][8] Homotopy type of the space of homeomorphisms and diffeomorphisms of compact smooth manifolds;^[9][10] Algebraic K-theory and cyclic homology of topological spaces, groups (including simplicial groups) and commutative algebras (including differential graded commutative algebras);^[11][12][13] Zeta-regularized determinants of elliptic operators and implications to torsion invariants for Riemannian manifolds.^{[14][15][16][17]}

Burghelea has also proposed and studied a computer friendly alternative to Morse–Novikov theory which makes the results of Morse–Novikov theory a powerful tool in topology, applicable outside topology in situations of interest in fields like physics and data analysis.^[18] He was the first to generate concepts of semisimple degree of symmetry and BFK-gluing formula.

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.^[19]

Awards and honors

• 1966 – Simion Stoilow Prize, the Romanian Academy
• 1995 – Doctor Honoris-Causa, West University of Timișoara^[20]
• 2003 – National Order of Faithful Service, Commander rank
• 2005 – Honorary membership, IMAR, Romania^[21]
• 2009 – Distinction Academic Merit, Romanian Academy of Sciences
• 2019 – Medal of Honor, the Romanian Mathematical Society

Personal life

Dan Burghelea married Ana Burghelea, in 1965. They have a daughter, Gabriela Tomescu.^[22]

Bibliography

Selected books

• The concordance-homotopy groups of geometric automorphism groups (1971) ISBN 978-0387055602
• Introducere în topologia diferențială (1973)
• Burghelea, Dan; Lashof, Richard; Rothenberg, Melvin (1975). Groups of Automorphisms of Manifolds. Lecture Notes in Mathematics. Vol. 473. Berlin, Heidelberg: Springer. doi:10.1007/bfb0079981. ISBN 978-3-540-07182-2. MR 0380841.
• New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-Novikov Theory, World Scientific (2017) ISBN 978-9814618267

Selected articles

• Burghelea, Dan; Kuiper, Nicolaas H. (1969). "Hilbert Manifolds". Annals of Mathematics. 90 (3): 379–417. doi:10.2307/1970743. JSTOR 1970743. MR 0253374.
• Burghelea, Dan; Verona, Andrei (1972). "Local homological properties of analytic sets". Manuscripta Mathematica. 7 (1): 55–66. doi:10.1007/BF01303536. MR 0310285. S2CID 54527826.
• Burghelea, Dan; Lashof, Richard K. (1977). "Stability for concordances and the suspension homomorphism". Annals of Mathematics. 105 (3): 449–472. doi:10.2307/1970919. JSTOR 1970919. MR 0438365.
• Burghelea, Dan (1979), "The rational homotopy groups of ${\displaystyle \operatorname {Diff} (M)}$  and ${\displaystyle \operatorname {Homeo} (M^{n})}$  in the stability range", Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, Aarhus, 1978), Lecture Notes in Mathematics, vol. 763, Berlin: Springer, pp. 604–626, MR 0561241
• Burghelea, Dan; Lashof, Richard K. (1982). "The geometric transfer and the homotopy type of automorphisms group of a manifold". Transactions of the American Mathematical Society. 269 (1): 1–38. doi:10.2307/1998592. JSTOR 1998592. MR 0637027.
• Burghelea, Dan (1986), "Cyclic homology and the algebraic 𝐾-theory of spaces. I", in Bloch, Spencer J.; Dennis, R. Keith; Friedlander, Eric M.; Stein, Michael R. (eds.), Applications of algebraic K-theory to algebraic geometry and number theory, Part 1 (Proc. Summer Institute on algebraic K-theory, Boulder, Colorado, 1983), Contemporary Mathematics, vol. 55, Providence, Rhode Island: American Mathematical Society, pp. 89–115, doi:10.1090/conm/055.1/862632, MR 0862632
• Burghelea, Dan (1985). "The cyclic homology of the group rings". Commentarii Mathematici Helvetici. 60 (1): 354–365. doi:10.1007/BF02567420. MR 0814144. S2CID 120829283.
• Burghelea, Dan; Fiedorowicz, Zbigniew (1986). "Cyclic homology and algebraic K-theory of spaces—II". Topology. 25 (3): 303–317. doi:10.1016/0040-9383(86)90046-7. MR 0842427.
• Burghelea, Dan; Poirrier, Micheline Vigué (1988), "Cyclic homology of commutative algebras I", in Félix, Yves (ed.), Algebraic topology—rational homotopy (Louvain-la-Neuve, 1986), vol. 1318, Berlin: Springer, pp. 51–72, doi:10.1007/bfb0077794, MR 0952571
• Burghelea, Dan; Friedlander, Leonid; Kappeler, Thomas (1992). "Meyer-Vietoris type formula for determinants of elliptic differential operators". Journal of Functional Analysis. 107 (1): 34–65. doi:10.1016/0022-1236(92)90099-5. MR 1165865.
• Burghelea, Dan; Friedlander, Leonid; Kappeler, Thomas (1992). "Meyer-Vietoris type formula for determinants of elliptic differential operators". Journal of Functional Analysis. 107 (1): 34–65. doi:10.1016/0022-1236(92)90099-5. MR 1165865.
• Burghelea, Dan; Kappeler, Thomas; McDonald, Patrick; Friedlander, Leonid (1996). "Analytic and Reidemeister torsion for representations in finite type Hilbert modules". Geometric and Functional Analysis. 6 (5): 751–859. arXiv:dg-ga/9502001. doi:10.1007/BF02246786. MR 1415762. S2CID 16656673.
• Burghelea, Dan; Haller, Stefan (2007). "Complex-valued Ray–Singer torsion". Journal of Functional Analysis. 248 (1): 27–78. arXiv:math/0604484. doi:10.1016/j.jfa.2007.03.027. MR 2329682. S2CID 31221717.
• Burghelea, Dan; Haller, Stefan (2008), "Torsion, as a function on the space of representations", in Burghelea, Dan; Melrose, Richard; Mishchenko, Alexander S.; Troitsky, Evgenij V. (eds.), ${\displaystyle C^{*}}$ -algebras and Elliptic Theory II, Basel: Birkhäuser, pp. 41–66, arXiv:math/0507587, doi:10.1007/978-3-7643-8604-7_2, ISBN 978-3-7643-8603-0, MR 2408135, S2CID 160308
• Burghelea, Dan; Haller, Stefan (2017). "Topology of angle valued maps, bar codes and Jordan blocks". Journal of Applied and Computational Topology. 1 (1): 121–197. doi:10.1007/s41468-017-0005-x. hdl:21.11116/0000-0004-672E-6. MR 3975551. S2CID 54930426.

