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