PRIMES: Ritesh Ragavender's Story
Mathematics has always appealed to me. It has a beauty and an interconnected nature in which topics from one field can give truly stunning proofs in another. It has a distinct lack of rigidity despite its level of rigor, which often results in the existence of many creative solutions to a single problem. I enjoy doing math in search of such solutions, seeking to challenge my critical thinking skills. But research presents a twist: the solutions are not known to anyone, and it may take days to understand even the smallest example or to make good conjectures. While it certainly seems intimidating to tackle a novel and difficult problem, I found that it could be done quite effectively through MIT PRIMES USA, with the outstanding guidance of my mentor, Alex Ellis.
It took me nearly a month to fully understand the free, associative, graded algebras that comprise the first few sentences of Alex’s paper on odd symmetric functions. Nevertheless, I quickly discarded the notions that I wouldn’t be able to discover anything significant or that it would be impossible to investigate high-level mathematics. Alex was always there to help me, offering guidance, resources, and ideas when I was stuck (sometimes for weeks) while pushing me towards mathematical independence. In just a couple months, he helped me understand not only his paper and important parts of Richard Stanley’s Enumerative Combinatorics, but also other papers involving my research. As a result of MIT PRIMES USA, I have learned many new mathematical principles, I have attended many intriguing conferences, and I have better understood just how vast and incredible mathematics is. It’s an amazing experience when the final simplification in an inductive proof works out, or when numerous symbols cancel after days of effort. It also feels wonderful to be able to say that my project has connections to categorification and 4D topology!
MIT PRIMES USA is an excellent program for those with mathematical curiosity. All the mentors and organizers do an exceptional job in organizing the conference, providing general assistance, and in helping young students realize their mathematical potential. The long hours and dedication were certainly worth it, and the last six months have been the best of my life. I strongly recommend MIT PRIMES USA to any student interested in mathematics.
Ritesh Ragavender worked on the project q-analogues of symmetric polynomials and nilHecke algebras under the mentorship of Alex Ellis.