Research Interests

algebraic geometry and computational algebra


Awards

2005-2020 NSERC Discovery Grants
2012 Coxeter-James Prize
2007 André-Aisenstadt Prize
2001 Clay Mathematics Institute Liftoff Fellow
2001 American Mathematical Society Project NExT Fellow


Preprints

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Virtual resolutions for a product of projective spaces (with Christine Berkesch Zamaere and Daniel Erman), available at arXiv:1703.07631 [math.AC]

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Sharp degree bounds for sum-of-squares certificates on projective curves (with Grigoriy Blekherman and Mauricio Velasco), available at arXiv:1605.08330 [math.AG]


Publications

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Toric vector bundles and parliaments of polytopes (with Sandra Di Rocco and Kelly Jabbusch), to appear in Transactions of the American Mathematical Society, available at arXiv:1409.3109 [math.AG]

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Sums of squares and varieties of minimal degree (with Grigoriy Blekherman and Mauricio Velasco), Journal of the American Mathematical Society, 29 (2016) 893–913

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Cones of Hilbert functions (with Mats Boij), International Mathematics Research Notices 20 (2015) 10314–10338

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Log-concavity of asymptotic multigraded Hilbert Series (with Adam McCabe), Proceedings of the American Mathematical Society 141 (2013) 1883–1892

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Linear determinantal equations for all projective schemes (with Jessica Sidman), Algebra & Number Theory 5 (2011) 1041–1061

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Laurent Polynomials and Eulerian Numbers (with Daniel Erman and Anthony Várilly-Alvarado), Journal of Combinatorial Theory, Series A 118 (2011) 396–402

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Smooth and irreducible multigraded Hilbert schemes (with Diane Maclagan), Advances in Mathematics, 223 (2010) 1608–1631

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Projective toric varieties as fine moduli spaces of quiver representations (with Alastair Craw), American Journal of Mathematics 130 (2008) 1509–1534

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Syzygies, multigraded regularity and toric varieties (with Milena Hering and Hal Schenck), Compositio Mathematica 142 (2006) 1499–1506

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The orbifold Chow ring of a toric Deligne-Mumford stack (with Lev A. Borisov and Linda Chen), Journal of the American Mathematical Society 18 (2005) 193–215

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Uniform bounds on multigraded regularity (with Diane Maclagan), Journal of Algebraic Geometry 14 (2005) 137–164

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Multigraded Castelnuovo-Mumford Regularity (with Diane Maclagan), Journal für die reine und angewandte Mathematik (Crelle's Journal) 571 (2004) 179–212

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Monomial Ideals (with Serkan Hoşten), In Computations in algebraic geometry with Macaulay 2, Algorithms and Computations in Mathematics 8, pp. 73–100, Springer-Verlag, New York, 2001

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Teaching the geometry of schemes (with Bernd Sturmfels), In Computations in algebraic geometry with Macaulay 2, Algorithms and Computations in Mathematics 8, pp. 55–70, Springer-Verlag, New York, 2001

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Irreducible components of characteristic varieties, Journal of Pure and Applied Algebra 165 (2001) 291–306

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D-modules on smooth toric varieties (with Mircea Mustaţă, Harrison Tsai and Uli Walther), Journal of Algebra 240 (2001) 744–770

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Computing global extension modules, Journal of Symbolic Computation 29 (2000) 729–746

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Some remarks on Hilbert functions of Veronese algebras (with H. E. A. Campbell, Anthony V. Geramita, Ian P. Hughes and David L. Wehlau), Communications in Algebra 28 (2000) 1487–1496