Kelly Isham

Assistant Professor of Mathematics

Department/Office Information

Mathematics

214 McGregory Hall

Contact

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.

Education

BA, Skidmore College
MS, University of California, Irvine
PhD, University of California, Irvine

Research Interests

Number theory, combinatorics, arithmetic geometry, arithmetic statistics, graph theory and network design

Teaching

CORE S148 Making and Breaking Codes

MATH 161 Calculus I

MATH 163 Calculus III

MATH 214 Linear Algebra

MATH 250 Number Theory and Mathematical Reasoning

MATH 375 Abstract Algebra I

MATH 483 Senior Seminar: Mathematics

Mentorship and Diversity

I am dedicated to supporting and increasing diversity on campus through mentorship and other programming. I am part of a pilot program called Peers as Mentors, which provides a peer mentor to the students in an introductory STEM course.

Publications

K. Isham Is the number of subrings of index p^e in Z^n a polynomial in p?, Communications in Algebra 51 (12) (2023).
K. Isham An algorithm for counting arcs in higher-dimensional projective space, Finite Fields and Their Applications, 80 (2022).
K. Isham Lower bounds for the number of subrings in Z^n , Journal of Number Theory, 234 (2022).
K. Lahotia, L. Monroe, K. Isham, M. Besta, N. Blach, T. Hoefler, and F. Petrini. PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks in Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA ’24), Accepted.
K. Lakhotia, K. Isham, L. Monroe, M. Besta, T. Hoefler, and F. Petrini. "In-network Allreduce with Multiple Spanning Trees on PolarFly." In Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA ’23).
K. Lakhotia, M. Besta, L. Monroe, K. Isham, P. Iff, T. Hoefler, F. Petrini. PolarFly: A Cost-Effective and Flexible Low-Diameter Topology in 2022 SC22: International Conference for High Performance Computing, Networking, Storage and Analysis (Supercomputing '22).

Other Experience

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

Grants

Colgate Picker ISI Grant: April 2024 - August 2026

Los Alamos National Laboratory LDRD Reserve Grant: November 2022 - September 2023