About
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.
Here's my CV.
Research
- Perfectoid Shimura Varieties of Exceptional Type (draft)
We show that all minimally compactified Shimura varieties at infinite level are perfectoid spaces, including those of exceptional type for sufficiently large primes.
- Compactification of Reductive Group Schemes pdf arXiv
We prove that any isotrivial reductive group scheme over an arbitrary base admits a smooth projective equivariant compactification, verifying a conjecture of Česnavičius. In the adjoint case, we recover fiberwise the wonderful compactification. Finally, we give an example of a non-isotrivial torus admitting no equivariant compactification.
Seminars
Notes
- 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