"Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate." David Mumford

My Current Role

• Professor of Mathematics at Central Michigan University.

 

Publications

• Line arrangements modeling curves of high degree: equations, syzygies and secants, joint with Gregory Burnham, Zvi Rosen, and Jessica Sidman, in Recent Advances in Algebraic Geometry, London Math. Soc. Lecture Notes 417 (2015), pp. 52-70.
• An Effective Bound for Reflexive Sheaves on Canonically Trivial 3-folds, Journal of Pure and Applied Algebra 219 (2015) pp. 170-174.
• Betti Tables of Reducible Algebraic Curves, joint with Juliette Bruce, Pin-Hung Chris Kao, Evan D. Nash, and Ben Perez, Proc. Amer. Math. Soc. 142 (2014) 4039-4051.
• Generation and Syzygies of the First Secant Variety to a Smooth Curve, Proc. Amer. Math. Soc. 140 (2012) pp. 2639-2646.
• Equations Defining Secant Varieties: Geometry and Computation, joint with Jessica Sidman, in Combinatorial Aspects of Commutative Algebra and Algebraic Geometry, Abel Symposia 6, Springer-Verlag (2011) pp. 155-174.
• Arithmetic properties of the first secant variety to a projective variety, preprint. (updated 10/12/10)
• Syzygies of the Secant Variety of a Curve, joint with Jessica Sidman, Algebra and Number Theory 3 (2009) no. 4, pp. 445-465.
• Singularities of Secant Varieties, Journal of Pure and Applied Algebra 213 (2009) pp. 1129-1132.
• Regularity and Normality of the Secant Variety to a Projective Curve, Journal of Algebra 319 (2008) no. 3, pp. 1264-1270.
• The Hilbert Scheme of Elliptic Curves and Reflexive Sheaves on Fano 3-folds, Osaka Journal of Mathematics 45 (2008) no. 1, pp. 85-89.
• Classes of Stable Complex Matrices Defined via the Theorems of Gershgorin and Lyapunov, joint with Bryan Cain, Terry Lenker, and Sivaram Narayan, Linear and Multilinear Algebra 56 (2008) no. 6, pp. 713-724.
• Moduli of Reflexive Sheaves on Smooth Projective 3-folds, Journal of Pure and Applied Algebra 211 (2007) no. 3, pp. 622-632.
• Stable Reflexive Sheaves on Smooth Projective 3-folds, Pacific Journal of Mathematics 219 (2005) no.2, pp. 391-398.
• The Parity of Invariants of Coherent Sheaves on Smooth 3-Fold Hypersurfaces, Communications in Algebra 33 (2005) pp. 319-321.
• A Counter Example to Fulton's Conjecture on $\overline{M}_{0,n}$, Journal of Algebra 248 (2002) pp. 780-784.
• On the Regularity of Powers of Ideal Sheaves, Compositio Mathematica, 131 (2002) no. 2, pp. 161-172.
• Secant Varieties and Birational Geometry, Mathematische Zeitschrift 242 (2002) no. 1, pp. 75-95.
• Some Results on Secant Varieties Leading to a Geometric Flip Construction, Compositio Mathematica 125 (2001) no. 3, pp. 263-282.
• Some Results on Secant Varieties Leading to a Geometric Flip Construction, thesis, University of North Carolina at Chapel Hill, 1998.