William D. Taylor
Assistant Professor
Tennessee State University
Curriculum Vitae
Research Statement

I am an assistant professor in the Department of Mathematical Sciences at Tennessee State University, an HBCU in Nashville, Tennessee. I began working at TSU in the Fall of 2018. I received my Ph.D. from the University of Arkansas, working under Mark Johnson. My disseration was titled Interpolating Between Multiplicities and F-thresholds. I was born and raised in Reno, Nevada, and I received my Bachelor's (B.A.) and Master's (M.S.) in mathematics from the University of Nevada, Reno.


My research interest is in commutative algebra, specifically on singularities in positive characteristic, with a special interest in problems relating to F-purity, graded rings, and tight closure-like operations. In particular, I am working on problems involving and relating Hilbert-Samuel and Hilbert-Kunz multiplicities with each other and with other numerical invariants. I have recently also begun studying differential operators and fixed ideals of ring self-maps.

My other mathematical interests include group theory and combinatorics. My Bachelor's thesis, "p-adic Square Roots," develops an algorithm for calculating the square root of any p-adic rational number in a degree four field extension of the p-adic rationals (for p greater than 2). My Master's thesis, "Finding minimal n-power Extensions of Groups" explores the minimal degree of a group extension H of a group G such that every element of G has an n-th root in H (for a fixed n).