CRISTIAN D. POPESCU                      University of California, San Diego          Department of Mathematics          9500 Gilman Drive, Dept 0112          La Jolla, CA 92093-0112          Phone: (858)534-6297          Fax: (858)534-5273          E-mail: cpopescu@math.ucsd.edu

CONFERENCES AND SEMINARS ORGANIZED


Conference on Stark's Conjecture and related topics

Johns Hopkins University, August 5-9, 2002
Organized by D. Burns (London), C. Popescu (Baltimore), J. Sands (Burlington), D. Solomon (London), with support from the National Science Foundation, the Number Theory Foundation, and Johns Hopkins University.


• National Science Foundation Grant DMS-0200541
• Press coverage - Johns Hopkins Magazine, November 2002.
• Press coverage - JHU Gazette, Aug 5, 2002.

My main mathematical interests are in the fields of number theory and arithmetic algebraic geometry,
with a focus on special values of L-functions. My main results and research projects aim at formulating
and providing evidence for strong versions ("over Z", in Tate's and Rubin's  terminology) of Stark's
Conjectures for Artin L-functions,  studying Gross-type p-adic refinements of these statements, and their
relations with:

• The Equivariant Tamagawa Number Conjecture of Burns-Flach;
• Equivariant Main Conjectures in Iwasawa theory and their function field analogues, formulated in terms l-adic and crystalline homology of 1-motives;
• Euler Systems, as defined by Kolyvagin, Rubin, and Kato-Perrin Riou;
• The Galois module structure of ideal class-groups and groups of units: Gras-type conjectures,
Kummer-Ribet-type theorems, Brumer's Conjecture, and Chinburg's Omega_3 Conjecture;
• Leopoldt's Conjecture.
  

My research is currently funded through the National Science Foundation Research Grants  DMS-0600905,   DMS-0200543 and DMS-0350441



Recent Preprints


• On a Refined Stark Conjecture for Function Fields  ( stark.ps,    stark.dvi,    stark.pdf ); Compositio Mathematica, Vol. 116 (1999),  No.3 ,  pp. 321-367.  See  Featured Review .
  
 
• Gras-type Conjectures for Function Fields ( gras.ps,  gras.dvi,   gras.pdf ); Compositio Mathematica, Vol. 118 (1999),  No. 3,  pp. 263-290. See  Featured Review .
  
 
• Base Change for Stark-type Conjectures "over Z" ( bc.ps, bc.dvi, bc.pdf); Journal fur die Reine und Angew. Mathematik, Vol. 542 (2002), pp 85-111.
  
                                                                                                                                          (Awarded the Simion Stoilow Prize of the Romanian Academy of Science , 2004)

• Stark's Question and a strong form of Brumer's Conjecture (sq.ps,  sq.dvi,sq.pdf);  Compositio Mathematica , Vol. 140 (2004), pp. 631-646.
  

• The Rubin-Stark Conjecture for imaginary abelian fields of odd prime power conductor  (r-st2.dvi,  r-st2.ps,  r-st2.pdf); Mathematische Annalen Vol.. 330 (2004), No. 2, pp. 215-233.           
  
 
• On the Rubin-Stark Conjecture for a special class of CM extensions of totally real number fields  (r-st1.dvi, r-st1.ps, r-st1.pdf); Mathematische Zeitschrift, Vol. 247 (2004), pp. 529-547.
  

• Rubin's integral refinement of the abelian Stark Conjecture ( rint.dvi, rint.ps, rint.pdf );  Contemporary Mathematics, Vol. 358 (2004), pp. 1-35.


• Stark's Conjectures: Recent Work and New Directions, Contemporary Mathematics, Vol. 358 (2004), 232 pages.   (co-edited with D. Burns, J. Sands, and D. Solomon)
  

• Torsion points of Brauer groups and extensions of local constant degree for global function fields ( brauer.dvi, brauer.ps, brauer.pdf ); Journal of Number Theory. Vol. 115 (2005), No.
  


• The Rubin-Stark Conjecture for a special class of function field extensions ( special.dvi, special.ps, special.pdf );  Journal of Number Theory,   Vol. 113 (2005), No. 2, pp. 276-307.
  


• A class-field theoretical calculation ( cf.dvi, cf.ps, cf.pdf );  Jour. de Theorie des Nombres de Bordeaux, Vol. 18 (2006), No. 1, pp. 27-44.

• Stark's Question on Special Values of L-functions (starkq22.pdf), Math. Research Letters, Volume 14 (2007), No. 3,  pp. 531-545

• N-torsion of Brauer groups as relative Brauer groups of abelian extensions  (with J. Sonn and A. Wadsworth) (brauer2.pdf); Journal of Number Theory,Vol. 125 (2007), No. 1, Pages 26-38

• Special Values of Abelian L-functions at s=0 (with Caleb Emmons) (hosc4.pdf) ; to appear in Journal of Number Theory (2008).
  

• On the Coates-Sinnott Conjecture (cs.pdf) ; to appear in Mathematische Nachrichten (2008).
  

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TEACHING

        Winter 2010 Topics in Number Theory (Math 201); Multivariable Calculus (Math 20C).

        Summer 2009, II Number Theory (Math 104A)
       
        Winter 2009 Topics in Number Theory (Math 205); Abstract Algebra (Math 100B).

        Fall 2008      Abstract Algebra (Math 100A).

        Winter 2008 Graduate Number Theory (Math 204B);   Undergraduate Number Theory (Math 104B).

        Fall 2007     Number Theory (Math 104A)

        Winter 2007 Topics in Algebraic Number Theory (Math 205B) - Global Class Field Theory.   (Local/global diagram.)

        Fall 2006     Topics in Algebraic Number Theory (Math 205A) - Local and Global Class Field Theory;   Calculus (Math 20C).

        Spring 2006 Topics in Algebraic Number Theory (Math 205) - LOCAL CLASS FIELD THEORY

        Winter 2006 Graduate Algebra (Math 200B); Introduction to Differential Equations (Math 20D)      

        Fall 2005     Graduate Algebra (Math 200A);  Mathematical Reasoning (Math 109)      

        Spring 2005 Number Theory (Math 104C)

        Winter 2005 Number Theory (Math 104B);    Calculus (Math 20C)

        Fall 2004      Mathematical Reasoning (Math 109)
      
        Spring 2004  Mathematical Reasoning (Math 109)

        Winter 2004  Linear Algebra (Math 20F)

        Fall 2003        Introduction to Differential Equations (Math 20D)

                                       


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USEFUL LINKS

The American Mathematical Society

Number Theory Web

MathSciNet (Mathematical Reviews on the Web)

Algebraic Number Theory Archives

Journal Storage

Encyclopaedia Britannica

Book Finder (book dealers on line)

The MacTutor History of Mathematics Archive

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This page was last modified on Sept 17, 2004.
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