Proofs & Goofs

I really enjoy teaching math. I also really enjoy making silly songs. I’m trying to put these together and make a youtube channel! Check it out:

Here’s a song I put together for an upcoming Proofs & Goofs video about the Fourier Transform.

MIT Primes

For the past year, I’ve had the fantastic opportunity to mentor two high school students, Michael Han and Ashley Yu, through the MIT Primes program. This was their first real dive into open-ended research. With Michael, we tackled a theoretical problem on novelty games. This led to our paper, “Improved Bounds for Novelty Games”, and earned Michael recognition as a National Finalist and International Semifinalist in the S.-T. Yau High School Science Award. With Ashley, we did an experimental project testing a conjecture about swap regret minimization.

The project with Michael focused on a problem in combinatorics known as the “novelty game,” which has direct implications for strengthening time-hierarchy separations in time-bounded Kolmogorov complexity. The first step of our research was to prove a formal reduction between winning strategies in this game and the existence of directed graphs possessing specific properties: namely, having no small cycles and ensuring that every \(k\)-tuple of vertices shares a common outgoing neighbor. The goal was then to explicitly construct such graphs. Michael dove into this complex topic with remarkable speed. The culmination of our efforts was a co-authored research paper in which we present a series of six novel optimizations simplifying the known constructions of such graphs and producing more efficient winning strategies in these games.

The goal of my project with Ashley was to establish experimental evidence for a conjecture I’ve had for a few years: that the per-iteration runtime of swap regret minimization algorithms can be significantly sped up. Classic algorithms for swap regret, which are important for finding robust strategies in games, require computing the exact stationary distribution of a Markov chain at each step. This calculation is often a major computational bottleneck. My hypothesis is that this exact, slow step can be replaced by an efficient approximation, like a short random walk. The main theoretical worry is that the small errors from these approximations might pile up over time and lead to high regret. To investigate this, Ashley and I ran extensive experiments. We tested variants of the Blum-Mansour algorithm, replacing the exact computation with different types of random walk approximations. The results were very promising: we found that, in practice, our modified algorithms achieved effectively the same low swap-regret as the standard algorithm, but with a much faster runtime.

Overall, it has been a wonderful experience working with Michael and Ashley and being there for the start of their research journeys!

Musical Improv Comedy

I’m part of a musical improv comedy troupe called Moonshine. We improvise scenes and songs from musicals that don’t exist. It’s a lot of fun! Here’s a recent performance of ours:

MIT Theory Lunch

In my first year as a PhD student, Justin Chen and I co-hosted the biweekly talk series Theory Lunch. When the COVID-19 pandemic hit, these usually buffet-style gatherings moved to Zoom. To keep enthusiasm high, I started including in the announcement emails some songs I had written and raps I had freestyled. Here’s a playlist of some of my favorites:

Dancin’

I love dancing! I’m a regular at a hip hop dance class at the dance complex. Sharon is the best teacher ever! Here are a few of my favorite dances

Thank you Akamai!

Akamai Technologies awarded me a graduate fellowship for my first year of PhD. To show my gratitude, I wrote them this little tune.

Burton Conner i3

During my undergrad at MIT, I lived in the dorm Burton Conner. Being part of the BC family was extremely formative and something I am forever grateful for. As a token to this fabulous community, I volunteered to make the dorm tour video for incoming freshman my junior year.

Making this video was a hilarious process. Burton Conner consists of 9 floors spread over two towers, each with its own culture and traditions. I interviewed residents, wrote a rap for each floor, taught someone on each floor to rap, planned and shot the footage, and did all the music and editing myself. Overall, I couldn’t have been more proud of the result.

Acting

Over the course of undergrad, I participated in two plays directed by Professor Jay Scheib. He has a very unique directing style. He is a pioneer of the Live Cinema medium. Here’s footage of me playing Shlink in Bertolt Brecht’s “In The Jungle of Cities”. In this scene, I am forfeiting my company and all of my possessions to a person named Garga. Shlink is a calloused man who hasn’t been able to emotionally connect with another individual for years. He hopes that, through such blinding rage, he will finally be able feel something.