I am a National Science Foundation postdoctoral fellow at the University of Utah. Before joining the math department at the University of Utah I was a PhD student at the University of Missouri under the advisement of Ian Aberbach.
My research interests are in commutative algebra and algebraic geometry. I particularly enjoying studying these subjects using prime characteristic techniques. I have also made contributions using basic element techniques and combinatorics.
Global Frobenius Betti numbers and F-splitting ratio, with Alessandro De Stefani and Yongwei Yao, submitted.
F-signature under birational morphisms, with Linquan Ma, Karl Schwede, and Kevin Tucker, submitted.
Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals, with Pham Hung Quy, submitted.
Continuity of Hilbert-Kunz multiplicity and F-signature, with Ilya Smirnov, submitted.
Globalizing F-invariants, with Alessandro De Stefani and Yongwei Yao, submitted.
F-signature and Hilbert-Kunz Multipicity: a combined approach and comparison, with Kevin Tucker, Algebra & Number Theory 12-1 (2018), 61--97.
Generalizing Serre's Splitting Theorem and Bass's Cancellation Theorem via free-basic elements, with Alessandro De Stefani and Yongwei Yao, Proc. Amer. Math. Soc. 146 (2018), no. 4, 1417--1430.
Uniform bounds in F-finite rings and lower semi-continuity of the F-signature, Trans. Amer. Math. Soc. 370 (2018), no. 5, 3147--3169.
Depths and Stanley depths of path ideals of spines,, with Daniel Campos, Susan Morey, and Chelsey Paulsen, Involve, 9(1): 155-170, 2016.
Depths and Cohen-Macaulay Properties of Path Ideals, with Daniel Campos, Susan Morey, and Chelsey Paulsen, Journal of Pure and Applied Algebra, 218: 1537-1543, 2014.
I am currently teaching MATH 1260: Honors multivariable calculus.
MATH 8411 (Algebra II), Teaching Assistant, Spring 2016, Spring 2017.
MATH 8410 (Algebra I), Teaching Assistant and Reciatation Instructor, Fall 2016.
MATH 4720 (Introduction to Abstract Algebra) Recitation Instructor, Spring 2015, Fall 2015, Spring 2017.
MATH 4140 (Matrix Theory) Instructor, Summer 2015, Summer 2017.
MATH 3000 (Introduction to Advanced Mathematics) Recitation Instructor, Fall 2016.
MATH 2320 (Discrete Mathematical Structures) Instructor, Spring 2017.
MATH 2300 (Calculus III) Instructor, Summer 2014, Summer 2016.
MATH 1700 (Calculus II) Recitation Instructor, Fall 2015.
MATH 1100 (College Algebra) Instructor, Fall 2013, Fall 2014.
MATH 0110 (Intermediate Algebra) Instructor, Spring 2014.
Myself and Linquan Ma gave a series of lectures and exercises in prime characteristic commutative algebra and the RTG mini-course in Commutative Algebra at the University of Utah during the week of May 7-11, 2018. Notes are currently being developed and we will make them publicly available at the Thematic Program in Commutative Algebra and its Interaction with Algebraic Geometry at the University of Notre Dame.