I am a PhD student at MIT since Fall 2024.
My advisors are Bjorn Poonen and Keerthi Madapusi.Previously, I was an undergraduate student at Chennai Mathematical Institute.
I am interested in number theory.
Versions hosted here are more up-to-date than those on the arXiv.
- Compactification of reductive group schemes [pdf] [arXiv]
Let $\mathrm G$ be an isotrivial reductive group over a scheme $S$. We construct a smooth projective $S$-scheme containing $\mathrm G$ as a fiberwise-dense open subscheme equipped with left and right actions of $\mathrm G$ which extend the translation actions of $\mathrm G$ on itself. This verifies a conjecture of Česnavičius (arXiv:2201.06424). When $\mathrm G$ is adjoint, we recover fiberwise the wonderful compactification. Finally, we give an example of a non-isotrivial torus admitting no equivariant compactification.
- Almost Purity [pdf]
- Tilting equivalence for perfectoid algebras [pdf]
- Special cycles on unitary Shimura varieties [pdf]
- Hodge-Tate decomposition for abelian varieties with good reduction [pdf]
- Moduli schemes of elliptic curves [pdf]
- Deligne's construction of $\ell$-adic Galois representations attached to normalized cuspidal newforms of weight $k\ge 2$ [pdf]
- Ribet's converse to Herbrand's theorem [pdf]
- Galois representations attached to modular forms of weight 1 [pdf]
- Tate uniformization of Drinfeld modules [pdf]
- An introduction to the mod $p$ local Langlands correspondence for $\text{GL}_2(\mathbb Q_p)$ [pdf] [slides]
- Alterations [pdf] [slides]
- The Hochster-Roberts theorem [pdf]
- (old) Olympiad handout on analytic number theory [pdf] [AoPS Page]