William D. Taylor
Ph.D. Candidate
University of Arkansas
Curriculum Vitae
Research Statement

I am a Ph.D. candidate studying at the University of Arkansas under Mark Johnson. 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.

Research

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 together with other numerical invariants of rings and ideals.

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).

Outreach

I am the co-founder of the OMNI Graduate Student Seminar and was the organizer of the 5th and 6th annual Celebration of Mind math festivals, both at the University of Arkansas.

Personal Life

I am a member of Covenant Church in Fayetteville (PCA), and have interests in theology and religion as well as computer science and gaming.