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Research

My research interests are in Algebraic Geometry. More specifically, I work with algebraic curves, vector bundles, and their moduli.  I am a part of the Algebraic Geometry group at UGA, a co-PI on the AGANT (Algebraic Geometry, Algebra and Number Theory) NSF RTG grant, and currently supported by NSF grant DMS-1201268 “Conformal blocks and positive cycles on the moduli space of curves.”
Publications and preprints:

  • Scaling of conformal blocks and generalized theta functions over Mg,n (with Prakash Belkale and Anna Kazanova), Mathematische Zeitschrift, 1-27, online  2016, (arxiv, journal);
  • Nonvanishing of conformal blocks divisors on M0,n (with Prakash Belkale and Swarnava Mukhopadhyay), Transformation Groups, 21(2), 329-353, 2016  (BGMB, journal);
  • Vanishing and identities of conformal blocks divisors, (with Prakash Belkale and Swarnava Mukhopadhyay),  Algebraic Geometry,  2 (1) (2015) 62–90 (arxiv, journal);
  • Conformal blocks divisors on M0,n from sl2, (with Valery Alexeev, and David Swinarski), Proceedings of the Edinburgh Mathematical Society, Volume 57, Issue 01, February 2014, (arxiv, journal);
  • Veronese quotient models of M0,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 Mg,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 M0,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 Mg 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 Mg,n, (with S. Keel and I. Morrison), J. Amer. Math. Soc. (2), 15: 273–294, 2002, (arxiv, journal).