# PRIMES: Surya Bhupatiraju's Story

Mathematics has been the defining feature of my life - my academic and even social success can be attributed to my fervor for mathematics. As an avid student of competition math and a lover of problem solving, it became only natural for me to look ahead to the kind of mathematics I would be engaged in after graduating high school, and entering the world of college math. The abstraction was the first thing that always loomed over me when I thought about college math - it seemed so distant and out of reach. I started my study with group theory and linear algebra, and the abstraction was overwhelming at first. But eventually, as I continued to read, I realized that this kind of mathematics offered a "quiet, softer" kind of success than the type of competition math offers. In competition math, your success was measured by the number of achievements and prizes you held, and if you weren't fast enough, you just couldn't make the cut. Abstract math had its own gratifications, and for me, they were more than enough to pull me into deeper into the subject. My fascination for the beauty of the subject grew, I discovered many more kinds of mathematics, and soon, I wanted to be at the forefront of the expansions of the field of mathematics.

My mentors played a key part in developing my interest. They were the first teachers I had who taught mathematics at this level, and with their help and suggestions, my interest became more streamlined, and I understood how to really appreciate abstract math. Besides teaching the background for our project, my mentors also introduced me to programming with computer algebra systems like SAGE, MAGMA, and GAP, and these abstractions now became much more concrete and calculable. Indeed, writing programs and crunching huge amounts of numbers was critical in forming our conjectures and testing our hypotheses. In short, we continued the study of something that was recently introduced by two authors Feigin and Shoikhet, and their work involving the lower central series. It turns out that when you take these filtrations of free associative algebras over finite fields, brand new phenomena arise, and we helped to calculate these differences and form conjectures about the structure of these new objects.

During the entire process, it was always really satisfying to be able to work on problems that no one else had attempted. Every time I walked into the computer lab at MIT and started writing the programs, I never wanted to leave. I loved the feeling of being able to sit and think about problems without having anything else in my mind. It was a stress-free environment, and I thrived here. PRIMES is an excellent program - it's a remarkable way to start research at a young age with the help of incredible professionals and mentors who love the math and science that you do, and will help you learn more and more. I'm very glad I chose to come to PRIMES, and it has truly changed my life as a student and a mathematician.

Thank you, PRIMES, for everything!

Surya Bhupatiraju, together with William Kuszmaul and Jason Li, worked on the project  Lower central series of associative algebras in characteristic p under the supervision of Pavel Etingof and David Jordan.

Email us: primes@math.mit.edu