Mathematics

I am currently a PhD student 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.

Papers

• Deep Points of Cluster Algebras (arXiv)
  Joint with Greg Muller
  Int. Math. Res. Not. IMRN, accepted
  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.

In Preparation

• Separating Dots with Circles
  Joint with Jaewon Min and Greg Muller
  We study partitions of dots on the sphere using circles and show that this admits a natural cluster structure. A demo application can be viewed here.

• Separating Curves in the Genus 2 Surface and the \( X_7 \) Cluster Algebra
  Joint with Greg Muller
  We establish a correspondence between separating curves in the genus 2 surface and a subset of cluster variables in the \( X_7 \) cluster algebra. We use this correspondence to show that the separating curve complex of the genus 2 surface is a six-dimensional pseudomanifold.

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Recreation

• OEIS sequence A308821
  Semiprimes where the sum of the digits equals the difference between the prime factors.

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Old Stuff

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