English Version

Prof.dr. Popescu Dorin - sef catedra

 


Data si locul nasterii: 21 martie 1947, in comuna Patarlagele, jud.Buzau.

Nationalitate: Romana
Cetatenie: Romana

Adresa oficiala:
     - Universitatea din Bucuresti, Facultatea de Matematica, Str. Academiei 14, Bucuresti, 70109, Romania;
     - Institutul de Matematica al Academiei Romane, P.O.Box 1-764, Bucuresti 70700, Romania, Tel.: 0040/21/2125648, Fax: 0040/21/2125126.

E-Mail: dorin.popescu  imar.ro, dpopescu  gta.math.unibuc.ro


STUDII:
1964-1969 - Absolvent al Facultatii de Matematica, Universitatea din Bucuresti.
1974 - titlul de doctor obtinut cu lucrarea "Proprietatea de aproximare forte pentru inele de valuare discreta"; conducator stiintific Prof.Dr. I.Bucur.

ACTIVITATEA PROFESIONALA

  • 1969-1979 - Asistent univ. la Facultatea de Matematica, Universitatea din Bucuresti, Romania;
  • 1979-1990 - CP III, Institutul National pentru Stiinta si Creatie Tehnica, Bucuresti, Romania;
  • 1990-1993 - CP II, Institutul de Matematica al Academiei Romane, Bucuresti, Romania;
  • 1991-1993 - Conf. univ. la Facultatea de Matematica, Universitatea din Bucuresti, Romania;
  • 1993 - prezent - CP I, Institutul de Matematica al Academiei Romane, Bucuresti, Romania;
  • 1993 - prezent - Prof. univ. la Facultatea de Matematica, Universitatea din Bucuresti, Romania.


DOMENII DE CERCETARE
Algebra comutativa, combinatorica in algebra comutativa, computer algebra, geometrie algebrica.

PREMII OBTINUTE
Premiul I pentu cercetare, Atena (1973), acordat de Uniunea Balcanica de Matematica
Premiul Academiei Romane, 1979.

CONFERINTE SUSTINUTE
Am sustinut conferinte la urmatoarele universitati din strainatate: MIT, Berkeley, Los Angeles, Salt Lake City, Urbana-Champaigne (USA), Montreal (Canada), Edinburgh, Glasgow, Sheffield (Marea Britanie), Kyoto, Nagoya (Japonia), Genova, Ferrara, Catania, Cortona (Italia), Barcelona (Spania), Bordeaux, Luminy, Grenoble (Franta), Utrecht (Olanda), Innsbruck (Austria), Max-Planck Institut Bonn, Bochum, Essen, Stuttgart, Koln, Berlin, Cottbus, Eisenach, Gottingen, Bielefeld, Kaiserslautern, Oldenburg, Oberwolfach, Osnabruck, Vechta (Germania), Salonic (Grecia), Oslo (Norvegia), Islamabad, Lahore (Pakistan), Varsovia (Polonia), Budapesta (Ungaria).

