End of SMALL

This summer has made me see more clearly what I like to do. I really like research. It is very refreshing to just do mathematics without worrying about a million other things. I really enjoyed the process of thinking through problems in the company of people who appreciate math as much as I do. This summer, I was fortunate to contribute to multiple projects. On one project, I mostly did coding, building and testing algorithms for $k$-bonacci vector representations. On another, I proved a central theorem in a probabilistic framework for signal recovery. I also had the chance to be the main contributor on a paper that strengthened uncertainty principles using additive combinatorics—this one taught me a lot about pushing past dead ends and finding new angles. And finally, I came up with the idea for a new combinatorial game inspired by Zeckendorf’s Theorem, where I did both coding and a big part of the proving and writing. Working on these projects has already given me the chance to present at two conferences, and I’m really looking forward to at least two more coming up next year.

Working on these projects has really helped me understand what I enjoy in math. I have for a long time felt a pull towards the analysis side of things, and I believe my signal recovery project just helped me confirm my leanings. I'm really excited that I'll be learning more about analysis, specifically functional analysis as part of my thesis work. I have already started reading Simon's "Methods of Modern Mathematical Physics: Functional Analysis," so I'm a bit ahead when the semester starts with all of its craziness. I'm really sad I had not done an REU earlier. It was a wonderful experience that I would love to go through again.