Gavril Farkas

Professor of Mathematics
Humboldt Universität zu Berlin
Institut für Mathematik
Rudower Chaussee 25, Raum 1.401
10099 Berlin
Phone: +49 (30) 2093-5412
e-mail: farkas@math.hu-berlin.de

Secretary: Christa Dobers
Phone: +49 (30) 2093-5823
Fax: +49 (30) 2093-5853
e-mail: dobers@math.hu-berlin.de

Teaching/Lehre

  • The Algebraic Geometry Group at Humboldt University

  • The Humboldt Algebraic Geometry Seminar meets every Wednesday between 3:00-4:30 pm in Rudower Chaussee 25, Raum 3.006 (Haus 3, Erdgeschoss). Talks are expected to run for 90 minutes.

  • Moduli: A conference at the Humboldt University in Berlin (August 21- 28, 2009).

  • Complex Algebraic Geometry: A workshop on the occasion of Herbert Kurke's 70th birthday ( 9-10 October 2009).

  • Moduli spaces in algebraic geometry (10-16 January 2010). A new algebraic geometry workshop at Oberwolfach, co-organized with D. Abramovich (Brown) and S. Kebekus (Freiburg).

    Editorial work/Herausgebertätigkeit

  • Documenta Mathematica -the Journal of the German Mathematical Society (DMV)

  • Mathematica (Cluj) -a publication of the Romanian Academy

    Research/Forschungsgebiet

    My field of work is algebraic geometry. A significant part of my research is concerned with the study of the geometry and topology of various moduli spaces. Among other things I am interested in moduli of curves, enumerative geometry and Gromov-Witten theory, vector bundles on curves, abelian varieties and theta functions, Prym varieties, K3 surfaces, Brill-Noether type problems and syzygies of algebraic varieties.
    My research is integrated in the DFG Sonderforschungsbereich 647 Space-Time-Matter. Geometric and Analytic Structures . In this SFB, I am the leader of the Project A9 "Enumerative geometry of moduli spaces". I am a member of the Graduiertenkolleg Arithmetic and Geometry (Berlin-Zürich), as well as a faculty member of the Berlin Mathematical School. I have recently completed an Alfred P. Sloan Research Fellowship. Until 2007 I was Associate Professor at the University of Texas at Austin.

    Vita/Lebenslauf: dvi pdf

    Publications/Veröffentlichungen

    The geometry of the moduli space of curves of genus 23 dvi pdf
    Mathematische Annalen 318 (2000), 43-65

    Brill-Noether loci and the gonality stratification of M_g dvi pdf
    J. reine angewandte Mathematik 539 (2001), 185-200

    Divisors on M_{g,g+1} and the minimal resolution conjecture for points on canonical curves dvi pdf
    (with M. Mustata and M. Popa), Annales Scientifiques de L'Ecole Normale Superieure 36 (2003), 553-581

    The Mori cones of moduli spaces of pointed curves of small genus dvi pdf
    (with A. Gibney), Transactions American Mathematical Society 355 (2003), 1183-1199

    Regular components of moduli spaces of stable maps dvi pdf
    Proceedings American Mathematical Society 131 (2003), 2027-2036

    Gaussian maps, Gieseker-Petri loci and large theta-characteristics dvi pdf
    J. reine angewandte Mathematik 581 (2005), 151-174

    Effective divisors on M_g, curves on K3 surfaces and the Slope Conjecture dvi pdf
    (with M. Popa) Journal of Algebraic Geometry 14 (2005), 241-267

    Syzygies of curves and the effective cone of M_g dvi pdf
    Duke Mathematical Journal 135(2006), 53-98

    Higher ramification and varieties of secant divisors on the generic curve dvi pdf
    Journal of the London Mathematical Society 78 (2008), 418-440

    The global geometry of the moduli space of curves dvi pdf
    Algebraic Geometry Seattle 2005, Proceedings of Symposia in Pure Mathematics 80 (2009), 125-147

    Koszul divisors on moduli spaces of curves dvi pdf
    American Journal of Mathematics 131 (2009), 819-867

    The birational type of the moduli space of even spin curves dvi pdf
    Advances in Mathematics 223 (2010), 433-443

    Rational maps between moduli spaces of curves and Gieseker-Petri divisors dvi pdf
    Journal of Algebraic Geometry 19 (2010), 243-284

    The Kodaira dimension of the moduli space of Prym varieties dvi pdf
    (with K. Ludwig) Journal of the European Mathematical Society (2010), in press

    The Fermat cubic and special Hurwitz loci in M_g dvi pdf
    Bulletin of the Belgian Mathematical Society "Simon Stevin" 5 (2009), 831-851.
    Special volume dedicated to the conference "Linear series and subschemes"-Ghent 2007.

    The intermediate type of certain moduli spaces of curves dvi pdf
    (with A. Verra)

    The Green Conjecture for smooth curves lying on arbitrary K3 surfaces dvi pdf
    (with M. Aprodu)

    The Brill-Noether geometry of moduli spaces of spin curves dvi pdf

    Aspects of the birational geometry of M_g dvi pdf
    To appear in "Geometry of Riemann surfaces and their moduli spaces"
    Surveys in Differential Geometry (2010).

    M_{22} is of general type dvi pdf

    Koszul cohomology and applications to moduli dvi pdf
    (with M. Aprodu) To appear in "Grassmannians, vector bundles and moduli"
    Clay Mathematical Institute Volume 10 (2010)

    Effective divisors on M_g and a counterexample to the Slope Conjecture dvi pdf
    (with M. Popa)

    The effective cone of M_g and the Slope Conjecture dvi pdf
    Max Planck Institute preprint (2003)
    This is an extended version of my talk at the Mathematische Arbeitstagung 2003

    Notes on limit linear series for vector bundles on curves dvi pdf
    (with M. Popa, unpublished preprint, 2002)

    Lectures on moduli of curves
    Proceedings of the Korean Institute for Mathematical Sciences, Volume 2, No. 1 (2007), 1-20

    The birational geometry of the moduli space of curves pdf
    Thesis, Universiteit van Amsterdam (2000), book (85 pages), available upon request

    A multiplicity theorem in equivariant setting
    Mathematica 38 (1996), 221-226

    Lusternik-Schnirelmann theory on closed subsets of C^1-manifolds
    (with Cs. Varga), Studia Univ. Babes-Bolyai Math. 38 (1993), no. 2, 75-89

    On the completeness of Riemanniann manifolds
    (with Cs. Varga), Studia Univ. Babes-Bolyai Math. 37 (1992), no. 4, 96-101

    My papers reviewed on MathSciNet

    Algebraic geometry activities

    A list of conferences that I am either organizing or attending