STAGII de CERCETARE in STRAINATATE
  • 1980-1981: bursa NSF la Institute for Advanced Study, Princeton, USA;
  • 1990-1991: bursa Alexander von Humboldt la Universitatea din Essen, Germania;
  • 1992: bursa Alexander von Humboldt (6 luni) la Universitatea din Osnabruck, Abteilung Vechta, Germania;
  • 1993-1997: in fiecare an am fost cate 6 luni profesor invitat la Sonderforschungsbereich 170 Gottingen, Universitatea din Kaiserslautern, respectiv Universitatea din Essen, Germania, cu bursa DFG, respectiv bursa Alexander von Humboldt;
  • 1998: profesor invitat cate o luna la Universitatea din Edinburgh, Scotia; Universitatea din Kaiserslautern, Germania; Sonderforschungsbereich Bielefeld, Universitatea din Bielefeld, Germania;
  • mai-iunie 1999: profesor invitat la Universitatea din Edinburgh, Scotia, cu un grant EPSRC;
  • aprilie 1999: profesor invitat la Universitatea din Kaiserslautern;
  • iulie-septembrie 1999: profesor invitat la Universitatea din Essen, Germania, cu bursa Alexander von Humboldt;
  • ianuarie-martie 2000: profesor invitat la Universitatea din Kaiserlautern, respectiv Universitatea din Essen, Germania, cu un grant DFG, respectiv o bursa DAAD;
  • mai-iunie 2000: profesor invitat la University din Edinburgh, Scotia, cu un grant EPSRC;
  • ianuarie-martie 2001: profesor invitat la Universitatea din Kaiserslautern, respective Universitatea Humboldt Berlin, Germania, cu un grant DFG;
  • iunie 2001: profesor invitat la Universitatea din Bordeaux, Franta;
  • ianuarie-martie 2002: profesor invitat la Universitatea din Essen, Germania, cu bursa Alexander von Humboldt;
  • aprilie 2002: profesor invitat la Universitatea din Barcelona, Spania;
  • mai-august 2002: profesor invitat la Universitatea Humboldt Berlin, Germania;
  • februarie-martie 2003: profesor invitat la MSRI Berkeley, USA;
  • iunie-iulie 2003: profesor invitat la Universitatea din Kaiserslautern, Germania, cu un grant DFG;
  • august 2004 - iulie 2005: profesor invitat la Universitatea din Essen, Germania, cu o bursa Marie Curie Intra-European Fellowship MEIF-CT-2003-501046.


ALTE INFORMATII
  • sunt editor pentru 2 jurnale: Central European Math J, preluat de Springer sub numele de Versita J. (revista internationala indexata ISI); Bull. Math. Soc. Sc. Math. Roumanie (indexata ISI);
  • presedintele Societatii de Stiinte Matematice din Romania in perioada 2004-2008;
  • vice-presedinte MASSEE (Asociatia Societatilor de Stiinte Matematice din Balcani), 2004-2007;
  • am fost conducatorul de doctorat pentru: Viviana Ene, Marius Vladoiu, Mircea Cimpoeas, Alin Stefan (Romania), Imran Anwar, Sarfraz Ahmad (Pakistan).


DESCRIEREA REZULTATELOR SEMNIFICATIVE
Am obtinut diverse rezultate originale privind: aproximare Artin si inele Henseliene, desingularizare Neron, module proiective ale inelelor de polinoame peste un inel regulat, module maximale Cohen-Macaulay, module Quasi-Buchsbaum si module generalizate Cohen-Macaulay, algebre Rees si combinatorica in algebra. Solutiile mele la cateva conjecturi ale lui M.Artin, Bass-Quillen au fost prezentate la Seminarul Bourbaki de B.Teissier (1993-1994) si de R.Swan in "Neron Popescu Desingularization" in Algebra and Geometry, Ed.Ming-Chang Kang, International Press, Boston, 1998. Impreuna cu J.Herzog si L.O'Carroll, am generalizat o teorema a lui Knorrer, pe care am folosit-o in descrierea modulelor maximale Cohen-Macaulay peste anumite hipersuprafete. Mai tarziu, impreuna cu Herzog am demonstrat Conjectura lui Pardue privind regularitatea Mumford-Castelnuovo a idealelor p-Borel si am obtinut rezultate partiale unei conjecturi a lui Eisenbud-Green-Harris in Cayley-Bacharach Theory and Higher Castelnuovo Theory. Folosind clasificarea Atiyah a fibratilor peste V(f), am reusit impreuna cu R.Laza si G.Pfister sa descriem modulele maximale Cohen-Macaulay peste conul curbei proiective V(f), unde f=X^3+Y^3+Z^3. De asemenea impreuna cu C.Baciu, V.Ene si G.Pfister am descris modulele maximale Cohen-Macaulay peste suprafata f=X^3+Y^3+Z^3+U^3 de rang <= 2. Recent, impreuna cu J.Herzog am extins conceptul de complex simplicial shelabil si am studiat proprietatile echivalentului algebric, i.e. asa numitul modul "pretty clean". Impreuna cu I.Anwar am demonstrat conjectura lui Stanley pentru ideale monomiale in patru variabile si ulterior am demonstrat aceeasi conjectura pentru 5 variabile.

