With my friends Renzo, Hannah, and Paul. In 2013, Renzo, Hannah, and I wrote this paper, which ended up being the base of my thesis. Welcome to my homepage. I am presently a CLE Moore Instructor at the Massachusetts Institute of Technology. Starting in January 2019 I will join the faculty at the University of Cambridge. After growing up in South India and South Africa, I came to MIT by way of Harvey Mudd College and Yale University where I got my B.S. and Ph.D. respectively. I worked with Dagan Karp as an undergraduate, exploring the geometry of a classical symmetry of projective space, called the Cremona transformation, in the context Gromov-Witten theory. I had a lot of fun working with Dagan on my undergraduate thesis, which you can find here. After a wonderful four years at Harvey Mudd College, I studied under Sam Payne at Yale. I worked on problems relating Berkovich spaces, tropical geometry, and Gromov-Witten theory. My thesis took shape in 2015, thanks to a substantial helping hand from Dan Abramovich. Dan hosted me as a visiting student at Brown University, and taught me about logarithmic structures, which quickly became central to my work. During my time at MIT, Davesh Maulik has been keeping me out of trouble. and also getting me into trouble. My research is centered around the development of combinatorial methods in algebraic geometry, with a particular emphasis on applications to questions of classical and contemporary interest in the geometry of curves, moduli theory, and Gromov-Witten theory. Much of my work has concerned non-archimedean analytic spaces and logarithmic structures, studied through their combinatorial shadows. The discrete structures that arise from this interaction are part of tropical geometry, a striking collection of modern degeneration techniques that often reduce rich algebro-geometric problems into (sometimes impossible) combinatorics. My thesis, linked here, concerned the development of a unified geometric framework, involving Berkovich spaces and stable maps, for (re)-proving the correspondence theorems at the heart of tropical curve counting. More recent work has focused on the global geometry of the Kontsevich space of stable maps, classical questions in the theory of linear series, and the combinatorial topology of moduli spaces. I am also working to create opportunities for high school and undergraduate students across a diverse range of backgrounds to participate in mathematics. I particularly enjoy working with young students on mathematical research projects. Fortunately, MIT offers a range of possibilities for high school and undergraduate students to dive into mathematical research. Take a look at the PRIMES and UROP programs. While at Yale, I put a great deal of time into helping the SUMRY program and was part of the team that got it off the ground. I served as a research mentor in the summers of 2013,2014, and 2016. In 2017 I returned to Yale as coordinator of the SUMRY program, where I also directly advised six students. A record of past undergraduate research is archived here. |