For my senior thesis under the mentorship with Professor Christopher Umans, I am working to enlarge the pseudorandomnesss of expander random walks by finding classes of functions that cannot distinguish between the vertices sampled from an expander walk on vertices labeled \(\{1,\dots,n\}\) and the vertices sampled from the uniform distribution on \([n]\). Building off of previous research (see below), we are working to show that expander random walks are fooled by functions computed by \(\mathrm{ACC}^0\) circuits. See my fall write-up for the project below!

During my Junior year, I focused on understanding expander graphs. Over the year, we constructed a framework to study the model of random walks on expander graphs. A prior result shows that the sticky random walk can be a useful model to understand the full-scale expander graph. My research generalized the sticky random walk from \(2\) to \(\mathrm m\) characters. See my write-up for the project below!