Articole stiintifice

  1. Quelques applications de la decomposition triangulaire, Publ. Dept. Math. Lyon 3-4 (1967), p.63-68.
  2. On the algebraic categories, Rev. Roum. Math. Pures et Appl. 13 (1968), p.337-342 (cu G.Georgescu).
  3. Les faisceaux d'une theorie, C.R. Acad. Sci. Paris 269 (1969), p.380-382.
  4. Sur les categories des (t,T)-faisceaux, C.R. Acad. Sci. Paris 269 (1969), p.413-415.
  5. Deux extensions des ensembles preordonnes, Rev. Roum. Math. Pures et Appl. 15 (1970), p.569-572 (cu N.Manolache).
  6. Some remarks on complete cogenerated categories, Rev. Roum. Math. Pures et Appl. 15 (1970), p.1027-1033.
  7. Monoconuri proiective si epiconuri inductive, Stud. Cerc. Mat. 22 (1970), p.641-647.
  8. Categories de faisceaux, J. of Algebra 18 (1971), p.343-365.
  9. Les faisceaux d'une classe des morphismes, C.R.Acad. Sci. Paris 272 (1971), p.101-103.
  10. Cofaisceaux d'une categorie, C.R. Acad. Sci. Paris 272 (1971), p.299-302.
  11. A strong approximation theorem over discrete valuation rings, Rev. Roum. Math. Pures et Appl. 20 (1975), p.659-692.
  12. Die strenge Approximationseigenschaft lokaler Ringe, Inventiones Math. 30 (1975), p.145-174 (cu G.Pfister).
  13. Some algorithmic methods in the theory of local complete rings, Bull. Math. de la Soc. Math. de la Roumaine 22 (70), nr.1 (1978), p.61-69.
  14. Algebraically pure morphisms, Rev. Roum. Math. Pures et Appl. 24 (1979), p.947-977.
  15. Die approximation von Primidealen, Bull. de l'Acad. Polonaise Sci. 27 (1979), p.771-778 (cu G.Pfister).
  16. A remark on two-dimensional local rings with the property of approximation, Math. Z. 173 (1980), p.235-240.
  17. Approximation properties and existential completeness for ring mophisms, Manuscripta Math. 33 (1981), p.227-282 (cu S.Basarab si V.Nica).
  18. On three dimensional local rings with the property of approximation, Rev. Roum. Math. Pures et Appl. 26 (1981), p.301-307 (cu G.Pfister).
  19. Some extensions of Neron's p-desingularization and approximation, Rev. Roum Math. Pures et Appl. 26 (1981), p.1299-1304 (cu M.Cipu).
  20. Global form of Neron's p-desingularization and approximation, Proceedings "Week of Algebraic Geometry", Bucharest, June 30 - July 6 (1980), Teubner Texte Band 40, Leipzig 1981.
  21. On Zariski's Uniformization Theorem, in Algebraic Geometry, Bucharest 1982, Proceedings, Springer Lect. Notes in Math., p.1056, Berlin 1984.
  22. Ultraproducts and big Cohen-Macaulay modules, Stud. si Cerc. Mat. 36 (1984), p.424-428 (cu C.Mateescu).
  23. A desingularization theorem of Neron type, Ann. Univ. Ferrara, 30 (1984), p.63-76 (cu M.Cipu).
  24. General Neron desingularization, Nagoya Math. J., 100 (1985), p.97-126.
  25. A structure theorem on formally smooth morphisms in positive characteristic, J. of Algebra, 100 (1986), p.436-455 (cu V.Nica).
  26. Some stucture theorems for valuation rings, Rev. Roum. Math. Pures Apl., 31 (1986), p.577-582.
  27. General Neron desingularization and Approximation, Nagoya Math. J., 104 (1986), p.85-115.
  28. Artin approximation theory and applications, Analele St. ale Univ. Iasi 31 (1985 supliment), p.11-14.
  29. A certain desingularization Theorem, Analele St. ale Univ. Iasi, 31 (1985 supliment), p.20-22 (cu M.Cipu).
  30. Ultraproducts and Hochster's modifications, Analele St. ale Univ. Iasi, 31 (1985 supliment), p.26-27 (cu C.Mateescu).
  31. On the structure of formally smooth morphisms, Analele St. ale Univ. Iasi, 31 (1985 supliment), p.33-34 (cu V.Nica).
  32. Algebraic extensions of valued fields, J. of Algebra, 108 (1987), p.513-533.
