ALGEBRE HOPF, GRUPURI CUANTICE, REPREZENTARI SI CATEGORII TENSORIALE

Pentru studenti:

Geometrie analitica (actualizat);

Geometrie computationala (actualizat 6 oct. 2009);

Data si locul nasterii: 25 Noiembrie 1968, Sibiu.
Educatia: Absolvent al Facultatii Matematica, Universitatea Bucuresti, in 1993.
Teza de doctorat: Doctor in matematica din 1998 cu teza "Corespondenta Kobayashi-Hitchin pentru ecuatii de tip vortex cuplate cu campuri Higgs", Universitatea Zürich.
Pozitii academice: Preparator din 1993, asistent din 1997, lector din 2005.
Cursuri predate: A tinut seminarii de Geometrie si Geometrie Diferentiala.

Articole stiintifice

On conformally semi-symmetric connections (cu L.Nicolescu si I.E.Hirica), Analele Univ. Oradea, Fasc. Matematica, Tom V, (1995-1996), 135-149.
Champs m-speciaux dans l'algebre de deformations (cu L.Nicolescu si I.E.Hirica), Analele Univ. Oradea, Fasc. Matematica, Tom V, (1995-1996), 119-134.
Sur les courbes caracteristiques associées a l'algebre de deformation des deux connexions lineaires, Studii si Cercetari Matematice, 5-6 (49), 1997, 423-427.
Dimensional reduction of monopole equations, Math. Reports, 3 (53) (2001), 3, 293-303.
The Kobayashi-Hitchin correspondence for vortex-type equations coupled with Higgs fields (I), Math. Reports, 3 (53) (2001), 4, 425-444.
The Kobayashi-Hitchin correspondence for vortex-type equations coupled with Higgs fields (II), Math. Reports, 4 (54) (2002), 1, 123-142.
Quotients in algebraic and symplectic geometry, Annual Report 2002, Mathematical Institute, Leiden University, 5-12.
On the monopole equations, Revue Roumaine Math. Pures et Appliqu�es, 48 (2003), 3, 311-326.
Stability in linear problems, Preprint MI-2003-22, Universitatea Leiden, 2003.
Rings of invariants for representations of quivers (cu M.Halic), C.R. Acad. Sci. Paris, Ser.I 340 (2005), 135-140.
Un studiu privind invatarea spatiilor vectoriale (cu C. Voica), Proceedings CAIM 13, Romai Educational Journal 1 (2006), 64-72.
Reprezentari mentale ale conceptelor de algebra liniara (cu C.Voica), in curs de aparitie in Bull. SSM, Proceedings al Conferintei SSM, mai 2006.
Teaching Linear Algebra to students in Informatics (cu C.Voica), in curs de aparitie in Proceedings CAIM 14.

Actualizat: 31 mai 2007

CNCSIS TE cod 45, contract nr.88/02.08.2010 finantat de UEFISCDI (CNCS), program PNII Resurse Umane 2007-2013

English version:

Descriere succinta a proiectului de cercetare

Studiem cateva probleme de interes curent in teoria algebrelor hopf, legate de produse incrucisate, algebre hopf punctate, si teoria reprezentarii algebrelor hopf si generalizari. Vizam de asemenea sa extindem si sa studiem metode categoricale in algebre hopf, cum ar fi categorii monoidale, braided si tensoriale, si sa examinam cateva probleme generale categoricale legate de aceastea.

Director de proiect

Asistent Dr. Miodrag C Iovanov, Facultatea de Matematica si Informatica a Universitatii din Bucuresti.

Echipa de cercetare a grantului:

Asistent Dr. Miodrag C Iovanov
CSIII Sebastian Burciu
Lector Dr. Adriana Balan (Steleanu)
drd. Ana Agore (on leave from UB)

Cercetare sprijinita financiar de acest grant:

Articole:

M.C.Iovanov, S. Raianu, The Bijectivity of the Antipode Revisited", acceptata spre publicare, Comm. Algebra (special issue); Arxiv
S. Burciu, Normal Coideal Subalgebras of Semisimple Hopf Algebras, AGMP-6 Proceedings, Journal of Physics - Conference Series, acceptat 2011.
A.Agore, G.Militaru, Unified products and split extensions of Hopf algebras, 15 pag, acceptat 2012, va aparea in AMS Contemporary Math.
M.C.Iovanov, Generalized Frobenius Algebras and Hopf Algebras, 33 pagini, acceptat spre publicare 2012, Canadian Journal of Mathematics.
http://arxiv.org/abs/0803.0775
http://cms.math.ca/10.4153/CJM-2012-060-7
M.C.Iovanov, FSZ-groups and Frobenius-Schur Indicators of Quantum Double, 19 pag, trimis spre publicare revista ISI, preprint arxiv:
http://arxiv.org/abs/1208.4153
M.C.Iovanov, Serial Categories, Quantum Groups and the Pure Semisimplicity Conjecture, preprint 34 pp.

Prezentari la conferinte:

A.Agore, participare la conferinta Hopf Algebras and Tensor Categories, Almeria, Spania, Iulie 2011, cu prezentare “Produse bicrossed pentru algebre Hopf”.
Adriana Balan, participare la conferinta Category Theory, Algebra and Geometry, Louvain-la- Neuve, Belgia, Mai 2011.
Adriana Balan, participare la conferinta Hopf Algebras and Tensor Categories, Almeria, Spania, Iulie 2011.
Sebastian Burciu, participare la conferinta Quantum Theory and Symmetry 7, Praga, Czech Republik, August 7-13 2011, cu prezentarea ”Kernels of representations of representations of semisimple Hopf algebras”. Aici a avut porilejul sa intalneasca numerosi matematicieni si fizicieni specialisti in grupuri quantice.
M.C.Iovanov, participare la conferinta AMS Joint Meetings, New Orleans, SUA, Ianuarie 2011, cu prezentare “Hopf algebras from graphs”.
M.C.Iovanov, participare la conferinta Hopf Algebras and Tensor Categories, Almeria, Spania, Iulie 2011, cu prezentare “Path and Incidence co-algebras, Frobenius properties and a class of Hopf algebras”.
M.C.Iovanov, participare la conferinta Western Section Meeting Fall 2011, Salt Lake City, USA, Octombrie 2011, cu prezentare “On the integrality of the Frobenius-Schur indicators of Tensor Categories”.
Sebastian Burciu, participare la conferinta “Algebra Geometry Mathematical Physics”, Brno Czech Republic, September 12-14, 2012 cu prezentare ”On the irreducible representations of generalized quantum doubles”.
M.C.Iovanov, participare la conferinta internationala “Maurice Auslander Distinguised Lectures and International Conference ”, Aprilie 24 – Mai 1, 2012, cu prezentare.
A.Agore, participare la conferinta internationala “AMS-SSMR Joint Inernational Meetings, Alba Iulia, 26-30 Iunie 2013”, cu prezentare.
M.C.Iovanov, organizator al unei sectiuni speciale “Hopf algebras, coalgebras, and their categories of representations”, in cadrul “AMS-SSMR Joint Inernational Meetings, Alba Iulia, 26-30 Iunie 2013”.
M.C.Iovanov, participare la conferinta “Conerence of the Americas”, Guanajuato, Mexic, 5-9 August 2013, cu prezentare.