Gavril Farkas


As of Summer 2007 I am Professor of Mathematics at the Humboldt University of Berlin. This webpage has not been updated since May 2007.

Associate Professor of Mathematics
Department of Mathematics
University of Texas at Austin
RLM, office 12.118
Austin, TX 78712
Office Phone: (512) 471-0175

e-mail: gfarkas@math.utexas.edu

Research

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 their moduli, theta functions, K3 surfaces, Brill-Noether type problems and syzygies of algebraic varieties. I am an Alfred P. Sloan Research Fellow and my research is partly funded by the National Science Foundation Grants DMS-0500747 and DMS-0450670.

  • Curriculum Vita: dvi pdf

    Publications


    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 Scient. 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) J. 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

    Koszul divisors on moduli spaces of curves dvi pdf

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

    The global geometry of the moduli space of curves dvi pdf
    Proceedings Summer Institute in Algebraic Geometry, Seattle, 2005

    Higher ramification and varieties of secant divisors on the generic curve dvi pdf

    Rational maps between moduli spaces of curves and Gieseker-Petri divisors dvi pdf

    M_{22} is of general type dvi pdf

    The effective cone of M_g and the Slope Conjecture dvi pdf
    MPIM preprint, this is an extended version of my talk at the Mathematische Arbeitstagung 2003

    The geometry of the moduli space of Prym varieties dvi pdf

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    (with M. Popa, unpublished preprint, 2002)

    The birational geometry of the moduli space of curves
    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

    Teaching

  • Here are links to the videos of my 2007 lectures on moduli spaces of curves in Daejeon, Korea for the NIMS Winter School on Algebraic Geometry

  • Teaching at the University of Texas: In the Fall of 2006 I taught Classical Algebraic Geometry. In the Spring of 2005 I taught Algebraic Geometry. Here is the link to the Multivariable Calculus course I gave in the Fall of 2005. In the Fall of 2006 I gave a course on Abelian Varieties

  • In August 2006 I taught a short course on moduli of curves in Cologne as part of a summer school on "Moduli Spaces and Arcs" organized by S. Kebekus. These are my notes in djvu format:
    First lecture, Second lecture, Third lecture

  • In July 2005 as part of the Warm Up week for the AMS Summer Institute in Algebraic Geometry in Seattle, I lead a workshop for graduate students on Degeneration Methods in Algebraic Geometry . You can also find here the notes for my talk about "Syzygies of varieties and Green's Conjecture"

    Conferences

    This is a list of conferences that I am either organizing or will be attending:

    Moduli Spaces and Arcs in Algebraic Geometry Cologne, August 2006

    Texas Algebraic Geometry Seminar 2006 Texas A&M University, May 2006

    Algebraic Geometry School on Moduli of Curves and Theta Functions Zacatecas, Mexico, June 2006

    Meetkunde in de Herfsttij II (Geometry in Autumn) Leiden, September 2006

    Mittag-Leffler Institute Stockholm, Special year on moduli spaces (2006-2007)

    Moduli of curves, Institudo Nacional de Matematica Pura e Aplicada, Rio de Janeiro, January-February 2007

    Texas Algebraic Geometry Symposium Austin, March 30-April 1 2007 (This is a conference I organize with D. Ben-Zvi and S. Keel)

    Workshop on Algebraic Geometry Sogang University, Seoul, January 2007

    Linear systems and subschemes Ghent, Belgium, April 2007

    Warwick Algebraic Geometry Symposium (2007-2008) (This is part of a year-long program run by M. Reid and A. Corti. I will organize with S. Mukai and M. Reid the period devoted to Moduli Spaces, date: June-July 2008)

    Modular Forms and Moduli Spaces St. Petersburg, Russia, July 2007 (A satellite meeting for the festival dedicated to the 300th birthday of Leonhard Euler)

    Moduli spaces of geometric and algebraic structures, Bonn, January 2008

    Recent progress on the moduli space of curves Banff, Canada, March 2008