## Welcome!

Thank you for taking the time to visit my website. My name is Ryleigh Moore and I will graduate in May 2022 with an Applied Mathematics Ph.D. from the University of Utah. I finished my Master's degree in Applied Mathematics from the Univesity of Utah in December 2021. My research has focused on problems using tools from numerical analysis, mathematical modeling, probability theory, and data science. 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 2017.

After I graduate, I will be joining MathWorks as an Engineer in the Engineering Development Group. I am very excited to continue working on problems from mathematics, computer science, and engineering.

In 2013, I began my first software job at a local software company. Now, during my Ph.D., I work in Python to develop algorithms and mathematical models daily. I was selected to work on two data driven projects with the U.S. Army Corps of Engineers. For one of the projects, I modeled the ocean tide using harmonic and time series analysis of data. For the other project, I worked on a team to predict ocean wave breaker types (plunging, spilling, surging waves) using machine learning. I am excited for the opportunity to join the MathWorks team to continue solving problems using tools from computer science, mathematics, and engineering.

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.