Ayan Nath

I am a third-year undergraduate student at Chennai Mathematical Institute. Starting this fall, I will be a PhD student at MIT. My current interests are in Arithmetic and Algebraic Geometry.

Notes

Number Theory:

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]
An introduction to the mod $p$ local Langlands correspondence for $\text{GL}_2(\mathbb Q_p)$ [pdf] [slides]
Tate uniformization of Drinfeld modules [pdf]

Algebraic Geometry:

Hodge-Tate decomposition for abelian varieties with good reduction [pdf]
Moduli schemes of elliptic curves [pdf]
Alterations [pdf] [slides]
Algebraic Geometry II lecture notes (Spring 2023 at CMI) [pdf]

Commutative Algebra:

The Hochster-Roberts theorem [pdf]

Olympiad (old):

A Taste of Analytic Number Theory [pdf] [AoPS Page]
Notes on some olympiad geometry configurations [pdf]

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] [code]
On the Divisibility $a!+b!\mid (a+b)!$, Amer. Math. Monthly (2022) [doi] [pdf]

Odds and ends

Get in touch

The best way to reach me is through email, at $\texttt{ayannath}{}\texttt{@}\texttt{cmi}{}{.}\texttt{ac}{.}\texttt{in}$.

LinkedIn: Ayan Nath
Github: ayan7744
AoPS: ayan.nmath