Ayan Nath
MIT Mathematics
ayannath[at]mit[dot]edu

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.

  • 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]