Curriculum Vitae

Education

Expected December 2026: B.S. in Mathematics, University of Utah. Honors thesis: "ON GAUSSIAN INTEGER TORSION POINTS OF ELLIPTIC CURVES"

April 2026 - Present: Eisenstein torsion points of elliptic curves, and division polynomials
March 2025 - April 2026: Gordan Savin, University of Utah honors thesis on Gaussian integer torsion points of elliptic curves and division polynomials

Unpublished manuscripts; see the research page for full abstracts.

T. N. Warnick, On Eisenstein Integer Torsion Fields of Elliptic Curves with Hexic Symmetries, 2026 (unpublished).
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T. N. Warnick, Cyclic extensions of elliptic curves of j-invariant 1728, 2026 (unpublished).
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T. N. Warnick, ON GAUSSIAN INTEGER TORSION POINTS OF ELLIPTIC CURVES, Honors Thesis, University of Utah, 2026.
PDF · University of Utah Library

April 2025: Induction into the University of Utah's branch of the mathematics honors society Pi Mu Epsilon

May 2023 – Present: Mentor and train incoming Controls Installation Specialists on system programming and installation practices, Harris
December 2020 – May 2021: Tutor (Sensei), Code Ninjas – taught foundational coding (JavaScript, Lua, C#) to youth students

Algebra: Modern Algebra I – Rings, Modules & Commutative Rings (MATH 5310; graduate-level MATH 6310 *); Modern Algebra II – Groups, Fields & Galois Theory (MATH 6320); Representation Theory of Finite and Compact Lie Groups (MATH 6260). Texts: Dummit & Foote, Abstract Algebra; Serre, Linear Representations of Finite Groups; Artin, Galois Theory.
Analysis: Foundations of Analysis I & II (MATH 3210, 3220); Real Analysis – measure theory & functional analysis (MATH 5210); Complex Variables (MATH 4200). Texts: Rudin, Principles of Mathematical Analysis; Munkres, Topology; Taylor, Complex Variables.
Number theory: Introduction to Number Theory (MATH 4400) – algebraic number theory, quadratic forms & residues, continued fractions, Diophantine equations, with Gordan Savin.
Geometry & topology: Differentiable Manifolds (MATH 6510*, with Kurt Vinhage); Introduction to Algebraic Geometry I (MATH 6130*, with Aaron Bertram).
Computational & other methods: Numerical Analysis (MATH 5600, Driscoll & Braun, Fundamentals of Numerical Computation, Julia edition); Linear Algebra (MATH 2270); Differential Equations (MATH 2280); Deductive Logic (PHIL 3200); Accelerated Intro to Object Oriented Programming (CS 1420).

Programming: Python (symbolic computation for division polynomials); Java (Based on coursework); Julia (Based on coursework)
Typesetting: LaTeX

* Auditing – sitting in on lectures, not formally registered for the course.