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Contact Information

Address
Professor Gregory G. Smith
Department of Mathematics and Statistics
512 Jeffery Hall, University Avenue
Queen's University
Kingston, Ontario
Canada K7L 3N6

Upcoming Activities

Recent Activities

Research Interests

Algebraic Geometry, Commutative Algebra, Computer Algebra, and Combinatorics

Awards

Published Articles

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Simplicial complexes in Macaulay2 (with Ben Hersey and Alexandre Zotine), Journal of Software for Algebra and Geometry, 13 (2023) 53–59
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Smooth Hilbert schemes: their classification and geometry (with Roy Skjelnes), Journal für die reine und angewandte Mathematik (Crelles Journal) 794 (2023) 281–305
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Ramification and discriminants of vector bundles and a quick proof of Bogomolov's theorem (with Hiro Abo and Robert Lazarsfeld ), Rendiconti dell'Istituto di Matematica dell'Università di Trieste 54 (2022) 1–15
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Sums of squares and quadratic persistence on real projective varieties (with Grigoriy Blekherman, Rainer Sinn, and Mauricio Velasco), Journal of the European Mathematical Society (JEMS) 24 (2022) 925–965
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Sums of squares: a real projective story (with Grigoriy Blekherman, Rainer Sinn, and Mauricio Velasco), Notices of the American Mathematical Society 68 (2021) 734–747
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Virtual resolutions for a product of projective spaces (with Christine Berkesch and Daniel Erman), Algebraic Geometry 7 (2020) 460–481
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Sharp degree bounds for sum-of-squares certificates on projective curves (with Grigoriy Blekherman and Mauricio Velasco), Journal de Mathématiques Pures et Appliquées 129 (2019) 61–89
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Toric vector bundles and parliaments of polytopes (with Sandra Di Rocco and Kelly Jabbusch), Transactions of the American Mathematical Society 370 (2018) 7715–7741
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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 (Crelles Journal) 571 (2004) 179–212
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Monomial Ideals (with Serkan Hoşten), In Computations in algebraic geometry with Macaulay2, 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 Macaulay2, 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

Book Edited

Combinatorial Algebraic Geometry (with Bernd Sturmfels), Fields Institute Communications 80, Springer, 2017

Potential Students

Over the next few years, I expect to take on a number of graduate students. Although I am primarily interested in PhD students, I like to have students start at the Master's level. Highly qualified applicants are encouraged to contact me directly.

Apply for graduate studies at Queen's
Graduate program in Mathematics & Statistics at Queen's
Terence Tao's career advice
Thoughts on graduate school from the Secret Blogging Seminar
Ravi Vakil's advice for graduate students

Current Students

Sasha Zotine (PhD 2024)
Julia McClellan (MSc 2023)

Successful Students

Benjamin Hersey (PhD 2021)
Owen Ren (MSc 2013, PhD 2018)
Andrew Staal (PhD 2016)
Adam McCabe (MSc 2011)

Past Teaching

Winter 2023
Rings and Fields (MATH 210)
Winter 2023
Introduction to Algebraic Geometry (MATH 413)
Fall 2022
Computational Homological Algebra (MATH 903)
2021–22
Linear Algebra (MATH 110)
Fall 2021
Enumerative Combinatorics (MATH 402)
Winter 2021
Linear Algebra (MATH 110B)
Winter 2021
Introduction to Algebraic Geometry (MATH 413)
Fall 2020
Core Course in Algebra I (MATH 893)
Winter 2020
The Symmetric Group (MATH 314)
Fall 2019
Linear Algebra (MATH 110A)
Fall 2019
Enumerative Combinatorics (MATH 402)
2017–18
Linear Algebra (MATH 110)
Winter 2018
Young Tableaux & the Symmetric Group (MATH 499)
Fall 2017
Enumerative Combinatorics (MATH 402)
2015–16
Linear Algebra (MATH 110)
Winter 2015
Elementary Geometry (MATH 387)
2013–14
Linear Algebra (MATH 110)
Fall 2012
Graph Theory (MATH 401)
Fall 2012
Ordinary Differential Equations (MTHE 225)
Winter 2012
Core Course in Algebra II (MATH 894)
2011–12
Differential and Integral Calculus (MATH 120)
Fall 2011
Graph Theory (MATH 401)
Winter 2011
Graph Theory (MATH 401)
Winter 2011
Computational Commutative Algebra (MATH 413)
Fall 2010
Advanced Calculus (MATH 280)
Fall 2008
Core Course in Algebra I (MATH 893)
Fall 2008
Vector Analysis (MATH 227)
2007–08
Linear Algebra (MATH 110)
Fall 2007
Core Course in Algebra I (MATH 893)
Winter 2007
Linear Algebra (MATH 312)
2006–07
Linear Algebra (MATH 110)
Fall 2006
Computational Commutative Algebra (MATH 413)
Winter 2006
Linear Algebra (MATH 312)
Fall 2005
Graph Theory (MATH 401)
Fall 2005
Advanced Calculus (MATH 280)
2004–05
Differential and Integral Calculus (MATH 120)