Held weekly office hours, graded students' homeworks and exams for CS 4220 - Numerical Analysis: Linear and Nonlinear Problems in Spring 2025

Working with Anil Damle to derive and study high probability and expectation bounds in randomized numerical linear algebra. Currently proving (2,∞)-norm bounds between low-rank subspaces of matrices from the randomized SVD and their true low-rank subspaces. Also writing numerical experiments to verify optimality and tightness of bounds.

Given a $5,000 stipend to conduct research with Alexander Vladimirsky on optimal control of sailboats under the influence of stochastically changing wind direction. Derived quasi-variational inequalities and equations of motion using the Hamilton-Jacobi-Bellman equations to construct the optimal policy for a single boat sailing upwind. Implemented explicit and iterative numerical methods to solve the equations of motion. Extended our findings to game-theoretic versions of the race with two competing boats moving upwind.

Worked with Nandini Ananth to update and verify computer programs simulating quantum mechanical systems. We designed novel and efficient algorithms that simulate N particles given a potential function. Performed detailed analysis on the speed of convergence of Monte Carlo integration methods developed. Implemented Message Passing Interface (MPI) to allow programs to run on parallel computing architecture. This work will result in a forthcoming publication to the Journal of Chemical Physics.

Worked with Tomás Arias on small coding projects on computational density functional theory. We parallelized existing code for sampling Fermi surfaces and computing Eliashberg spectral functions.We also derived integration schemes for computing integrals related to the overlap of Wannier functions and their gradients.

Given a $7,000 stipend to conduct research under Professor Alexander Hayes on the MastcamZ camera on the Perseverance Rover. Optimized processing procedures to read in data taken from the Mars rover. Implemented machine learning algorithms to develop model bias frames eliminating the need for image-specific bias frames. Presented my work to the program directors and selected to present findings at the Cornell Arts & Sciences Dean's Advisory Council Meeting.

Saratoga High School has had a long history of musical excellence, and in 2017, a new music building with state-of-the-art facilities was built. However, it lacked a proper location to display awards and the fruits of student musicians' labors as trophies were haphazardly placed on the floor. In response, after a lengthy approval process, I led five scouts in building a six-foot by four-foot trophy shelf with sliding glass doors and painting a mural on the back to give the music department's achievements a safe, well-respected, and visually appealing home. I fundraised over $700 by giving speeches at school concerts and performing at weddings, and I carefully budgeted the funds in purchasing tools and equipment. All unspent funds were donated to the music department.

> Prepared and graded labs, fixed lab equipment> Co-wrote tests with course teacher> Assisted students with understanding course material> Assisted in curriculum development of proceeding year's AP Physics C course