Dan Burghelea

Burghelea was born in Râmnicu Vâlcea, Romania, in 1943, where he attended Alexandru Lahovari National College (at that time lyceum Nicolae Bălcescu).{{cite web|url=https://www.lahovari.com/personalitati/ |title=Personalități. Foști elevi – evidențiați în diferite domenii|language=ro|publisher=Alexandru Lahovari National College|website=www.lahovari.com|access-date=May 26, 2025}} 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.{{citation|url=https://www.observatorcultural.ro/articol/in-generatia-mea-matematica-a-reprezentat-o-optiune-fericita/|title="În generația mea, matematica a reprezentat o opțiune fericită"|language=ro|first=Ovidiu|last=Șimonca|magazine=Observator Cultural|issue=582|date=July 8, 2011|access-date=May 26, 2025}}

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.{{cite web|url=https://imar.ro/en/publications/newsletter/newsletter-no-1/newsletter-no-1-1|title=Institutul de Matematică este casa mea din București| language=ro|first=Anca|last=Bonciocat|publisher=Institute of Mathematics of the Romanian Academy|website=imar.ro|access-date=May 27, 2025}}

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 {{ill|Horia Hulubei Institute of Nuclear Physics|lt=Institute of Nuclear Physics|ro|Institutul Național de Cercetare-Dezvoltare pentru Fizică și Inginerie Nucleară „Horia Hulubei”}} (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.{{cite web|url=https://people.math.osu.edu/burghelea.1/CV%20.pdf|title=Dan Burghelea}} He has significantly influenced the orientation of the geometry-topology research in Romania.{{cite web|url=https://people.math.osu.edu/burghelea.1/DAN-LAUDATIO.pdf|title=Professor Dan Burghelea - Doctor Honoris Causa}}

Burghelea has worked in algebraic, differential, geometrical topology, differential and complex geometry, commutative algebra, global and geometric analysis, and applied topology.{{cite web|url=https://people.math.osu.edu/burghelea.1/PUB2.pdf|title=Dan Burghelea Publications}}

His most significant contributions are on Topology of infinite dimensional manifolds;{{cite web|url=http://www.map.mpim-bonn.mpg.de/Hilbert_manifold|title=Hilbert manifold}}{{cite journal|url=https://www.jstor.org/stable/1970743|title=Hilbert Manifolds|jstor=1970743|last1=Burghelea|first1=Dan|last2=Kuiper|first2=Nicolaas H.|author2-link=Nicolaas Kuiper|journal=Annals of Mathematics|year=1969|volume=90|issue=3|pages=379–417|doi=10.2307/1970743}} Homotopy type of the space of homeomorphisms and diffeomorphisms of compact smooth manifolds;{{cite book|chapter-url=https://link.springer.com/chapter/10.1007/BFb0088105|chapter=The rational homotopy groups of Diff (M) and Homeo (Mn) in the stability range|doi=10.1007/BFb0088105|title=Algebraic Topology Aarhus 1978|series=Lecture Notes in Mathematics|year=1979|last1=Burghelea|first1=D.|volume=763|pages=604–626|isbn=978-3-540-09721-1}}{{cite journal|url=https://www.ams.org/journals/tran/1982-269-01/S0002-9947-1982-0637027-4/|title=Geometric transfer and the homotopy type of the automorphism groups of a manifold|year=1982 |doi=10.1090/S0002-9947-1982-0637027-4 |last1=Burghelea |first1=D. |last2=Lashof |first2=R. |journal=Transactions of the American Mathematical Society |volume=269 |page=1 |doi-access=free }} Algebraic K-theory and cyclic homology of topological spaces, groups (including simplicial groups) and commutative algebras (including differential graded commutative algebras);{{cite journal|title=Cyclic homology and algebraic K-theory of spaces—II|year=1986 |doi=10.1016/0040-9383(86)90046-7 |last1=Burghelea |first1=D. |last2=Fiedorowicz |first2=Z. |journal=Topology |volume=25 |issue=3 |pages=303–317 |doi-access= }}{{cite web|url=https://www.researchgate.net/publication/227109904|title=The cyclic homology of the group rings}}{{Cite book|chapter-url=https://link.springer.com/chapter/10.1007/BFb0077794|chapter=Cyclic homology of commutative algebras I|doi=10.1007/BFb0077794|title=Algebraic Topology Rational Homotopy|series=Lecture Notes in Mathematics|year=1988|last1=Burghelea|first1=Dan|last2= Vigué Poirrier|first2=Micheline|volume=1318|pages=51–72|isbn=978-3-540-19340-1}} Zeta-regularized determinants of elliptic operators and implications to torsion invariants for Riemannian manifolds.{{cite journal|title=Meyer-vietoris type formula for determinants of elliptic differential operators|year=1992 |doi=10.1016/0022-1236(92)90099-5 |last1=Burghelea |first1=D. |last2=Friedlander |first2=L. |last3=Kappeler |first3=T. |author3-link=Thomas Kappeler|journal=Journal of Functional Analysis |volume=107 |pages=34–65 |doi-access= }}{{cite journal|url=https://link.springer.com/article/10.1007/BF02246786|title=Analytic and Reidemeister torsion for representations in finite type Hilbert modules|year=1996|doi=10.1007/BF02246786|last1=Burghelea|first1=D.|last2=Kappeler|first2=T.|last3=McDonald|first3=P.|last4=Friedlander|first4=L.|journal=Geometric and Functional Analysis|volume=6|issue=5|pages=751–859|s2cid=16656673|arxiv=dg-ga/9502001}}{{cite journal|title=Complex-valued Ray–Singer torsion|year=2007 |doi=10.1016/j.jfa.2007.03.027 |last1=Burghelea |first1=Dan |last2=Haller |first2=Stefan |journal=Journal of Functional Analysis |volume=248 |pages=27–78 |s2cid=31221717 |doi-access=free |arxiv=math/0604484 }}{{cite book|chapter-url=https://link.springer.com/chapter/10.1007/978-3-7643-8604-7_2|chapter=Torsion, as a Function on the Space of Representations|doi=10.1007/978-3-7643-8604-7_2|title=C*-algebras and Elliptic Theory II|series=Trends in Mathematics|year=2008|last1=Burghelea|first1=Dan|last2=Haller|first2=Stefan|pages=41–66|arxiv=math/0507587|isbn=978-3-7643-8603-0|s2cid=160308}}

