__Kdb+ for Space Analytics__In the summer of 2017, I received the opportunity to travel to Mountain View, California, to work with the Solar Storm team at the NASA Frontier Development Lab. As the team was keen on performing time-series analysis on geomagnetic data to validate their neural network, I worked to create a database in kdb+ so they could find insights quickly and efficiently. In the spring of 2018, I took that work a few steps further and integrated it with jupyterq, and leveraged the power of Python to visualize the insights. You can find my work on my Github page and read more about my work here.

__Quantitative MRI__Under Dr. Ferdinand Schweser, I was responsible for creating mathematical models based on MRI sequence parameters. More specifically, I researched neuronal magnetic susceptibility on gradient echo MR signal formation using the Generalized Lorentzian Tensor Approach. By manipulating various sequence parameters and incorporating our current knowledge of the biology of the brain, specifically at the cellular level, we can simulate MR signals. The purpose of this research is to gain a better understanding into quantitative susceptibility mapping (QSM) and magnetic resonance imaging (MRI).

**Complex Dynamical Systems and the Exploration of Fractals**I explored the dynamics of Newton's Method in the complex plane with a system of equations to discover their basins of attraction, while mainly working in four dimensional and two dimensional space. Newton's method is an algorithm for finding the roots of differentiable functions that uses iterated local linearization of a function to approximate its roots. It also extends to systems of

*n*differentiable functions in

*n*variables. In collaboration with George Hauser, we examined the dynamics of Newton's method on systems of two bivariate polynomials and used computer programming to graphically visualize these systems. In particular, we investigated whether the attracting cycles that arise in the dynamics of Newton's Method on certain cubic polynomials of one complex variable also arise in the case of bivariate quadratics. This research project was conducted under Dr. Tim Flaherty at the Summer Undergraduate Applied Mathematics Institute (SUAMI) at the Center for Nonlinear Analysis at Carnegie Mellon University.

**Vascular Blood Flow Approximation**I investigated the spectral method for the approximation of vascular flows with a complex geometry. Working with Dr. Jae-Hun Jung, I applied a polynomial approximation I developed to a multi-domain region, where both the two-dimensional and three-dimensional cases were considered. Ultimately, the study of these methods can be implemented to determine if a patient is in need of a stent or not.