Graduate Research Experiences:
1. For my Research Tutorial Group project, I reviewed a paper on Combinatorial Manifolds: Bonnet-Myers Theorem and began to determine how to relate this discrete version of Bonnet-Myers Theorem to the continuous version. This project was under the guidance of Dr. Andrea Young. The paper and presentation are below.
2. My Master's Thesis is in progress and is a study of the structure of the group of equivariant meromorphic functions on a Riemann surface with an antiholomorphic reflection symmetry under the guidance of Dr. Doug Pickrell.
Undergraduate Research Experiences:
1. A Mathematics and Music investigation of Irish Jigs/SlipJigs and the mathematical relationships defining the melodies. The Mathematics and Music research was performed under the guidance of Dr. Thomas Morley. We wrote a Mathematica program which created new Jigs based on the frequency and probability that the progression fit the model of a Jig. We used Markov Chains.
2. A Hyperbolic Geometry problem regarding metrics, cylindrical coordinates, complex hyperbolic, and real hyperbolic 2-spaces. The Hyperbolic Geometry research was performed under the guidance of Dr. Igor Belegradek. The paper, Complex Hyperbolic Plane in Cylindrical Coordinates About the Real Hyperbolic Plane, is available below to the left.