## Welcome!

Thank you for taking the time to visit my website. My name is Ryleigh Moore and I plan to graduate in May 2022 with my applied mathematics PhD from the University of Utah. I graduated Summa Cum Laude with a double major in pure and applied mathematics and a minor in computer science from Boise State University in 2014.

I work with Dr. Akil Narayan on developing numerical algorithms for solving high dimensional stochastic differential equations (SDEs). We utilize a method called density tracking by quadrature (DTQ) which discretizes the SDE in time using the Euler-Maruyama method then interprets the result as a Markov chain. The method then uses a Hermite interpolatory quadrature rule on Leja points to approximate the associated Chapman-Kolmogorov equation in order to update the probability density function (PDF) of the Fokker-Planck equation associated to the SDE being solved. Our procedure utilizes an adaptive, non-tensorized mesh to reduce the degrees of freedom necessary for computing the PDF of the associated Fokker-Planck equation of the SDE.

I have also conducted research with Dr. Ken Golden on Arctic melt pond evolution. As snow melts on top of sea ice, water pools into melt ponds. As simple ponds grow and coalesce, they form more complex, space-filling ponds. The darker melt ponds absorb more sunlight than the reflective sea ice which directly impacts the albedo of the Arctic region. Albedo, the ratio of incident and reflected sunlight, plays an important role in climate modeling.

Furthermore, Dr. Robert Schmidt and I have developed a mathematical model for minimizing the risk of blood platelet contamination during blood transfusion. We also conducted research on cross level quality control.