Visiting Assistant Professor

Department of Mathematics and Computer Science

Rhodes College

Memphis, Tennessee

Office: Briggs 207

My email is superdockm at rhodes.edu.

I'm a visiting assistant professor in the Department of Mathematics and Computer Science at Rhodes College, in Memphis, Tennessee. I do research in topological combinatorics, as well as interactive theorem proving. I obtained my Ph.D. in Algorithms, Combinatorics, and Optimization, from Carnegie Mellon University in August 2021, advised by Florian Frick.

Here are some research questions and topics I'm interested in, in two areas:

*Topological combinatorics.*

- Are there topological obstructions to the existence of finite projective planes?
- What is the smallest simplicial complex with a given fundamental group?

*Interactive theorem proving & dependent types.*

- Constructing formal, computer-verifiable proofs (about math or code).
- Making dependently typed programming languages (especially Agda) easier to use.
- Building a code editor that prevents syntax errors.

If you're a Rhodes student, and you'd like to talk about research, please reach out!

*Simplicial complexes from projective planes and colored
configurations*
(pdf)

(submitted)

*Vertex numbers of simplicial complexes with free abelian fundamental
group*
(pdf)

(submitted)

With Florian Frick.

*A nonlinear Lazarev-Lieb theorem: \(L^{2}\)-orthogonality via motion
planning*
(doi,
pdf)

Journal of Topology and Analysis, to appear.

With Florian Frick.

*Clean tangled clutters, simplices, and projective geometries*
(pdf)

Journal of Combinatorial Theory, Series B 154 (2022)

With Ahmad Abdi, Gérard Cornuéjols.

*A new infinite class of ideal minimally non-packing clutters*
(html,
pdf)

Discrete Mathematics 344(7):112413 (2021)

With Ahmad Abdi, Gérard Cornuéjols.

*Topics in topological combinatorics:
Simplicial complexes, finite geometries, and the topology of circle-valued
maps.*
(pdf,
slides)

Advisor: Florian Frick

March 29, 2022

*Small simplicial complexes with fundamental group
\(\mathbb{Z}^{n}\)*

Iowa State University Discrete Math Seminar
(link)

November 21, 2021

*Simplicial complexes, finite projective planes, and colored
configurations.*

AMS Special Session on Topological Methods in Discrete Mathematics

October 22, 2020

*The necklace splitting problem and robot motion planning.*

Algorithms, Combinatorics, and Optimization Seminar,
Carnegie Mellon University

*Rhodes College.*

- COMP141 - CS I: Programming Fundamentals (Fall 2021, Spring 2022)
- COMP355 - Advanced Algorithms (Fall 2021)

*Carnegie Mellon University.*

- 21-240 - Matrix Algebra with Applications (Fall 2019)

*Charles E. Jordan High School.*

- AP Calculus AB/BC (2014-15, 2015-16, 2016-17)
- AP Computer Science A (2014-15, 2016-17)
- Mobile Computer Science Principles (2015-16)

The links below are Github repositories:

agda-unused - Check for unused code in an Agda project (Haskell).

vim-agda - Asynchronous type-checking for Agda 2.6.1 (Vimscript).

vim-foldout - Outline-based folding with syntax highlighting (Vimscript).