**Publications**

Counting Hats with the Lopsided Lovász Local Lemma

*In progress*

Spanning Subgraph Isomorphism Using Cut Vertices

with Andrew Meier and Thomas Schuler

*In progress*

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**Unpublished Work**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)

Lovász Local Lemma and Related

- The Lopsided Lovász Local Lemma and Hypergraphs
- Quest for Negative Dependency Graphs
- Diamonds in the Rough (The Lovász Local Lemma)

Beyond Infinity (The Uncountability of the Reals)

**Student Presentations**

**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