# 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

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

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

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]`

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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