Undergraduate Research

I regularly mentor undergraduate students on research projects. The types of projects that I work on come from analysis, (partial) differential equations, and spectral theory, and usually involve understanding the behaviour of eigenfunctions in various settings. They can also have a programming component, typically using MATLAB.

If you are an undergraduate student interested in working with me during the summer, please contact me early in the Spring semester. This will give us time to discuss the project that you will work on, and allow you to do some of the required reading during the semester. Students interested in applying for one of Fordham's internal Research Grants, should contact me well ahead of the deadline.

Recent work with undergraduates

Here are some recent projects with undergraduate students from Fordham that I have supervised:

• Brooke Warner: Counting Nodal Domains of Chain Domain Eigenfunctions Using Graph Theory, Honors Senior Thesis for the Fordham College at Rose Hill Honors Program, and presented at the Spring 2023 Undergraduate Research Symposium

• Joseph Denham and Steve Zucca: Nodal Domains of Eigenfunctions in a Dumbbell Domain, presented at the Spring 2023 Undergraduate Research Symposium

• Farhan Azad and Karolina Lokaj: The isoperimetric inequality for convex subsets of the sphere, published in Involve, a Journal of Mathematics, and presented at the Spring 2022 Undergraduate Research Symposium

Here are two papers that I wrote with undergraduate students (in bold) from the University of North Carolina at Chapel Hill:

• (with M. Gupta, J. Marzuola) Nodal Set Openings on Perturbed Rectangular Domains, submitted, https://arxiv.org/abs/2204.12009.

• (with I. Bors, G. Conte, G. Cox, J. Marzuola) Limiting eigenfunctions of Sturm-Liouville operators subject to a spectral flow, Ann. Math. Québec, 45 (2020), 249–269.