A visual from a research paper, out of context.

Research

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

  • New upper bounds for the Erdős-Gyárfás problem on generalized Ramsey numbers (with Emily Heath), Submitted (2020). arXiv version.
  • A lower bound for the saturation number, and graphs for which it is sharp (with Gregory J. Puleo), Submitted (2020). arXiv version.
  • Distance Domatic Numbers for Grid Graphs (with Jiasheng Yan), Submitted (2019). arXiv version.
  • An explicit edge-coloring of the complete graph with six colors on every 5-clique, The Electronic Journal of Combinatorics, 26(4), P4.13 (2019). Published version and early arXiv version.
  • A (5,5)-colouring of the complete graph with few colours (with Emily Heath), Combinatorics, Probability and Computing, Cambridge University Press (2018). Published version and early arXiv version.
  • Extremal numbers for directed hypergraphs with two edges, The Electronic Journal of Combinatorics, 25(1), P1.56 (2018). Published version and early arXiv version: part 1, part 2.
  • Extremal problems on generalized directed hypergraphs, a set of research notes (2016). arXiv version.
  • Counting ring homomorphisms, The Pi Mu Epsilon Journal, 13:2(Spring 2010), 65–67.

Talks

  • March 5, 2020: Improved upper bounds on the Erdős-Gyárfás function, a variation of Ramsey theory, Combinatorics Seminar, Auburn University, Auburn, AL.
  • November 12, 2019: Intro to Quantum Computing: The Deutsch-Jozsa Algorithm (talk given with Lauren Ruth), Math Undergraduate Seminar, Vanderbilt University, Nashville, TN.
  • October 5, 2019: Improved upper bounds on the Erdős-Gyárfás function, a variation of Ramsey theory, Combinatorics Seminar, University of Manitoba, Winnipeg, Manitoba.
  • May 3, 2019: Next steps for the Erdős-Gyárfás function, a variation of Ramsey theory, Discrete Seminar, University of Colorado Denver, Denver, CO.
  • March 28, 2019: The Erdős-Gyárfás function, a variation of classical Ramsey theory, Discrete Mathematics Seminar, Middle Tennessee State University, Murfreesboro, TN.
  • March 4, 2019: The Saturation Number of Pineapples, 50th Southeastern International Conference on Combinatorics, Graph Theory & Computing, Florida Atlantic University, Boca Raton, FL.
  • February 25, 2019: The Saturation Number of Pineapples, Graph Theory & Combinatorics Seminar, Vanderbilt University, Nashville, TN.
  • September 10, 2018: The Erdős-Gyárfás function: A variation of the Ramsey problem for graphs, Graph Theory & Combinatorics Seminar, Vanderbilt University, Nashville, TN.
  • April 26, 2018: Thesis Defense, UIC, Chicago, IL.
  • January 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, San Diego, CA.
  • May 20, 2017: A (5,5)-coloring of the complete graph with few colors, 29th Cumberland Conference on Combinatorics, Graph Theory and Computing, Vanderbilt University, Nashville, TN.
  • March 27, 2017: A variation of the Ramsey problem: (p,q)-colorings, Combinatorics Seminar, UIC, Chicago, IL.
  • November 18, 2016: Extremal Problems on Directed Hypergraphs, Combinatorics Seminar at the University of Szeged, Szeged, Hungary.
  • November 17, 2016: Extremal Problems on Directed Hypergraphs, Combinatorics Seminar at the Rényi Institute, Budapest, Hungary.
  • September 14, 2016: Extremal Living: Why you should go into combinatorics research, Undergraduate Math Club, UIC, Chicago, IL.
  • August 8, 2016: Extremal Problems on Generalized Directed Hypergraphs (poster presentation), EXCILL III: Extremal Combinatorics at Illinois, IIT, Chicago, IL.
  • July 20, 2016: (p,q)-colorings, Rocky Mountains - Great Plains Graduate Research Workshop in Combinatorics, University of Wyoming, Laramie, WY.
  • April 3, 2016: Extremal Problems on Directed Hypergraphs: Forbidden Subgraphs with Two Edges, Graduate Student Combinatorics Conference, Clemson University, Clemson, SC.
  • July, 2015: Ehrenfeucht-Fraïssé Games, Combinatorics Student Seminar, UIC, Chicago, IL.
  • April 8-22, 2015: Flag Algebras (a series of three talks), Combinatorics Student Seminar, UIC, Chicago, IL.
  • April 1, 2006: Counting Ring Homomorphisms, The Oklahoma-Arkansas MAA meeting, University of Arkansas, Fayetteville, AR.