Contact
coneill «at» math.ucdavis.edu
Mathematical Sciences
Building, Room 3149
Department of Mathematics
University of California Davis
One Shields Ave
Davis, CA 95616
U.S.A.
Research
My research lies in the intersection of commutative algebra, discrete optimization, and semigroup theory, using methods from algebraic and enumerative combinatorics. The primary objects of study are combinatorial invariants arising in discrete geometry, with connections to computation, algorithms, and the development and use of software in mathematical research.
As a graduate student at Duke University, I worked under Ezra Miller on combinatorial commutative algebra questions related to mesoprimary decomposition of binomial ideals. After assisting Scott Chapman, Roberto Pelayo, and Vadim Ponomarenko at various summer research programs, I now study problems in semigroup theory and discrete optimization. Recently, I have contributed to several interesting projects in algebraic statistics, stemming from the 2016 Mathematics Research Communities on the topic. In my undergraduate studies at San Fransicso State University, I worked with Matthias Beck in Ehrhart theory and lattice point enumeration, and with Federico Ardila in the study of matroids.
See my complete research statement and annotated publication list for more detail.
Expository publications
Factoring in the Chicken McNugget monoid
(with Scott Chapman)
to appear, Mathematics Magazine. [arXiv:1709.01606]
How do you measure primality?
(with Roberto Pelayo)
American Mathematical Monthly 122 (2015), no. 2, 121-137. [doi] [arXiv:1405.1714]
Peer-reviewed research publications (* indicates an undergraduate coauthor)
On arithmetical numerical monoids with some generators omitted
(with *Sung Hyup Lee and *Brandon Van Over)
to appear, Semigroup Forum. [arXiv:1712.06741]
On mesoprimary decomposition of monoid congruences
to appear, Rocky Mountain Journal of Mathematics. [arXiv:1708.03441]
The elasticity of Puiseux monoids
(with Felix Gotti)
to appear, Journal of Commutative Algebra. [arXiv:1703.04207]
On the computation of factorization invariants for affine semigroups
(with Pedro García-Sánchez and *Gautam Webb)
to appear, Journal of Algebra and its Applications. [arXiv:1504.02998]
Some algebraic aspects of mesoprimary decomposition
(with Laura Matusevich)
Journal of Pure and Applied Algebra 223 (2018), no. 1, 380-394. [doi] [arXiv:1706.07496]
Realizable sets of catenary degrees of numerical monoids
(with Roberto Pelayo)
Bulletin of the Australian Mathematical Society 97 (2018), no. 2, 240-245. [doi] [arXiv:1705.04276]
Apéry sets of shifted numerical monoids
(with Roberto Pelayo)
Advances in Applied Mathematics 97 (2018), 27-35. [doi] [arXiv:1708.09527]
Minimal presentations of shifted numerical monoids
(with *Rebecca Conaway, Felix Gotti, *Jesse Horton, Roberto Pelayo, *Mesa Williams, and Brian Wissman)
International Journal of Algebra and Computation 28 (2018), no. 1, 53-68. [doi] [arXiv:1701.08555]
Unimodular hierarchical models and their Graver bases
(with Daniel Bernstein)
Journal of Algebraic Statistics 8 (2017), no. 2, 29-43. [doi] [arXiv:1704.09018]
On the periodicity of irreducible elements in arithmetical congruence monoids
(with *Jacob Hartzer)
Integers 17 (2017), #A38. [arXiv:1606.00376]
On factorization invariants and Hilbert functions
Journal of Pure and Applied Algebra 221 (2017), no. 12, 3069-3088. [doi] [arXiv:1503.08351]
Mesoprimary decomposition of binomial submodules
Journal of Algebra 480 (2017), 59-78. [doi] [arXiv:1511.00161]
Sparse solutions of linear Diophantine equations
(with Iskander Aliev Jesus De Loera, and Timm Oertel)
SIAM Journal on Applied Algebra and Geometry 1 (2017), no. 1, 239-253. [doi] [arXiv:1602.00344]
Factorization invariants in numerical monoids
(with Roberto Pelayo)
Contemporary Mathematics 685 (2017), 231-349. [doi] [arXiv:1508.00128]
On dynamic algorithms for factorization invariants in numerical monoids
(with *Thomas Barron and Roberto Pelayo)
Mathematics of Computation 86 (2017), 2429-2447. [doi] [arXiv:1507.07435]
On the set of elasticities in numerical monoids
(with *Thomas Barron and Roberto Pelayo)
Semigroup Forum 94 (2017), no. 1, 37-50. [doi] [arXiv:1409.3425]
Irreducible decomposition of binomial ideals
(with Thomas Kahle and Ezra Miller)
Compositio Mathematica 152 (2016), 1319-1332. [doi] [arXiv:1503.02607]
On the set of catenary degrees of finitely generated cancellative commutative monoids
(with Vadim Ponomarenko, *Reuben Tate, and *Gautam Webb)
International Journal of Algebra and Computation 26 (2016), no. 3, 565-576. [doi] [arXiv:1506.07587]
Numerical semigroups on compound sequences
(with Vadim Ponomarenko and *Claire Kiers)
Communications in Algebra 44 (2016), no. 9, 3842-3852. [doi] [arXiv:1503.05993]
Factorization properties of Leamer monoids
(with *Jason Haarmann, *Ashlee Kalauli, *Aleesha Moran, and Roberto Pelayo)
Semigroup Forum 89 (2014), no. 2, 409-421. [doi] [arXiv:1309.7477]
On the linearity of ω-primality in numerical monoids
(with Roberto Pelayo)
Journal of Pure and Applied Algebra 218 (2014), no. 9, 1620-1627. [doi] [arXiv:1309.7476]
Monoid congruences, binomial ideals, and their decompositions
Doctoral dissertation, Duke University (2014).
Preprints (submitted)
The geometry and combinatorics of discrete line segment hypergraphs
(with Deborah Oliveros, and Shira Zerbib)
[arXiv:1807.04826]
Augmented Hilbert series of numerical semigroups
(with *Jeske Glenn, Vadim Ponomarenko, and *Benjamin Sepanski)
[arXiv:1806.11148]
Squarefree divisor complexes of certain numerical semigroup elements
(with *Jackson Autry, *Paige Graves, *Jessie Loucks, Vadim Ponomarenko, and *Samuel Yih)
[arXiv:1804.06632]
Factorization length distribution for affine semigroups I: numerical semigroups with three generators
(with Stephan R. Garcia and *Samuel Yih)
[arXiv:1804.05135]
Random numerical semigroups and a simplicial complex of irreducible semigroups
(with Jesus De Loera and Dane Wilbourne)
[arXiv:1710.00979]
A computer algebra system for R: Macaulay2 and the m2r package
(with David Kahle and Jeff Sommars)
[arXiv:1706.07797]