  33. Algebrization of deformation of exceptional couples, Rev. Roum. Math. Pures et Appl., 33 (1988), p.251-260 (cu M.Roczen).
  34. Polynomial rings and their projective modules, Nagoya Math. J., 113 (1989), p.121-128.
  35. Flatness in non-Noetherian ring theory, Rev. Roum. Math. Pures et Appl., 34 (1989), p.839-854.
  36. Immediate extensions of filtered rings, Annali di Ferrara, 35 (1989), p.35-37 (cu W.Morariu).
  37. Indecomposable Cohen-Macaulay modules and the Brauer-Thrall Conjectures, Proceedings of the Algebra Conference 9-10 June 1988, Brasov.
  38. Indecomposable Cohen-Macaulay modules and irreductible maps, Compositio Math., 76 (1990), p.277-294 (cu M.Roczen).
  39. Letter to the Editor, General Neron desingularization and approximation, Nagoya Math. J., nr.118 (1990), p.45-53.
  40. Indecomposable Cohen-Macaulay modules and their multiplicities, Trans, AMS 323 (1989), p.369-387.
  41. The second Brauer-Thrall conjecture, Manuscripta Math., 71 (1991), p.375-383 (cu M.Roczen).
  42. Liftings of finite injective dimension modules, Analele Univ. Bucuresti XL (1991), p.65-75.
  43. Indecomposable generalized Cohen-Macaulay modules, Trans. Amer. Math. Soc. 342 (1994), p.107-136 (cu M.Cipu si J.Herzog).
  44. Relative liftings, J. Pure Appl. Algebra, 108 n.3 (1996).
  45. Maximal Cohen-Macaulay modules over isolated singularities, J. of Algebra 178 (1995), p.710-732.
  46. Deformations of maximal Cohen-Macaulay modules, Math. Z., 223 (1996), p.309-332 (cu G.Pfister).
  47. Maximal Cohen-Macaulay modules and their deformations, Analele St. Univ. Constanta, v.II (1994), p.112-119.
  48. Thom-Sebastiani problems for maximal Cohen-Macaulay modules, Math.Ann., 309 (1997), 677-700 (cu J.Herzog).
  49. Infinitesimal module deformations in the Thom-Sebastiani problem, Archiv der Math. 69 (1997), p.196-208 (cu F.Enescu si G.Pfister).
  50. Hilbert functions and generic forms, Compositio Math. 113 (1998), p.1-22 (cu J.Herzog).
  51. Maximal Cohen-Macaulay modules over singularities of type Xt+Y3, Revue Roum. Math. Pures et Appl., 42, no.7-8 (1997), p.591-619 (cu B.Martin and G.Pfister).
  52. Special Cohen-Macaulay modules over singularities of type X3r+Y3, Analele Stiintifice Constanta, 5, no.2 (1997), p.112-119.
  53. A family of Cohen-Macaulay modules over singularities of type Xt+Y3, Commun. in Alg., 27(6)(1999), p.2555-2572 (with G.Pfister).
  54. Variations on Green Theorem concerning the Hilbert functions, in: "Commutative Algebra and Algebraic Geometry" editor F.Van Oystaeyen, Dekker Lect. Notes in Pure and Appl. Math. 206(1999), p.237-244.
  55. Steps in the classification of Cohen-Macaulay modules over singularities of type Xt+Y3, Algebras and Representation Theory, vol.2, no.2 (1999), p.137-175 (cu V.Ene).
  56. Free resolutions for deformations of maximal Cohen-Macaulay modules, Commun. In Alg., 28 (11) (2000), p.5329-5352 (cu L.O'Carroll).
  57. On a Theorem of Knörrer concerning Cohen-Macaulay modules, J. of Pure and Appl. Alg. (2000) (cu L.O'Carroll).
  58. Betti numbers for p-stable ideals, Communications in Algebra, 28 (3), (2000), p.1515-1531 (cu V.Ene si G.Pfister).
  59. Combinatorics in Algebra and Geometry, Italian Journal of Pure and Appl. Math., no.7 (2000), p.27-32.
  60. Variations on Néron desingularization, in: Sitzungsberichte der Berliner Mathematischen Gesselschaft, Berlin, 2001, p.143-151.
  61. Splitting syzygies, J. of Alg. 228 (2000), p.682-709 (cu L.O'Carroll).
  62. On the regularity of p-Borel ideals, Proceedings of AMS 129 (2001), p.2563-2570 (cu J.Herzog).
