# Greg Knapp

## Number Theory

Most of my research attention is devoted
to number theory from an analytic perspective (which is different from
analytic number theory), where my interests include diophantine
approximation,
root separation of polynomials, height functions, the geometry of
numbers, and other topics. My advisor
is Shabnam
Akhtari.

My research statement is here.

### Papers

The Number of Solutions to the Trinomial Thue Equation. arXiv preprint.
Accepted for publication in Functiones et Approximatio
Commentarii Mathematici.

Here is the associated Jupyter notebook: trinomial_computations.ipynb

Here are the .csv files containing data about the number of solutions
to trinomial Thue equations of fixed degree and height: trinomial_solution_data.zip

### Talks

I have given several versions of the same talk on my research into
Thue equations.
All have been titled something like "Bounds on the Number of
Solutions to Thue's Inequality."
The slides for the best version of the talk (which will be given
in the Oregon State number theory seminar on February 7, 2023) are
here: thue_equation_talk.pdf

I will also be speaking at the upcoming Oregon Number Theory Days conference about some of my work on root separation of polynomials. Slides will be posted when they are ready.

## Logic

I did my master's thesis under Colin McLarty
at Case Western Reserve University in
2017. I am currently working on completing some of the finer
details with Zach Jandrasi and I hope to publish the results some time
in 2022.

"Minkowski's
Linear Forms Theorem in Elementary Function Arithmetic." Electronic
Thesis or Dissertation. Case Western Reserve University, 2017. OhioLINK Electronic Theses and
Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1495545998803274