Mathematics – JacksonHurley.com

Thesis Work — Overview

For my senior thesis in math at Pomona, I completed a 60-page senior thesis containing original proofs of the main theorems, co-wrote and published two papers with my professors, and presented my work.

Both papers were published in the Canadian Mathematical Bulletin

Published Work

“Norms on Complex Matrices Induced by Random Vectors.” This paper, published before I completed my thesis work, defines a class of random vector norms. I contributed the bit about the Pareto distribution and not much else.

Published in Canadian Mathematical Bulletin, 2022. Link, Archiv

The second paper, “Norms on Complex Matrices Induced by Random Vectors II: Extension of Weakly Unitarily Invariant Norms” is substantially based on my thesis, including my novel proofs. It clarifies the definition of random vector norms and extends them beyond Hermitian matrices.

Published in Canadian Mathematical Bulletin, 2023. Link, Archiv

Senior Thesis

Some unit circles produced using exponential random vectors. Link to Thesis. Link to a Mathematica file I wrote to calculate unit circles/unit balls of random vector norms in Rn and produce illustrations like the one above.

Read my thesis!

Watch my thesis presentation!