Popescu Dorin-Mihail

Address

Institute of Mathematics of the Romanian Academy
P.O. Box 1-764, RO-70700 Bucharest, Romania
phone: (401) 650 05 92
fax: (401) 222 98 26

Education

• Faculty of Mathematics, University of Bucharest, 1964-1969
• PhD, University of Bucharest, 1974

Employment

• 1969-1970: Asistant Professor, Faculty of Mathematics, University of Bucharest.
• 1979-1990: Senior researcher III, National Institute for Scientific and Technical Creation, Mathematics department
• 1990-present: Senior Researcher II, then Senior Researcher I at the Institute of Mathematics of the Romanian Academy
• Since October 1, 1991: Associate Professor, and since 1993 Professor, Faculty of Mathematics, Bucharest University, with half position Senior Researcher I at the Institute of Mathematics

Research interest

• Commutative Algebra
• Algebraic Geometry

Scientific awards

• First prize for research (1973, Atena) of Balkanic Mathematics Union
• Prize of the Romanian Academy, 1979

Additional information

• 1980-1981: NSF fellowship at the Institute for Advanced Study, Priceton, USA
• 1990-1991: Humboldt fellowship at Essen University which was extended with 6 months in 1992 at University of Osnabrück, Abteilung Vechta
• 1993-1997: each year 6 months, visiting professor at Sonderforschungsbereich 170 Gottingen, Universität Kaiserslautern and Universität Essen.

Scientifical Research

The main result of D. Popescu is the so called General Néron Desingularization which says that a morphism of Noetherian rings is regular iff it is a filtered inductive limit of smooth finite type algebras (see [27], [28], [39]). This result has the following two consequences:

1. An excellent Henselian local ring has the Artin approximation property (in brief AP) [28].
2. A regular local ring containing a field is a filtered inductive limit of regular local rings essentially of finite type over Z [34].

1. is a positive answer of a conjecture of M. Artin and it gives in particular the approximation on nested subrings which was required by mathematicians working in singularity theory [28].

2. is a partial answer to a conjecture of Swan and proves the Bass-Quillen conjecture in the equal characteristic case (that is a finitely generated projective module of a polynomial ring over a regular local ring containing a field is free [34]) using the Lindel's results.

Another result of D. Popescu (with G. Pfister) says that every noetherian local ring, which has AP has also the strong approximation property (see [12]). A very easy proof applying the General Néron Desingularization is given in [28].

Other results of D. Popescu are in the theory of maximal Cohen-Macaulay modules (in brief MCM). Some of them show the Brauer-Thrall Conjectures for MCM in some cases of unequalcharacteristic [38], [40], [41]. Others extend Knörrer's Periodicity Theorem in characteristic 2 (with Pfister) [46], or give an algorithm to describe the MCM modules over a singularity of type f(X)+Y_1^{s_1}+...+Y_r^{s_r} if you know the MCM modules over f (see some joint papers [47], [48], [51]-[53], [55]-[57]).

Recently D. Popescu has some results in Combinatorics in Commutative Algebra. Together with J. Herzog an extension of Green's theorem concerning the Hilbert functions is proved. As a consequence it shows some partial positive answers to some conjectures of Eisenbud-Green-Harris in the Cayley-Bacharach theory and the Higher Castelnuovo Theory ([50], [54]). Also the Betti numbers of some monomial ideals (p-stable) are computed [58] and it is shown that the Pardue conjecture holds in such cases.

List of publications