**Publications**

Connected Balanced Subgraphs in Random Regular Multigraphs Under the Configuration Model

with Linyuan Lu and László Székely

*Journal of Combinatorial Mathematics and Combinatorial Computing* **86**, 2013

Quest for Negative Dependency Graphs

with Linyuan Lu and László Székely

*Recent Advances in Harmonic Analysis and Applications* (in honor of Konstantin Oskolkov), Springer Proceedings in Mathematics and Statistics **25**, 2013, 243 – 258

Applications of Stirling Numbers Involving Chromatic Polynomials

with Thomas Porter

*Journal of Combinatorial Mathematics and Combinatorial Computing* **70**, 2009, 57 – 64

Some Applications of Spanning Trees in K(s,t)

with Lane Clark and Thomas Porter

*Journal of Combinatorial Mathematics and Combinatorial Computing* **62**, 2007, 139 – 146

**Unpublished Work**

Doctoral Dissertation (2013)

- Applications of the Lopsided Lovász Local Lemma Regarding Hypergraphs
- Applications of the Lopsided Lovász Local Lemma Regarding Hypergraphs (Defense Presentation)
- Notes by Rod Canfield on the Moser-Wyman Expansion of the Bell Numbers
- Asymptotics Using the Moser-Wyman Expansion for the Bell Numbers (Maple Worksheet)

Negative Dependency Graphs in Spaces of Random Matchings (2011)

Master’s Thesis (2008)

- Partitioning the Labeled Spanning Trees of an Arbitrary Graph into Isomorphism Classes
- Defense Presentation (PowerPoint)
- Images of Nonisomorphic Spanning Trees of Graphs
- Java Program (generates all labeled spanning trees of a graph and partitions them according to isomorphism – see paper for details)

Abstraction Techniques for Markov Decision Processes (2008)

A Survey of Zero-Knowledge Proofs with Applications to Cryptography (2007)

Quantum Computing in Complexity Theory and Theory of Computation (2007)

**Presentations**

Mastery-Based Exams Are Self-Evidently Better Than Traditional Exams

Order from Chaos (Math Circle on Ramsey Numbers)

Lopsided Lovász Local Lemma

- University of Nebraska at Lincoln (Fall 2013)
- Georgia Southern University (Spring 2013)
- Joint Mathematics Meetings (Spring 2013)
- AMS Sectional Meeting at University of Akron (Fall 2012)
- 8th Annual Graduate Student Combinatorics Conference (Spring 2012)
- University of South Carolina (Part 2, Spring 2012)
- University of South Carolina (Part 1, Spring 2012)

Beyond Infinity (The Uncountability of the Reals)

Partitioning the Labeled Spanning Trees of an Arbitrary Graph into Isomorphism Classes (MS Thesis Defense, 2008)

**Miscellaneous**

Mathematics StackExchange Profile

Images of Unlabeled Spanning Trees in Sage (by Andrew Meier)

**Graduate Coursework**

The following documents are riddled with errors. Please contact me if you find one.

Linear Algebra Methods in Combinatorics