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 researching under the advice of Professor Nick Trefethen, investigating the link between numerical quadrature, hyperfunctions, and the Cauchy transform of associated quadrature weight functions. Our work has also led me to collaborate with Professor Andrew Horning on research relating to his and Prof. Trefethen’s recent paper. This work has been especially exciting 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.