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

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

- 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

- Commutative Algebra
- Algebraic Geometry

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

- 1980-1981:
NSFfellowship at theInstitute for Advanced Study, Priceton, USA- 1990-1991:
Humboldtfellowship atEssen Universitywhich was extended with 6 months in 1992 atUniversity of Osnabrück, Abteilung Vechta- 1993-1997: each year 6 months, visiting professor at
Sonderforschungsbereich 170 Gottingen,Universität KaiserslauternandUniversität Essen.

The main result of D. Popescu is the so calledGeneral Néron Desingularizationwhich 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. is a positive answer of a conjecture ofM. Artinand 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 ofSwanand proves theBass-Quillenconjecture 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 theLindel's results.

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

Other results of D. Popescu are in the theory of maximalCohen-Macaulaymodules (in brief MCM). Some of them show theBrauer-ThrallConjectures for MCM in some cases of unequalcharacteristic [38], [40], [41]. Others extendKnörrer'sPeriodicity Theoremin characteristic 2 (withPfister) [46], or give an algorithm to describe the MCM modules over a singularity of typef(X)+Y_1^{s_1}+...+Y_r^{s_r}if you know the MCM modules overf(see some joint papers [47], [48], [51]-[53], [55]-[57]).

Recently D. Popescu has some results inCombinatorics in Commutative Algebra. Together withJ. Herzogan extension ofGreen's theorem concerning theHilbertfunctions is proved. As a consequence it shows some partial positive answers to some conjectures ofEisenbud-Green-Harrisin theCayley-Bacharachtheory and theHigher([50], [54]). Also theCastelnuovoTheoryBettinumbers of some monomial ideals (p-stable) are computed [58] and it is shown that thePardueconjecture holds in such cases.

dorin@stoilow.imar.ro, dpopescu@gta.unibuc.ro