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
- ggsmith@mast.queensu.ca
Upcoming Activities
- 2025.06.30–07.04
- Macaulay2 workshop, University of Wisconsin, Madison, WI
- 2025.04.06–04.11
- Toric Geometry, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany
- 2025.01.24–01.26
- Combinatorial Algebra meets Algebraic Combinatorics, Toronto, ON
- 2024.12.11
- Computations and Applications of Algebraic Geometry and Commutative Algebra, Joint Meeting of the New Zealand, Australian, and American Mathematical Societies, Auckand, New Zealand
- 2024.12.09
- Algebraic Combinatorics and Matroids, Joint Meeting of the New Zealand, Australian, and American Mathematical Societies, Auckand, New Zealand
Recent Activities
- 2024.11.08
- Batmobile, Dartmouth College, Hanover, NH
- 2024.11.02
- Route 81 Conference, Cornell University, Ithaca, NY
- 2024.10.18
- Mathematics Colloquium, University of Hawai'i at Mānoa, Honolulu, HI
- 2024.10.18
- Algebra lab, University of Hawai'i at Mānoa, Honolulu, HI
- 2024.09.30
- Pure Mathematics Colloquium, University of Waterloo, Waterloo, ON
- 2024.09.24–09.28
- Syzygies and Hilbert schemes, Krakow, Poland
- 2024.05.28–06.05
- Macaulay2, computational algebraic geometry and string theory, University of Utah, Salt Lake City, UT
- 2024.01.16–05.24
- Commutative algebra program, SLMATH, Berkeley, CA
- 2024.05.04–05.05
- Homological methods in commutative algebra and algebraic geometry, San Francisco State University, San Francisco, CA
- 2024.03.27
- COMA/NAG Joint Lunch Seminar, Commutative algebra, SLMATH, Berkeley, CA
- 2024.02.28
- AGC Seminar, San Francisco State University, San Francisco, CA
- 2024.02.15
- COMA Seminar, Commutative algebra, SLMATH, Berkeley, CA
Research Interests
Algebraic Geometry, Commutative Algebra, Computer Algebra, and Combinatorics
Awards
- 2012
- Coxeter–James Prize
- 2007
- André–Aisenstadt Prize
- 2001
- Clay Mathematics Institute Liftoff Fellow
- 2001
- Project NExT Fellow
Preprints
-
Nonnegativity certificates on real algebraic surfaces
(with
Grigoriy Blekherman,
Rainer Sinn,
and
Mauricio Velasco),
available at
arXiv:2409.08834 [math.AG]
Published Articles
- Simplicial complexes in Macaulay2 (with Ben Hersey and Alexandre Zotine), Journal of Software for Algebra and Geometry, 13 (2023) 53–59
- Smooth Hilbert schemes: their classification and geometry (with Roy Skjelnes), Journal für die reine und angewandte Mathematik (Crelles Journal) 794 (2023) 281–305
- 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
- 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
- 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
- Virtual resolutions for a product of projective spaces (with Christine Berkesch and Daniel Erman), Algebraic Geometry 7 (2020) 460–481
- 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
- Toric vector bundles and parliaments of polytopes (with Sandra Di Rocco and Kelly Jabbusch), Transactions of the American Mathematical Society 370 (2018) 7715–7741
- 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 (Crelles Journal) 571 (2004) 179–212
- 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
- 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
- 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
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
- Ravi Vakil's advice for graduate students
Current Students
- Julia McClellan (MSc 2023, PhD 2027)
Successful Students
- Sasha Zotine (PhD 2024)
- Benjamin Hersey (PhD 2021)
- Owen Ren (MSc 2013, PhD 2018)
- Andrew Staal (PhD 2016)
- Adam McCabe (MSc 2011)
Future Teaching
- Winter 2025
- Rings and Fields (MATH 210)
- Winter 2025
- Introduction to Algebraic Geometry (MATH 413)
Present Teaching
- Fall 2024
- Core Course in Algebra I (MATH 893)
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)