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.
- 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.
- Finite Generation in Cohomology of Artin Stacks [pdf]
The $\ell$-adic cohomology ring of an Artin stack need not be finitely generated. We prove that, under natural geometric hypotheses, the algebra of self-extensions of its intersection complex is nevertheless finitely generated and Noetherian. For smooth stacks, this gives finite generation of the cohomology ring itself. We also construct examples of torus gerbes over nodal curves where the cohomology ring fails to be finitely generated, answering a question of Hansen.
- 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.
- 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]