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. Here's my CV.

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

Seminars

Reading seminar: Perfectoid Spaces (Fall 2024)

Notes

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

(These works were carried out during high school and 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