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 programming languages. 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 currently thinking about, in two areas:

*Programming languages.*

- Constructing formal, computer-verifiable proofs (about math or code).
- Building interactive editors for dependently typed data.
- Defining metacircular programming languages.

*Topological combinatorics.*

- Can we extend Borsuk-Ulam and its applications to slightly discontinuous functions?
- Are there topological obstructions to the existence of finite projective planes?
- What is the smallest simplicial complex with a given fundamental group?

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

*Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes*
(pdf)

(preprint)

with Henry Adams, Johnathan Bush, Nate Clause, Florian Frick, Mario Gómez, R. Amzi Jeffs, Evgeniya Lagoda, Sunhyuk Lim, Facundo Mémoli, Michael Moy, Nikola Sadovek, Daniel Vargas, Qingsong Wang, Ling Zhou.

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

(preprint)

with Florian Frick.

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

Discrete Mathematics 346(1):113117 (2023)

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

Journal of Topology and Analysis 14, No. 3, 569-585 (2022)

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

April 28, 2022

*Simplicial complexes and fundamental groups*

Rhodes College Math Seminar

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.*

- COMP241 - CS III: Data Structures & Algorithms (Fall 2022)
- COMP355 - Advanced Algorithms (Fall 2021, Fall 2022)
- COMP141 - CS I: Programming Fundamentals (Fall 2021, Spring 2022)

*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 2.6.2 (Vimscript).

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