**Publications**

Counting Hats with the Lopsided Lovász Local Lemma

*In progress*

Pruning Techniques for Subgraph Isomorphism Using Matchings and Vertex Cuts

with Andrew Meier and Thomas Schuler

*In progress*

Enumeration of Regular Uniform Hypergraphs by Girth

with Linyuan Lu and László Székely

*In progress*

Mastery-Based Exams in Undergraduate Mathematics

with many others

*Submitted to PRIMUS*

Analogies Between the Crossing Number and the Tangle Crossing Number

with many others

*Submitted to Electronic Journal of Combinatorics*

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**Unpublished Work**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**

Lovász Local Lemma and Related

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

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

Order from Chaos (Math Circle on Ramsey Numbers)

Beyond Infinity (The Uncountability of the Reals)

**Student Conference Presentations**

Spanning Subgraph Isomorphism

Andrew Meier and Thomas Schuler

2016 MAA MathFest

Classification and Generation of Spanning Trees by Isomorphism

Andrew Meier

2016 Joint Mathematics Meetings

Palindromic nth Power Sums

Ann Marie Murray

2016 Joint Mathematics Meetings

Subgraph Isomorphism: Spanning Trees in Graphs

Thomas Schuler

2016 Joint Mathematics Meetings

**Miscellaneous**

Mastery-Based Testing in Undergraduate Mathematics Blog (with many others)

Spanning Subgraph Isomorphism in Sage (courtesy Andrew Meier and Thomas Schuler)

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

Miscellaneous Images of Unlabeled Spanning Trees

Pi-Base (courtesy James Dabbs)

Mathematics StackExchange Profile

**Graduate Coursework**

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

Linear Algebra Methods in Combinatorics