References

1. "Personalitati".
2. ""În generația mea, matematica a reprezentat o opțiune fericită"".
3. "No 1 - December 2021".
4. "Dan Burghelea" (PDF).
5. "Professor Dan Burghelea - Doctor Honoris Causa" (PDF).
6. "Dan Burghelea Publications" (PDF).
7. "Hilbert manifold".
8. Burghelea, Dan; Kuiper, Nicolaas H. (1969). "Hilbert Manifolds". Annals of Mathematics. 90 (3): 379–417. doi:10.2307/1970743. JSTOR 1970743.
9. Burghelea, D. (1979). "The rational homotopy groups of Diff (M) and Homeo (Mn) in the stability range". Algebraic Topology Aarhus 1978. Lecture Notes in Mathematics. Vol. 763. pp. 604–626. doi:10.1007/BFb0088105. ISBN 978-3-540-09721-1.
10. Burghelea, D.; Lashof, R. (1982). "Geometric transfer and the homotopy type of the automorphism groups of a manifold". Transactions of the American Mathematical Society. 269: 1. doi:10.1090/S0002-9947-1982-0637027-4.
11. Burghelea, D.; Fiedorowicz, Z. (1986). "Cyclic homology and algebraic K-theory of spaces—II". Topology. 25 (3): 303–317. doi:10.1016/0040-9383(86)90046-7.
12. "The cyclic homology of the group rings".
13. Burghelea, Dan; Vigué Poirrier, Micheline (1988). "Cyclic homology of commutative algebras I". Algebraic Topology Rational Homotopy. Lecture Notes in Mathematics. Vol. 1318. pp. 51–72. doi:10.1007/BFb0077794. ISBN 978-3-540-19340-1.
14. Burghelea, D.; Friedlander, L.; Kappeler, T. (1992). "Meyer-vietoris type formula for determinants of elliptic differential operators". Journal of Functional Analysis. 107: 34–65. doi:10.1016/0022-1236(92)90099-5.
15. Burghelea, D.; Kappeler, T.; McDonald, P.; Friedlander, L. (1996). "Analytic and Reidemeister torsion for representations in finite type Hilbert modules". Geometric and Functional Analysis. 6 (5): 751–859. arXiv:dg-ga/9502001. doi:10.1007/BF02246786. S2CID 16656673.
16. Burghelea, Dan; Haller, Stefan (2007). "Complex-valued Ray–Singer torsion". Journal of Functional Analysis. 248: 27–78. arXiv:math/0604484. doi:10.1016/j.jfa.2007.03.027. S2CID 31221717.
17. Burghelea, Dan; Haller, Stefan (2008). "Torsion, as a Function on the Space of Representations". C*-algebras and Elliptic Theory II. Trends in Mathematics. pp. 41–66. arXiv:math/0507587. doi:10.1007/978-3-7643-8604-7_2. ISBN 978-3-7643-8603-0. S2CID 160308.
18. Burghelea, Dan; Haller, Stefan (2013). "Topology of angle valued maps, bar codes and Jordan blocks". arXiv:1303.4328 [math.AT].
19. Dan Burghelea at the Mathematics Genealogy Project
20. "Professor Dan Burghelea" (PDF).
21. "Honorary members of the "Simion Stoilow" Institute of Mathematics of the Romanian Academy".
22. "Ana H Burghelea".

External links

• Dan Burghelea publications indexed by Google Scholar
• Publications by Dan Burghelea at ResearchGate