Talk titles and abstracts

  • Maxim Arap, Johns Hopkins University

    Classes of special subvarieties of Pryms modulo algebraic equivalence

    ABSTRACT: Special subvarieties, also known as special divisor
    varieties, of Prym varieties have been introduced by Welters in his
    study of Abel-Jacobi isogenies for certain Fano 3-folds. Beauville has
    shown that special subvarieties unify the trigonal construction of
    Recillas and tetragonal construction of Donagi (and several other
    constructions). Also, special subvarieties play a key role in
    Smith-Varley study of Prym-Torelli problem. This talk will discuss
    the classes of special subvarieties modulo algebraic equivalence and
    some applications.

  • Sebastian Casalaina-Martin, University of Colorado at Boulder

    Log canonical models and variation of GIT for genus four
    canonical curves

    ABSTRACT: The Hassett–Keel program aims to give modular
    interpretations of certain log canonical models of the moduli space of
    stable curves. The genus two and three cases were completed recently
    by Hassett and Hyeon–Lee respectively. Work of Hassett–Hyeon,
    Hyeon–Lee and Fedorchuk has also provided a description of some of
    the spaces arising in genus four. In this talk I will discuss a
    variation of GIT construction that gives modular interpretations of
    most of the remaining genus four spaces. This is joint work with D.
    Jensen and R. Laza.

  • Herb Clemens, Ohio State University

    The topological height pairing

    ABSTRACT: In joint work with Mirel Caibar we show that the classical
    height pairing between algebraic (n-1)-cycles on a (2n-1)-dimensional
    complex projective manifold X is the imaginary part of a natural
    (multivalued) bi-holomorphic function on components of the Hilbert
    scheme of X. This pairing is intimately related to the Abel-Jacobi
    image of the respective cycles. Furthermore this pairing can be
    extended to integral currents whose support is a real
    (2n-2)-dimensional oriented submanifold of X. Properties and
    potential applications of the extended pairing will be presented.

  • Izzet Coskun, University of Illinois at Chicago

    The birational geometry of the Hilbert scheme of points on the
    plane and Bridgeland stability

    ABSTRACT: In this talk, I will discuss joint work with Daniele
    Arcara, Aaron Bertram and Jack Huizenga on the birational geometry of
    the Hilbert scheme of points on $\mathbb{P}^2$. After explaining basic
    results about ample and effective cones, I will describe a
    correspondence between the Mori walls in the stable base locus
    decomposition and the Bridgeland walls in the stability manifold.
    Finally, I will interpret the birational models as moduli spaces of
    Bridgeland stable objects.

  • Olivier Debarre, IRMA

    On the period map of certain Fano varieties

    ABSTRACT: The period maps for cubic hypersurfaces are now
    well-understood. We will recall their main properties and explain the
    similarities and differences with period maps for another class of
    Fano varieties. This is joint work in progress with A. Iliev and L.

  • Gavril Farkas, Humboldt University, Berlin (part II) and
    Sam Grushevsky, Stony Brook University (part I)

    Singularities of theta divisors and the geometry of A_5

    It is well-known that the theta divisor of a general principally
    polarized abelian variety is smooth. The locus of ppav with singular
    theta divisors is a divisor in A_g; the generic point of each
    component corresponds to theta divisors with ordinary quadratic
    singularities. In joint work with Salvati-Manni and Verra, we study
    the structure of the codimension two locus in A_g of ppav whose theta
    divisor has a non-ordinay quadratic singularity. In dimension five,
    using the combinatorics of the Prym map, we show that this locus has
    two unirational components which we explicitly describe. As a
    byproduct, we determine the slope of the moduli space A_5. The
    component N_0′ of the Andreotti-Mayer divisor has minimal slope 54/7
    and its Iitaka dimension is equal to zero. The first of the two talks
    will focus on general structure theorems of the singularity loci in
    A_g and modular form aspects of the problem, whereas the second will
    be devoted mostly to A_5.

  • Angela Ortega, Humboldt University, Berlin

    The Brill-Noether curve and Prym-Tyurin varieties

    ABSTRACT: It is a result of L. Masiewicki that the Jacobian of a
    non hyperelliptic curve of genus 5 can be recovered as the Prym
    variety corresponding to the natural involution on the theta divisor
    of the curve. We show that this result can be generalized to a curve C
    of arbitary odd genus g=2a+1. Precisely, the Jacobian of C can be
    realized as the Prym-Tyurin variety for the Brill-Noether curve
    W^1_{a+2}(C) of pencils of minimal degree on C. Applications to the
    enumerative geometry of the secants to C are presented.

  • Gregory Sankaran, University of Bath

    Towards stable homology of toroidal compactifications

    ABSTRACT: I shall describe some work in progress with Jeff
    Giansiracusa, giving an approach to homological stability for suitable
    toroidal compactifications using methods of homotopy theory.

  • Mike Schlessinger, University of North Carolina at Chapel

    Moduli of Rational Homotopy Types


  • Charles Siegel, University of Pennsylvania

    The Schottky Problem

    ABSTRACT: The Schottky problem, that of characterizing the locus of Jacobians among all abelian varieties, is a central problem in the geometry of A_g.  I will discuss previous work on the defining equations of the Jacobian locus, as well as my own work characterizing Jacobians of genus 5 curves.

  • Montserrat Teixidor i Bigas, Tufts University

    Limit linear series for vector bundles and applicatons

    ABSTRACT: An overview of limit linear series for higher rank and
    applications to Brill-Noether theory.