Ayan Nath

I am a math PhD student at MIT starting from Fall 2024. Previously, I was an undergraduate student at Chennai Mathematical Institute. I am interested in number theory.

Email: $\texttt{ayannath}{}\texttt{@}\texttt{mit}{}{.}\texttt{edu}$

Seminars

Reading seminar: Perfectoid Spaces (Fall 2024)

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) A Taste of Analytic Number Theory [pdf] [AoPS Page]

Publications

(Do not reflect current interests.)

On the Least Common Multiple of Polynomial Sequences at Prime Arguments (with Abhishek Jha), Int. J. Number Theory (2022) [doi] [arXiv] [slides]
On Quotients of Values of Euler's Function on Factorials (with Abhishek Jha), Bull. Aust. Math. Soc. (2021) [doi] [arXiv]
On the Divisibility $a!+b!\mid (a+b)!$, Amer. Math. Monthly (2022) [doi] [pdf]

Seminars

Notes

Publications

Odds and ends