  63. Betti numbers and the regularity of p-Borel ideals, Bul. St. Univ. Pitesti, Ser. Mat.Inf., 5 (2001), 1-7.
  64. Regularity of Rees algebras, J. London Math. Soc., (2) 65, (2002), p.320-338 (cu J.Herzog si N.V.Trung).
  65. Explicit linear minimal free resolutions over a natural class of Rees algebras, Archiv Math., 81 (2003), p.636-645 (cu J.Herzog si L.O'Carroll).
  66. Maximal Cohen-Macaulay modules over Y13+ … +Yn3 with few generators, Math. Reports 3 (53), 2 (2001), p.177-185 (cu R.Laza si L.O'Carroll).
  67. Cohen-Macaulay representation, in Algebra-Representation Theory, Eds. K.W.Roggenkamp si M. Stefanescu, Kluwer, 2001, p.249-256.
  68. Maximal Cohen-Macaulay modules over the cone of an elliptic curve, J. Alg., 253, (2002), p.209-236 (cu R.Laza, G.Pfister).
  69. Gröbner basis and depth of Rees algebras, Anal. Univ. Ovidius, Constanta, IX (2001), p.81-88.
  70. On the Ext-modules of ideals of Borel type, in Commutative Algebra, Interactions with Algebraic Geometry, Eds: L. Avramov et al, Contemporary Math. Nr 331, AMS, Providence, 2003, 171-186 (cu J. Herzog, M. Vladoiu).
  71. Rank one maximal Cohen-Macaulay modules over singularities of type Y13+Y23+Y33+Y43, in Commutative Algebra, Singularities and Computer Algebra, Eds: J. Herzog, V. Vuletescu, NATO Science Series, Vol 115, Kluwer Acad. Publ., Dordrecht-Boston-London, 2003, 141-157 (cu V.Ene).
  72. Rank two maximal Cohen-Macaulay modules over singularities of type Y13+Y23+Y33+Y43, J. Alg., 292, (2005), p.447-491 (cu C.Baciu, V.Ene, G.Pfister).
  73. On a question of Quillen, Bull. Math. Soc. Sci. Roum., Vol.45 (93), no.3-4 (2002), p.209-212.
  74. Finite filtrations of modules and shellable multicomplexes, Manuscripta Math., 121, no.3, (2006), p.385-410 (cu J. Herzog).
  75. Extremal Betti numbers and regularity of Borel type ideals, Bull Math. Soc. Sc. Roum. Vol.48 (96), no.1 (2005), p.65-72.
  76. Lifting an ideal from a tight Bourbaki sequence and maximal Cohen-Macaulay modules, in NATO Science Series, Vol.196, Kluwer Acad. Publ., Dordrecht-Boston-London, Eds: G.Pfister, S.Cojocaru, V.Ufnarovski, 2005, 90-103.
  77. Criterions for shellable multicomplexes, Annalele St. Univ. Ovidius, Constanta, 14(2), (2006), 73-84.
  78. A monomial cycle basis of Koszul homology modules, J. of Pure and Appl. Algebra, 212(2008), 132-139.
  79. The strong Lefschetz property and simple extensions, (with J.Herzog), arXiv:math.AC/0506537.
  80. The strong Lefschetz property and certain complete intersection extensions, Bull. Math. Soc. Sc. Math. Roumanie, 48(96), no.4, (2005), 421-431.
  81. Strong Lefschetz property on algebras of embedding dimension three, (with M. Vladoiu), Bull. Math. Soc. Sc. Math. Roumanie, 49(97), no.1, (2006), 75-86.
  82. On the structure of MCM-modules over the ring K[[x,y]]/(x^n), (with V. Ene), Algebras and Representation Theory, ( 11) no.2, (2008), 191-205.
  83. Binomial cycle basis on Koszul homology modules, Communications in Algebra, (36), (2008), 1789-1800.
  84. Sequentially Cohen-Macaulay monomial ideals of embedding dimension four, (with S.Ahmad), Bull. Math. Soc. Sc. Math. Roumanie, 50(98), no.2, (2007), 99-110.
  85. Stanley conjecture in small embedding dimension, (with I.Anwar), J. Algebra (318), (2007), 1027-1031.
  86. Stanley depth of monomial ideals, Proc. of the 6-th Congress of Romanian Mathematicians, 2009, Ed.Academiei, 67-70.
  87. Stanley depth of multigraded modules, to appear in J. of Algebra.
  88. An inequality between depth and Stanley depth, Preprint 2009.

