My research interests are primarily in graph theory and combinatorics. In particular, I work on Ramsey theory and extremal problems for graphs, hypergraphs, and other combinatorial structures. I am also interested in working on open problems from finite model theory, complexity theory, and the developing area of graph limits. Feel free to read my Research Statement for more information.

Here is a list of my papers and talks. The papers have links to pdf versions where available. Any comments or ideas are welcome!

Papers

An explicit edge-coloring of the complete graph with six colors on every 5-clique, April 5, 2017.

A (5,5)-colouring of the complete graph with few colours (with Emily Heath), Combinatorics, Probability and Computing, Cambridge University Press (2018), https://doi.org/10.1017/S0963548318000172.

Extremal Numbers for Directed Hypergraphs with Two Edges (early arxiv version: part 1, part 2), The Electronic Journal of Combinatorics, 25(1), P1.56 (2018).

Counting Ring Homomorphisms. The Pi Mu Epsilon Journal, 13:2(Spring 2010), 65–67.

Research Notes

Extremal Problems on Generalized Directed Hypergraphs, July 18, 2016.

Talks and Presentations

4/26/2018: Thesis Defense at UIC in Chicago, IL.

1/12/2018: "A (5,5)-coloring of the complete graph with few colors," Research from the Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics Special Session at the Joint Mathematics Meeting in San Diego, CA.

5/20/2017: "A (5,5)-coloring of the complete graph with few colors," 29th Cumberland Conference on Combinatorics, Graph Theory and Computing at Vanderbilt University in Nashville, TN.

3/27/2017: "A variation of the Ramsey problem: (p,q)-colorings," Combinatorics Seminar at UIC in Chicago, IL.

11/18/2016: "Extremal Problems on Directed Hypergraphs," Combinatorics Seminar at the University of Szeged in Szeged, Hungary.

11/17/2016: "Extremal Problems on Directed Hypergraphs," Combinatorics Seminar at the Rényi Institute in Budapest, Hungary.

9/14/2016: "Extremal Living: Why you should go into combinatorics research," a talk to the Undergraduate Math Club at UIC in Chicago, IL.

8/8/2016: "Extremal Problems on Generalized Directed Hypergraphs" (poster presentation) at EXCILL III: Extremal Combinatorics at Illinois held at IIT in Chicago, IL.

7/20/2016: "(p,q)-colorings" at the Rocky Mountains - Great Plains Graduate Research Workshop in Combinatorics held at the University of Wyoming in Laramie, WY.

4/3/2016: "Extremal Problems on Directed Hypergraphs: Forbidden Subgraphs with Two Edges" at the Graduate Student Combinatorics Conference held at Clemson University in Clemson, SC.

7/2015: "Ehrenfeucht-Fraïssé Games" for the Combinatorics Student Seminar at UIC in Chicago, IL.

4/2015: "Flag Algebras," a series of three talks for the Combinatorics Student Seminar at UIC.

4/1/2006: "Counting Ring Homomorphisms" at the Oklahoma-Arkansas MAA meeting held at the University of Arkansas in Fayetteville, AR.