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.
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[ro] (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.
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.
Burghelea, Dan; Hangan, Theodor; Moscovici, Henri; Verona, Andrei (1973). Introducere în topologia diferențială (in Romanian). București: Editura științifică. OCLC22096344.
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