Kelly Isham

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Kelly Isham

Assistant Professor of Mathematics

Department/Office Information

214 McGregory Hall


I am passionate about researching and teaching math. I am interested in using technology both in my research and in the classroom. My work bridges ideas and techniques from number theory and combinatorics.  My work often connects to other fields such as finite geometry, arithmetic geometry, or arithmetic statistics. I'm always happy to discuss these areas of math with students.

I am also dedicated to mentorship and diversity initiatives. My work in this area has focused on supporting minorities in STEM.

You can see more information about me at my website.

B.A., Skidmore College, 2016

M.S., University of California, Irvine, 2017

Ph.D., University of California, Irvine, 2021

Number theory, combinatorics, arithmetic geometry, arithmetic statistics

At Colgate, I have taught:

MATH 161 Calculus I

MATH 163 Calculus III


I have lead independent reading projects in:

Graph Theory

Grobner Bases and Ideals

Finite Geometry


I have previous experience as a teaching assistant at University of California, Irvine in the courses:

Number Theory

Introduction to Abstract Math

Linear Algebra

Calculus II and III

Abstract Algebra

I am dedicated to supporting and increasing diversity on campus through mentorship and other programming. Below are a list of programs I have been involved with.  Those marked with an asterisk are programs I created.

At University of California, Irvine:

Directed Reading Program*

Community, Mentoring, and Outreach Program*

Peer Mentor Program

Math Circles



An algorithm for counting arcs in higher-dimensional projective space, Finite Fields and Their Applications, 80 (2022).

Lower bounds for the number of subrings in Z^n , Journal of Number Theory, 234 (2022), 363-390.

(with M. I. de Frutos-Fernández, S. Garai, T. Murayama, and G. Smith) Rational Linear Subspaces of Hypersurfaces over Finite Fields, submitted.

(with Laura Monroe) Arithmetic of idempotents in Z/mZ, submitted.

(with Laura Monroe)  On the structure induced by the power sequences of (Z/mZ, ·), submitted.


NSF Mathematical Sciences Graduate Internship at Los Alamos National Laboratory (2019)

Student Researcher at New Mexico Consortium (2019 to 2020)

Guest Scientist at Los Alamos National Laboratory (2021 to Present)

Outstanding Teaching Assistant Award (2018)

President’s Dissertation Year Fellowship (2020 - 2021)

Kovalevsky Outstanding Ph.D. Thesis Award (2021)