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.{{cite arXiv|title=Topology of angle valued maps, bar codes and Jordan blocks|eprint=1303.4328|last1=Burghelea|first1=Dan|last2=Haller|first2=Stefan|year=2013|class=math.AT}} 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.{{MathGenealogy|id=12033}}

• 1966 – Simion Stoilow Prize, the Romanian Academy
• 1995 – Doctor Honoris-Causa, West University of Timișoara{{cite web|url=https://people.math.osu.edu/burghelea.1/DAN-LAUDATIO.pdf|title=Professor Dan Burghelea}}
• 2003 – National Order of Faithful Service, Commander rank{{citation|url=https://legislatie.just.ro/Public/DetaliiDocument/44401|title=

Decret nr. 370 din 11 iunie 2003|language=ro|work=Monitorul Oficial| issue=420|date=June 16, 2003|access-date=May 28, 2025}}

• 2005 – Honorary membership, IMAR, Romania{{cite web|url=http://www.imar.ro/organization/people/honoraryMembers.php|title=Honorary members of the "Simion Stoilow" Institute of Mathematics of the Romanian Academy}}
• 2009 – Distinction Academic Merit, Romanian Academy of Sciences
• 2019 – Medal of Honor, the Romanian Mathematical Society

Dan Burghelea married Ana Burghelea, in 1965. They have a daughter, Gabriela Tomescu.{{cite web|url=https://www.officialusa.com/names/Ana-Burghelea/|title=Ana H Burghelea}}

Burghelea's books include:

• {{Cite book|last1=Antonelli|first1=Peter L.|last2=Burghelea|first2=Dan| last3=Kahn|first3=Peter J.| title=The concordance-homotopy groups of geometric automorphism groups|year=1971|publisher=Springer-Verlag|series=Lecture Notes in Mathematics|volume=215|location=Berlin, New York|isbn=978-0387055602|doi=10.1007/BFb0061176|mr=0358834}}
• {{Cite book|last1=Burghelea|first1=Dan|last2=Hangan|first2=Theodor|last3=Moscovici|first3=Henri|author3-link=Henri Moscovici|last4=Verona|first4=Andrei| title=Introducere în topologia diferențială|language=ro|year=1973| publisher=Editura științifică|location=București|oclc=22096344}}
• {{Cite book|last1=Burghelea|first1=Dan|title=Groups of Automorphisms of Manifolds|last2=Lashof|first2=Richard|author2-link=Richard Lashof|last3=Rothenberg|first3=Melvin|date=1975|publisher=Springer-Verlag|isbn=978-3-540-07182-2|series=Lecture Notes in Mathematics|volume=473|location=Berlin, New York| doi=10.1007/bfb0079981|oclc=1527692|mr=0380841}}
• {{Cite book|last=Burghelea|first=Dan|title=New topological invariants for real- and angle-valued maps: an alternative to Morse–Novikov theory|publisher= World Scientific|location= Hackensack, NJ|year=2017|isbn=978-9814618267|doi=10.1142/9254|mr=3645481}}

{{reflist}}

• {{google scholar id|yKc9M2gAAAAJ}}
• {{ResearchGate|Dan_Burghelea}}

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Category:Living people

Category:1943 births

Category:People from Râmnicu Vâlcea

Category:Romanian emigrants to the United States

Category:University of Bucharest alumni

Category:Ohio State University faculty

Category:Topologists

Category:20th-century Romanian mathematicians

Category:21st-century Romanian mathematicians

Category:20th-century American mathematicians

Category:21st-century American mathematicians

Category:Institute for Advanced Study visiting scholars

Category:Recipients of the National Order of Faithful Service