Research

Publications & Preprints

  1. On Kaehler extensions of abelian groups (with C. Bregman)

  2. submitted

    1. We show that any Kaehler extension of a finitely generated abelian group by a surface group of genus g ≥ 2 is virtually a product. Conversely, we prove that any homomorphism of an even rank, finitely generated abelian group into the genus g mapping class group with finite image gives rise to a Kaehler extension. The main tools come from surface topology and known restrictions on Kaehler groups.

  3. Weak Approximation for Cubic Hypersurfaces and Degree 4 del Pezzo Surfaces

  4. Int Math Res Notices Oxford Journal 2016

    1. In this article we prove the following theorems about weak approximation of smooth cubic hypersurfaces and del Pezzo surfaces of degree 4 defined over global fields. (1) For cubic hypersurfaces defined over global function fields, if there is a rational point, then weak approximation holds at places of good reduction whose residual field has at least 11 elements. (2) For del Pezzo surfaces of degree 4 defined over global function fields, if there is a rational point, then weak approximation holds at places of good reduction whose residual field has at least 13 elements. (3) Weak approximation holds for cubic hypersurfaces of dimension at least 10 defined over a global function field of characteristic not equal to 2, 3, 5 or a purely imaginary number field.

  1. Character Formulas on Cohomology of Deformations of Hilbert Schemes of K3 Surfaces

  2. London Math. Soc. (2015) doi: 10.1112/jlms/jdv041

    1. Let X be a hyperKaehler manifold deformation equivalent to Hilbert scheme of n points on a K3 surface. We compute the graded character formula of the generic Mumford-Tate group representation on the cohomology ring of X, and derive a generating series for deducing the number of canonical Hodge classes on X. The formula indicates the number of Hodge classes on X that remain Hodge under any deformation.

  1. On Representation of Del Pezzo Surfaces

  2. We give a character formula of lattice structure of Hilbert Scheme of Points on Del Pezzo Surfaces.

  3. Deformations of Hilbert Schemes of Points on K3 Surfaces and Representation Theory

  4. ISBN: 978-1339-15573-9

  5. Modular Forms and Special Cubic Fourfolds (Joint with Z. Li)

  6. Advances in Mathematics Volume 245, 1 October 2013, Pages 315–326

    1. We study the degrees of special cubic divisors on moduli space of cubic fourfolds with at worst ADE singularities. In this paper, we show that the generating series of the degrees of such divisors is a level three modular form.

  1. OEIS Sequence A228073

  2. http://oeis.org/A228073