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I am currently in my sixth year at the University of Oklahoma, working under the direction of Greg Muller. My research is focused on cluster algebras, a type of commutative ring with connections to many different areas of mathematics and physics. Lately, I have been very interested in constructions that relate cluster algebras to low-dimensional topology - knots, curves, surfaces, mapping class groups, etc.

**Deep Points of Cluster Algebras**(arXiv)

*Joint with Greg Muller*

We initiate a systematic study of the deep points of a cluster algebra; that is, the points in the associated variety which are not in any cluster torus. We describe the deep points of cluster algebras of type A, rank 2, Markov, and unpunctured surface type.

For my MS, I wrote a survey paper on the curve complex. My advisor was Leah Childers.