Department of Mathematics, Rutgers University
Hill Center for the Mathematical Sciences
110 Frelinghuysen Rd.
Piscataway, NJ 08854-8019

Office number 230

Directions to Hill Center

Publications and preprints:

      • Basepoint free cycles on $\ovop{M}_{0,n}$ from Gromov-Witten theory (with Prakash Belkale) (preliminary draft, comments welcome) (arxiv)
      • Surveys on Recent Developments in Algebraic Geometry (Edited with Izzet Coskun, and Tommaso de Fernex), to appear in the Proceedings of Symposia in Pure Mathematics.  These are  articles, available on the Arxiv, about topics covered at the Bootcamp for the Summer Math Institute, written by the mentors. The book is described in the Introduction. 
      • On higher Chern classes of vector bundles of conformal blocks (with Swarnava Mukhopadhyay), submitted (arxiv)
      • On finite generation of the section ring of the determinant of cohomology line bundle (with Prakash Belkale), Transactions of the AMS, to appear (arxiv)
      • Scaling of conformal blocks and generalized theta functions over \overline{M}g,n (with Prakash Belkale and Anna Kazanova), Mathematische Zeitschrift, 1-27, online  2016, (arxiv, journal);
      • Nonvanishing of conformal blocks divisors on \overline{M}0,n (with Prakash Belkale and Swarnava Mukhopadhyay), Transformation Groups, 21(2), 329-353, 2016  (BGMBjournal);
      • Vanishing and identities of conformal blocks divisors, (with Prakash Belkale and Swarnava Mukhopadhyay),  Algebraic Geometry,  2 (1) (2015) 62–90 (arxiv, journal);
      • Higher level sl_2 conformal blocks divisors on \overline{M}0,n, (with Valery Alexeev, and David Swinarski), Proceedings of the Edinburgh Mathematical Society, Volume 57, Issue 01, February 2014, (arxiv, journal);
      • Veronese quotient models of \overline{M}0,n and conformal blocks, (with Dave Jensen, Han-Bom Moon, and David Swinarski), the Michigan Mathematical Journal, Volume 62, Number 4, December 2013, (arxiv, journal);
      • Conformal blocks divisors and the birational geometry of \overline{M}g,n, Mathematisches Forschungsinstitut Oberwolfach, Moduli Spaces in Algebraic Geometry 2013, (Abstract);
      • The cone of type A, level one conformal blocks divisors, (with Noah Giansiracusa), Advances in Mathematics, Volume 231, Issue 2, 1 October 2012, Pages 798-814, (arxiv, journal);
      • On extensions of the Torelli Map, EMS Series of Congress Reports, Geometry and Arithmetic, October 2012, (arxiv, journal);
      • Compact Moduli and Vector Bundles, Proceedings of the 2010 conference at the University of Georgia,  Athens, Editor, with Valery Alexeev, Elham Izadi, János Kollár, Eduard Looijenga, (book);
      • sln level 1 conformal blocks divisors on \overline{M}0,n, (with M. Arap, J. Stankewicz and D. Swinarski), International Maths. Research Notices,  no. 7, 1634-1680, 2012, doi: 10.1093/imrn/rnr064, 2011, (arxiv, journal);
      • Lower and upper bounds on nef cones, (with Diane Maclagan), International Maths. Research Notices,doi: 10.1093/imrn/rnr121, 2011, (arxiv, journal);
      • Equations for Chow and Hilbert Quotients, (with Diane Maclagan), Algebra and Number Theory, (7), No. 4, 2010, (arxiv, journal);
      • Numerical criteria for divisors on \overline{M}g to be ample, Compositio Mathematica, (5), 145: 1227–1248, 2009, (arxiv, journal);
      • Pointed trees of projective spaces, (with L. Chen and D. Krashen), Journal of Algebraic Geometry, (18) , no. 3, 477–509,  Nov., 2008, (arxiv, journal);
      • The Mori cones of moduli spaces of pointed curves of small genus, (with G. Farkas), Trans. Amer. Math. Soc., 355: 1183–1199, 2003, (arxiv, journal);
      • Towards the ample cone of \overline{M}g,n(with S. Keel and I. Morrison), J. Amer. Math. Soc. (2), 15: 273–294, 2002, (arxiv, journal).