*Me with bass viol. Photo credit: Ali Taqi.*

Kenny (Kenneth) Gill

About

I'm a mathematician who graduated with a Ph.D. from Penn State University in December 2023. My thesis advisors were Jan Reimann and Linda Westrick. I also compose music and play the violin and viola da gamba (treble and bass). You can contact me at lastname math psu at posteo dot net.

I am currently on the job market for postdoc positions in math or theoretical computer science.

Research interests

Logic: computability, Ramsey theory, Weihrauch complexity and computable combinatorics in reverse mathematics, computable analysis, probabilistic automata and complexity measures for strings.

Research statement (11/2024) / Curriculum vitae (11/2024)

Papers

Probabilistic automatic complexity of finite strings, submitted (2024). arXiv: 2402.13376. See also my Sage code for calculations with PFAs.
Indivisibility and uniform computational strength, submitted (2024). arXiv: 2312.03919.
A note on the indivisibility of the Henson graphs, submitted (2024). arXiv: 2310.20097.
Two studies in complexity, Ph.D. thesis at Penn State University, 2023. Nearly everything in it is subsumed in the three papers above, and in fact many results have been improved, so you should look at those instead.
(with D. Costa, V. Davis, G. Hinkle, and L. Reid) Eulerian properties of non-commuting and non-cyclic graphs of finite groups, Communications in Algebra 46 (2018), 2659-2665. doi: 10.1080/00927872.2017.1392534.
(with V. Niţică) Signed tilings by ribbon L n-ominoes, n even, via Gröbner bases, Open Journal of Discrete Mathematics 6 (2016), 185-206. doi: 10.4236/ojdm.2016.63017.

Other

SageMath code for the probabilistic complexity project, useful to explore numerical and combinatorial properties of PFAs, is now on Github here. (API should be regarded as unstable.)

If you want some better pictures to go with my proof of the classification of binary strings with PFA complexity equal to 2, you can look at the second half of my slides from the ASL conference. (The "pending" proof of the computability of PFA complexity has since been checked in detail, see current paper version.)

Last updated 29 November 2024.