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.
Undergraduate Research
I had the privilage 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 have motivated 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
Senior 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
Calvin Leng, Mathematics, University of California Davis
A sequence of quasipolynomials arising from random numerical semigroups
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
Samuel Yih, Mathematics, Pomona College (coadvisor: Stephan R. Garcia)
Average behavior of factorization lengths over numerical semigroups
[arXiv:1804.05135]
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 (coadvisor: Roberto Pelayo)
Dynamic computation of factorization invariants
On the set of elasticities of numerical monoids
[arXiv:1409.3425] [arXiv:1507.07435]