I am originally from south Jersey. For my undergraduate, I attended Rensselaer Polytechnic Institute in Troy, NY for Physics and Applied Mathematics. Upon graduating, I moved to Los Angeles in the summer of 2016 to pursue a PhD in applied mathematics at UCLA. Currently, I am a second year graduate student in the program, and I have passed all three of my qualifying exams.
In addition to being a graduate student and teaching assistant, I also do private tutoring for high school level, undergraduate, and intro graduate level mathematics. For more information, contact me!
My current interests fall under the mathemtaical theory of deep learning. My primary interest is in embodied intelligence, specifically analyzing methods for cheap control in reinforcement learning situations where the agent's physical morphology plays a role. Other interests are in analyzing deep learning architectures using tools from random matrix theory and information theory. In the recent past, I was interested in model-order reduction methods, high performance computing, and modeling stochastic phenomena. Many of these interests are relatively new to me, and I am looking forward to what these fields may hold.
At Rensselaer, I primarily did research on the evolution of thin film morphology. Here we were interested in developing a model of nanosurface growth under high ambient pressure, which has previously been found to result in time invariant surface roughness, a novel property for thin films to display. This model was then tested and verified by Monte Carlo simulations. Publications and results have been listed in my curriculum vitae found below. Other projects I worked on were computationally determining the universality class scaling coefficients for the stochastic KPZ growth equation in (2+1) dimensions, studying scaling coefficients for diffusion limited aggregation, and the accurate computation of resistivity in trapezoidal shaped nanowires.
Other projects I have worked on briefly include mathematically modeling neuron networks, and applying empirical dynamical modeling techniques to plasma thruster simulations. The former was a project I continued in the RPI mathematics department, where I implemented the leaky integrate-and-fire model on complex networks with intention of applying it to modeling spike time dependent plasticity. Although this project stopped to prioritize the above research, I still think there are many interesting topics to be explored in mathematical neuroscience. The latter was my research during the summer of 2017 at Edwards Air Force Research Lab. This research was a proof of concept study to show that methods in compressed sensing and optimization can be used to determine low dimensional models of dynamical systems directly from noisy time series measurements.