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Courtney Gibbons


Courtney Gibbons
Courtney Gibbons

Associate Professor of Mathematics

Christian A. Johnson Hall 109
315-859-4886

Courtney Gibbons received her M.S. and Ph.D. from the University of Nebraska-Lincoln where she studied homological properties of modules over quadratic algebras.

Her work appears in the Journal of Pure and Applied Algebra, the Journal of Commutative Algebra, the Journal of Symbolic Computation, and others. She codes for Macaulay 2, an open-source algebra software package.

While at Hamilton, Gibbons has developed a research program involving undergraduates in her work in commutative algebra, and their joint work appears in the Journal of Algebra and its Applications and, soon, in the International Journal of Algebra and Computation.

 A Connecticut native, Gibbons graduated summa cum laude with a bachelor's degree in mathematics from Colorado College in 2006.

Recent Courses Taught

Calculus I
Calculus II
Linear Algebra
Modern Algebra
Cryptography

Research Interests

My research area is commutative algebra, and I have a special interest in infinite free resolutions of modules over graded rings. Polynomial rings over a field (and quotients thereof) are especially nice because they can be viewed as a direct sum of finite dimensional vector spaces, and the same is true for their modules. These graded rings and modules arise in many settings - and have beautiful properties that make them interesting to study in their own right.

Distinctions

  • John R. Hatch Class of 1925 Excellence in Teaching Award, 2015
  • Project NExT Fellow, Academic Year 2013-14
  • Outstanding Graduate Teaching Assistant U. of Nebraska–Lincoln, 2011
  • Emeritus Faculty Fellow U. of Nebraska–Lincoln, 2010
  • Graduate fellowship U. of Nebraska–Lincoln, 2009
  • Outstanding qualifying exams U. of Nebraska–Lincoln, 2008
  • Florian Cajori Prize in Mathematics Colorado College, 2006

Selected Publications

  • Courtney Gibbons, Robert Huben, Branden Stone. “Recursive strategy for decomposing Betti tables of complete intersections.” arXiv:1708.05440, 2017.
  • Mike Annunziata, Courtney Gibbons, Cole Hawkins, Alex Sutherland. “Rational combinations of Betti diagrams of complete intersections.” Journal of Algebra and Its Applications 17 (05), 1850079, 2017.
  • Carlos Améndola, Nathan Bliss, Isaac Burke, Courtney R. Gibbons, Martin Helmer, Serkan Hosten, Evan D Nash, Jose Israel Rodriguez, Daniel Smolkin. “The Maximum Likelihood Degree of Toric Varieties.” Journal of Symbolic Computation (online), 2017.
  • Courtney Gibbons, Josh Laison, Eric J. Paul. “Critical pebbling numbers of graphs.” Journal of Combinatorial Mathematics and Combinatorial Computing 99, 199-224, 2015.
  • Courtney Gibbons, Jack Jeffries, Sarah Mayes, Claudiu Raicu, Branden Stone, Bryan White. “Non-simplicial decompositions of Betti diagrams of complete intersections.” Journal of Commutative Algebra 7 (2), 189-206, 2015.
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  • Richard Bedient, Courtney Gibbons. “Grandma makes Granola.” The College Mathematics Journal 46 (1), 58-60, 2015.
  • Christine Berkesch, Jesse Burke, Daniel Erman, Courtney Gibbons. “The cone of Betti diagrams over a hypersurface ring of low embedding dimension.” Journal of Pure and Applied Algebra 216 (10), 2256-2268, 2012.
  • Courtney Gibbons, Josh Laison. “Fixing numbers of graphs and groups.” The Electronic Journal of Combinatorics 16 (1), 39, 2012.

College Service

Honor Court
Phi Beta Kappa (vice president)
Vegan Club faculty advisor
Mathletics co-advisor

Professional Affiliations

American Mathematical Society
Association for Women in Mathematics
Mathematics Association of America
Society for Industrial and Applied Mathematics
Phi Beta Kappa

Appointed to the Faculty: 2013

Educational Background

Ph.D., University of Nebraska–Lincoln
M.S., University of Nebraska–Lincoln
B.A., Colorado College

Personal Interests

Rock climbing, reading, crocheting

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