Contact
cdoneill «at» sdsu.edu
GMCS Building, Room 570
5500 Campanile Dr
San Diego, CA 92182
U.S.A.
GMCS Building, Room 570
Math & Stats Department
San Diego State University5500 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.
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
Summer 2022 


Summer 2021 


Summer 2019 


Summer 2017 


Summer 2015 


Summer 2014 


Summer 2013 


Summer 2012 

Masters Thesis Projects
Brittney Marsters, Mathematics, San Diego State University
Optimizing polytopal norms with respect to numerical semigroups
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
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
The structure theorem for sets of length for numerical semigroups
Kiley Sprigg, Mathematics, San Diego State University
Quasipolynomial coefficients for block monoids
Zachary Dickinson, Mathematics, San Diego State UniversityQuasipolynomial coefficients for block monoids
Gröbner fans of 3generator numerical semigroups
Erin Grooms, Mathematics, San Diego State University
Maximal factorization length for affine semigroups in dimension 2
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]
Minimal presentations of shifted affine semigroups
[arXiv:2006.01396]
Other Masters Projects
Tara Gomes, Mathematics, San Diego State University
Free resolutions and the Kunz polyhedron
Free resolutions and the Kunz polyhedron
Gilad Moskowitz, Mathematics, San Diego State University
Primitive length sets under set addition
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]
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:affinesgpssage]
A software package for decomposing affine semigroups
[github:affinesgpssage]
Franklin Kerstetter, Mathematics, University of California Davis
Parametrized and shifted numerical semigroups
[arXiv:1909.04281]
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]
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:rnsdbplot]
A database of random numerical semigroups
[github:rnsdbplot]
Sviatoslav Zinevich, Applied Mathematics, University of California Davis
Factorization in numerical semigroup algebras
[github:numsgpsalg]
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 (copyediting)
[arXiv:1706.07797]
A computer algebra system for R: Macaulay2 and the m2r package (copyediting)
[arXiv:1706.07797]
Other Undergraduate Projects
Cole Brower, Mathematics, San Diego State University
A GPUaccelerated triangulation algorithm
A GPUaccelerated triangulation algorithm
Cole Brower, Mathematics, San Diego State University
Joseph McDonough, Mathematics, San Diego State University
Quasipolynomials and the Kunz polyhedron
Joseph McDonough, Mathematics, San Diego State University
Quasipolynomials and the Kunz polyhedron
Nils Olsson, Mathematics, San Diego State University
Derek Rawling, Mathematics, San Diego State University
Atomic density of singular arithmetical congruence monoids
Derek Rawling, Mathematics, San Diego State University
Atomic density of singular arithmetical congruence monoids
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)
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)
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]
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
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 3generated numerical semigroup with a given factorization length
Aditya Windy, Mathematics, San Diego State University
Elements of 3generated numerical semigroup with a given factorization length
Amy Petris, Computer Science, San Diego State University
Counting numerical semigroup elements with a given factorization length
Counting numerical semigroup elements with a given factorization length
Tim Wesley, Mathematics, Pomona College
Factorization length parity (coadvisor: Stephan R. Garcia)
[arXiv:2006.00121]
Factorization length parity (coadvisor: Stephan R. Garcia)
[arXiv:2006.00121]
Bryan Hayes, Mathematics, San Diego State University
Generalizations of a graphtheoretic puzzle from Myst IV: Revelations
Generalizations of a graphtheoretic puzzle from Myst IV: Revelations
Nils Olsson, Mathematics, San Diego State University
Atomic density of arithmetical congruence monoids
Atomic density of arithmetical congruence monoids
Sophie Quynn, Mathematics, University of California Davis
Rank of randomly selected positroids (coadvisor: Anastasia Chavez)
Rank of randomly selected positroids (coadvisor: Anastasia Chavez)
Ashley Schwartz, Mathematics, San Diego State University
Shifted affine semigroups
Shifted affine semigroups
Louis Selstad, Mathematics, San Diego State University
Refined bounds on random numerical semigroups
Refined bounds on random numerical semigroups
Eduardo Torres Davila, Mathematics, San Diego State University
Apéry posets of numerical semigroups
[arXiv:1912.04460]
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]
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
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]
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
Atomic density in arithmetical congruence monoids
Abdulhai Naqvi, Mathematics, University of California Davis
Generalizations of a graphtheoretic puzzle from Myst IV: Revelations
Generalizations of a graphtheoretic puzzle from Myst IV: Revelations
Gautam Webb, Mathematics, University of Oregon
A dymamic algorithm for computing the catenary degree
[arXiv:1504.02998]
A dymamic algorithm for computing the catenary degree
[arXiv:1504.02998]
David Fountain, Mathematics, Texas A&M University
Generalizations of a graphtheoretic puzzle from Myst IV: Revelations
Generalizations of a graphtheoretic puzzle from Myst IV: Revelations
Larry Harris, Computer Engineering, Texas A&M University
The dissonance point of ωprimality in numerical monoids
The dissonance point of ωprimality 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:acmsage]
On the periodicity of irreducible elements in arithmetical congruence monoids
[arXiv:1606.00376] [github:acmsage]
Jose Rivera Montes De Oca, Mathematics, Texas A&M University
Minimal presentations of shifted monoids
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]
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]