Carti si manuale

  1. Die Approximationseigenshaft lokaler Ringe, Springer Lect. Notes in Math. 634, 1978, Berlin (cu H.Kurke, T.Mostowski, G.Pfister si M.Roczen).
  2. Inele henseliene si proprietatea de aproximare, Ed. Univ. Bucuresti, 1979 (cu V.Nica).
  3. Elemente de teoria grupurilor finite si aplicatii, Ed. Stiintifica Enciclopedica, 1986 (cu C.Vraciu).
  4. Artin approximation, in Handbook of Algebra, vol.2, Ed. M.Hazewinkel, 2000 Elsevier Science, 321-356.
  5. Artin Approximation, in Encyclopaedia of Mathematics, Suplement II, Ed. M.Hazewinkel, Kluwer Academic Publishers, 2000, 30-32.
  6. Inele Cohen-Macaulay, in "Seminar de Algebra, Inele si Module Cohen-Macaulay", Ed.M.Stefanescu, Tip. Univ. Iasi, 1986, Cap.IV.
  7. Module Cohen-Macaulay si conjecturi omologice, in "Probleme actuale ale cercetarii matematice", vol.II, Tip. Univ. Bucuresti, 1992, 101-113.
  8. Bounds for Betti numbers, in "Combinatorics in algebra and geometry", Sem. Ser. Math. Algebra: 2, Tip. Univ. Ovidiu University, Constanta, 1998, 65-70.
  9. F-rational and strong F-rational rings, in "Tight Closure", Sem. Ser. Math., Tip. Univ. Ovidiu University, Constanta, 2001, 31-42.
  10. Criptografie, coduri, algoritmi, (cu C.Gherghe), Ed. Univ. din Bucuresti, 2005.



Actualizat: 20 martie 2009



2002 - 2015 -- Facultatea de Matematica si Informatica, Universitatea din Bucuresti
Str. Academiei nr. 14, sector 1, C.P. 010014, Bucuresti, Romania
Tel: (4-021) 314 2863, Fax: (4-021) 315 6990, secretariat  fmi.unibuc.ro