Kieran Vlahakis

Hello, my name is Kieran Vlahakis. My academic interests lie primarily in linear algebra, partial differential equations (particularly numerical solvers), and approximation theory. Much of my work so far, as outlined in the projects section, focuses on numerically solving differential equations. I also have a solid foundation in machine learning, with hands-on experience working with large language models (LLMs) and other neural network architectures, both in coursework and independent research projects.

I am currently working on a summer research project with Professor Nick Trefethen, investigating a recent claim he made stating that numerical quadrature rules can be re-expressed as rational hyperfunction approximations of the Cauchy transform of their associated quadrature weight function. This is an especially exciting project for me, because I owe much of my interest in applied mathematics to my first encounter with Chebyshev quadrature in my first year of university. This project’s success could also open many new avenues in applied mathematics and modern computational science as a whole.