**Liling Ko**

Email: lko@nd.edu

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.

**Research Interest**

*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.

**Papers**

- 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)

**Talks**

- 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.

**Teaching**

**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