Contact
cdoneill «at» sdsu.edu
GMCS Building, Room 570
Math & Stats Department
San Diego State University
5500 Campanile Dr
San Diego, CA 92182
U.S.A.
Student Research
I had the privilege of acting as a research assistant for the Pacific Undergraduate Research Experience in Mathematics (PURE Math) hosted at the University of Hawai'i Hilo, under the direction of John Little in 2012 and Scott Chapman in 2013. These 8 week summer programs gave promising undergraduates from underrepresented backgrounds the opportunity to experience mathematics research as they worked on open problems in algebra and number theory. I also served as a research assistant for the San Diego State University Mathematics REU in the summer of 2014, under the direction of Vadim Ponomarenko, and returned in the summer of 2017 in the role of codirector. Since 2019, I have been Co-PI on the SDSU REU grant, and directed projects most years the grant is active. My experiences in these REUs resulted in the frequent inclusion of undergraduate projects into my own research.
Undergraduate projects are an important part of my research, and several of my publications have undergraduate coauthors. If you are an undergraduate student and interested in mathematics research experience, please let me know!
REU Programs
Masters Thesis Projects
Jackson Autry, Mathematics, San Diego State University (Expected)
Graver bases and the Kunz polyhedron
Derek Rawling, Mathematics, San Diego State University (Expected)
Davenport constants of numerical semigroup algebras
Shadi Gaskari, Mathematics, San Diego State University
Counting numerical semigroups with fixed multiplicity and genus
Kieran Hilmer, Mathematics, San Diego State University
Examining minimal presentation cardinality of numerical semigroups via posets
[arXiv:2211.16283]
James Howard, Mathematics, San Diego State University
On Graver bases of shifted numerical semigroups with three generators
[arXiv:2212.02373]
Emily O'Sullivan, Mathematics, San Diego State University
Understanding the face structure of the Kunz cone
Anthony Park, Mathematics, San Diego State University
Calculating discrete volume using generating functions and partial fraction decomposition
Aurora Vogel, Mathematics, San Diego State University
Introducing the triangle path framework to generate the landscape of discrete convex shells (primary advisor: Antoni Luque Santolaria)
Andrew Morris, Mathematics, San Diego State University
Expected behavior of randomly selected numerical semigroups
Judy Wu, Mathematics, San Diego State University
Factoring polynomials in numerical semigroup algebras
Brittney Marsters, Mathematics, San Diego State University
Optimizing polytopal norms with respect to numerical semigroups
Mariah Moschetti, Mathematics, San Diego State University
Edges, loops, and hypercubes: an exploration of the topological structure of graphs
in numerical semigroup theory
Gilad Moskowitz, Mathematics, San Diego State University
The structure theorem for sets of length for numerical semigroups
[arXiv:2311.05786]
Kiley Sprigg, Mathematics, San Diego State University
Quasipolynomial coefficients for block monoids
Zachary Dickinson, Mathematics, San Diego State University
Gröbner fans of 3-generator numerical semigroups
Erin Grooms, Mathematics, San Diego State University
Maximal factorization length for affine semigroups in dimension 2
Isabel White, Mathematics, San Diego State University
Minimal presentations of shifted affine semigroups
[arXiv:2006.01396]
Other Masters Projects
Maryam Sabagh, Mathematics, San Diego State University
Arithmetical congruence monoids
Joseph McDonough, Mathematics, San Diego State University
Rays of Kunz polyhedron faces with low embedding dimension
[arXiv:2401.06025]
Tara Gomes, Mathematics, San Diego State University
Free resolutions and the Kunz polyhedron
[arXiv:2310.03612]
Gilad Moskowitz, Mathematics, San Diego State University
Primitive length sets under set addition
Jackson Autry, Mathematics, San Diego State University
Sequentially embeddable graphs
Piercing numbers of intersecting segment hypergraphs
Limiting elasticities in affine semigroups
[arXiv:1812.02904]
Undergraduate Thesis Projects
Madeline Chen, Computer Science and Mathematics, University of California Davis
A software package for decomposing affine semigroups
[github:affinesgps-sage]
Franklin Kerstetter, Mathematics, University of California Davis
Parametrized and shifted numerical semigroups
[arXiv:1909.04281]
Calvin Leng, Mathematics, University of California Davis
A sequence of quasipolynomials arising from random numerical semigroups
[arXiv:1809.09915]
Zachary Spaulding, Mathematics, University of California Davis
A database of random numerical semigroups
[github:rns-db-plot]
Sviatoslav Zinevich, Applied Mathematics, University of California Davis
Factorization in numerical semigroup algebras
[github:numsgpsalg]
Robert Harrison, Mathematics (through University Writing Program), University of California Davis
A computer algebra system for R: Macaulay2 and the m2r package (copy-editing)
[arXiv:1706.07797]
Other Undergraduate Projects
Kayla Andrus, Mathematics, San Diego State University
Nathanial Larsen, Mathematics, San Diego State University
Aly Maclennan, Mathematics, San Diego State University
