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 M_{g,n }(with Prakash Belkale and Anna Kazanova), Mathematische Zeitschrift, 1-27, online 2016, (arxiv, journal);

Nonvanishing of conformal blocks divisors on M_{0,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 M_{0,n} from sl_{2}, (with Valery Alexeev, and David Swinarski), Proceedings of the Edinburgh Mathematical Society, Volume 57, Issue 01, February 2014, (arxiv, journal);

Veronese quotient models of 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 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);

sl_{n} level 1 conformal blocks divisors on 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 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 M_{g,n}_{, }(with S. Keel and I. Morrison), J. Amer. Math. Soc. (2), 15: 273–294, 2002, (arxiv, journal).