Office: B26 Hayes-Healy
Advisor: Professor Peter Cholak
Current status: 5th year Graduate Student, Department of Mathematics, University of Notre Dame
Here is my CV.
Computability theory, randomness, reverse mathematics, combinatorics, discrete mathematics.
My PhD work is based on the structure of the recursively enumerable (r.e.) Turing degrees. The ability to embed some important and basic lattices below a r.e. degrees is characterized by the fickleness of that degree. I explore the notion of fickleness with nonlowness, another notion of degree strength, and prove both notions are independent. I also worked towards finding lattices to characterize important levels of fickleness. Fickleness at the ω and ω^ω levels have already been characterized, but no lattice has been found to characterize the ω^2 level, the first non-trivial level after ω. I explore candidate lattices, including those without meets, and seek to understand the challenges faced in finding an ω^2 lattice.
- Nonlowness is independent from fickleness. Pdf. Journal of the Association Computability in Europe. 2021.
- Fickleness and bounding lattices in the recursively enumerable Turing degrees (Forthcoming. Here is a draft)
- Towards Finding a Lattice that characterizes >ω^2-fickleness in the r.e. Turing Degrees. Slides. National University of Singapore. 18th March 2021.
- Bounding Lattices in the Recursively Enumerable Turing Degrees. Slides. AMS Special Session Computability Theory and Effective Mathematics. 7th January 2021.
- Fickleness and bounding lattices in the recursively enumerable degrees. Slides. Midwest Computability Seminar XXV. 27th October 2020.
- Nonlowness is independent from fickleness. Slides. 16th New England Recursion and Definability Seminar (NERDS). Bridgewater State University. 16th November, 2019.
Instructor: 2021 Spring, 2018 Fall – Introduction to Math Research, Calculus B
Teaching assistant (head): 2019 Spring – Calculus B
Teaching assistant: 2019 Fall, 2018 Spring, 2017 Fall – Calculus B, Calculus 1, Calculus A