Christian Vicars, Mathematics, San Diego State University
Multiplicity, embedding dimension, type, minimal presentation cardinality, and symmetry
Ty Bui, Computer Science, San Diego State University
Poincare series of numerical semigroup algebras
Emi Lycan, Mathematics, San Diego State University
Asymptotics of extremal \(t\)-lengths in arithmetical congruence monoids
Garrett Rutledge, Mathematics, San Diego State University
Arithmetical congruence monoids
Gabbi Engler, Mathematics, San Diego State University
Numerical semigroups parametrized by polynomials
Caleb Folorunso, Mathematics, San Diego State University
Max and min factorization length in affine semigroups
Hanh Nguyen, Computer Science, San Diego State University
Refining the KunzPoset package
Maryam Sabagh, Mathematics, San Diego State University
Betti numbers of shifted affine semigroups (coadvisor: James Howard, MA)
Cole Brower, Mathematics, San Diego State University
A GPU-accelerated triangulation algorithm
Rays of Kunz polyhedron faces with low embedding dimension
[arXiv:2401.06025]
Cole Brower, Mathematics, San Diego State University
Joseph McDonough, Mathematics, San Diego State University
Quasipolynomials and the Kunz polyhedron
Dacia Bond, Mathematics, San Diego State University
The McEliece cryptosystem (expository) (coadvisor: Carmelo Interlando)
Brenna Cosio, Mathematics, San Diego State University
New models for random numerical semigroups
Kieran Hilmer, Mathematics, San Diego State University
Counting numerical semigroups by genus via recurrences
Kaelia Okamura, Mathematics, San Diego State University
Quasipolynomials and parametrized families of numerical semigroups
Nils Olsson, Mathematics, San Diego State University
Derek Rawling, Mathematics, San Diego State University
Atomic density of singular arithmetical congruence monoids
[arXiv:2310.07924]
Cole Brower, Mathematics, San Diego State University
Travis Kulhanek, Mathematics, University of California Los Angeles
Joseph McDonough, Mathematics, San Diego State University
Vody Pavlyuk, Mathematics, San Diego State University
Length density of numerical semigroups (coadvisors: Scott Chapman and Vadim Ponomarenko)
[arXiv:2110.10618]
Tara Gomes, Mathematics, San Diego State University
Eduardo Torres Davila, Mathematics, San Diego State University
Faces of Kunz polyhedra
Wilf's conjecture as a combinatorial game
Free resolutions over numerical semigroup algebras
[arXiv:2009.05921]
Adam Hoyt, Mathematics, San Diego State University
Derek Rawling, Mathematics, San Diego State University
Atomic density of regular arithmetical congruence monoids
Jose Parra, Mathematics, San Diego State University
Aditya Windy, Mathematics, San Diego State University
Elements of 3-generated numerical semigroup with a given factorization length
Amy Petris, Computer Science, San Diego State University
Counting numerical semigroup elements with a given factorization length
Tim Wesley, Mathematics, Pomona College
Factorization length parity (coadvisor: Stephan R. Garcia)
[arXiv:2006.00121]
Bryan Hayes, Mathematics, San Diego State University
Generalizations of a graph-theoretic puzzle from Myst IV: Revelations
Nils Olsson, Mathematics, San Diego State University
Atomic density of arithmetical congruence monoids
Sophie Quynn, Mathematics, University of California Davis
Rank of randomly selected positroids (coadvisor: Anastasia Chavez)
Ashley Schwartz, Mathematics, San Diego State University
Shifted affine semigroups
Louis Selstad, Mathematics, San Diego State University
Refined bounds on random numerical semigroups
Eduardo Torres Davila, Mathematics, San Diego State University
Apéry posets of numerical semigroups
[arXiv:1912.04460]
Samuel Yih, Mathematics, Pomona College
Factorization length multisets (coadvisor: Stephan R. Garcia)
[arXiv:1804.05135] [arXiv:1911.04575]
Melanie Zhang, Applied Mathematics and Computer Science, University of California Davis
Atomic density of arithmetical congruence monoids
Sung Hyup Lee, Mathematics, University of California Berkeley
Brandon Van Over, Mathematics, University of California Berkeley
Arithmetical numerical monoids with some generators omitted
[arXiv:1712.06741]
Yuze Luan, Mathematics, University of California Davis
Atomic density in arithmetical congruence monoids
Abdulhai Naqvi, Mathematics, University of California Davis
Generalizations of a graph-theoretic puzzle from Myst IV: Revelations
Gautam Webb, Mathematics, University of Oregon
A dymamic algorithm for computing the catenary degree
[arXiv:1504.02998]
David Fountain, Mathematics, Texas A&M University
Generalizations of a graph-theoretic puzzle from Myst IV: Revelations
Larry Harris, Computer Engineering, Texas A&M University
The dissonance point of ω-primality in numerical monoids
Jacob Hartzer, Computer Engineering, Texas A&M University
On the periodicity of irreducible elements in arithmetical congruence monoids
[arXiv:1606.00376] [github:acm-sage]
Jose Rivera Montes De Oca, Mathematics, Texas A&M University
Minimal presentations of shifted monoids
Thomas Barron, Mathematics and Computer Science, University of Kentucky
Dynamic computation of factorization invariants (coadvisor: Roberto Pelayo)
On the set of elasticities of numerical monoids (coadvisor: Roberto Pelayo)
[arXiv:1409.3425] [arXiv:1507.07435]