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PRIMES: Shashwat Kishore's Story



I have been interested in math for as long as I can remember. I used to work through basic number riddles as a child, soon graduating to multiplication and division. My math education took a new turn in middle school, when I was introduced to math competitions. I found these experiences exhilarating, and they further stoked my interest in math.

In eleventh grade, I learned of the PRIMES-USA program for high schoolers. Several of my friends came back with great stories of the program and encouraged me to apply. Even though I wasn’t sure how I could work on an actual research problem, I trusted them and completed an application. I was accepted in December, and thus began my PRIMES journey.

My background reading, which was a set of notes for a first year representation theory course, proved to be quite difficult. However, my mentor, Gus Lonergan, patiently met with me every week to go over the material and answer any questions I had. Slowly but surely I advanced through the readings, and by February I had learned enough background to start work on the problem. Although progress was slow at first, I incrementally moved forward, following Professor Pavel Etingof’s advice: “Have something doable on your agenda at all times.” I analyzed small cases with the help of computer programs, and eventually formulated conjectures for the general case. Proving my conjectures for the general case was one of the most amazing mathematical experiences I’ve enjoyed so far. The feeling that accompanies the discovery of a completely new theorem is one that cannot be replicated in any setting other than research.

Looking back, I am amazed at how I’ve grown through the PRIMES-USA program. Gus and Professor Etingof have guided me through an amazing expedition into math, offering their experience and wisdom throughout. The decision to participate in PRIMES-USA was one of the best decisions I have ever made. I would strongly encourage any high schooler interested in mathematics research to apply!

Shashwat Kishore worked on the project Signatures of Multiplicity Spaces in Tensor Products of sl2 and Uq(sl2) Representations, and Applications under the mentorship of Gus Lonergan and Pavel Etingof.

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