I am a graduate of Georgia Southern University (BS 2012, MS 2016). While my current research interests lie in elementary, analytic, and combinatorial number theory, I had a series of successful projects reviewing and writing mathematical models of infectious diseases. The computational skills I developed during this time I now utilize to develop and prove conjectures in number theory.
I am a former secondary mathematics teacher and am passionate about math education at all levels. For the past two years I taught the math content course for the middle grades math education majors at UGA. I also tutor students of all ages with a wide range of learning differences.
While I enjoy research at the highest level, guiding younger students into the joys of research is a priority for me. I serve as a mentor for the Directed Reading Program (DRP) and the Undergraduate Research Mentor for combinatorics and number theory. I have mentored 10+ students in many areas of pure math and math education, and my collaborative efforts have led to 1 accepted publication, and multiple publications in preparation.
I am thankful for my wife, Erin, who supports my tireless passion for thinking about math, and my kids, Filly and August, who remind me to take a break and enjoy life. I am an accomplished runner and guitarist, and play for the UGA Duplicate Bridge Club.
My interests include problems in analytic and enumerative combinatorics, as well as analytic number theory. I seek to understand the subtle interplay between additive and multiplicative number theory, as highlighted by the connections between integers and integer partitions. The parallels between the combinatorial and analytic properties of power series, Dirichlet series, and modular forms remain a great mystery I strive to illuminate.
- Transmission models of historical Ebola outbreaks (w/ J. Drake, I. Bakach, S. O'Regan, M. Gambhir, I. Fung)
Emerging Infectious Diseases , 21(8) (2015), 1447-1450.
- Typhoid transmission: a historical perspective on mathematical model development (w/ I. Bakach, M. Gambhir, I. Fung)
Transactions of the Royal Society of Tropical Medicine and Hygiene , 109(11) (2015), 679-689.
- Colored patterns and their packing densities (w/ H. Wang)
Cong. Numer. , 225 (2015), 23-28.
- Note on packing patterns in colored permutations (w/ H. Wang)
Online J. Anal. Comb. , 11 (2016), 9 pp.
- The impact of shared sanitation facilities on diarrheal diseases with and without an environmental reservoir: a modeling study (w/ S. Carden, S. Li, K. Baker, M. Gambhir, and I. Fung)
Pathogens and Global Health , 112(4) (2018), 195-202.
- Note on restricted parts in cyclic compositions (w/ M. Gibson and H. Wang)
Integers , 18 (2018), 13 pp. (pdf)
- On upper bounds for the count of elite primes
Integers , 20 (2020), 5 pp. (arXiv)
- On factorizations into coprime parts (w/ N. Lebowitz-Lockard)
To appear in Int. J. Number Theory (arXiv)
- On a divisor of the central binomial coefficient (w/ M. Schneider)
To appear in Ramanujan J. (arXiv)
- Note on a binomial coefficient divisor
To appear in Math. Mag. (pdf)
- Comparing multiplicative orders mod p, as p varies (w/ P. Pollack)
To appear in New York J. Math (pdf)
- Compositions that are palindromic modulo m
- Numbers which are only orders of abelian or nilpotent groups
- Antipalindromic compositions (w/ G. E. Andrews and G. Simay)
- Partition Eisenstein series and semi-modular forms (w/ R. Schneider)
I am a recipient of the Outstanding Graduate Teaching Assistant (2019) and the David Galewski Outstanding Graduate Teaching Award (2020). The latter is the highest honor given to a graduate student for teaching.