notes and write-ups

Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.

— Bertrand Russell

To be uploaded...

Write-ups

  • Theta operators on Shimura varieties and applications (first two chapters of my upgrade report)
  • Local geometry of the eigencurve
  • The Ax—-Grothendieck Theorem
  • O-minimality and Diophantine applications
  • Geomtery and algebra of (B, N)-pairs
  • Automorphic forms on adele groups (my Master’s thesis)
  • The class number formula and beyond
  • Modular curves and dimension formulae for certain spaces of modular forms
  • Schoof’s algorithm
  • The BSD conjecture
  • Basics of hyperbolic geometry
  • A journey through combinatorics


Notes

Some of my notes are available below (upon request, as the handwritten ones are too large to host here). They come from the wonderful courses I attended and enjoyed in London (LSGNT / LTCC / TCC), ETH Zürich, UC Berkeley, Xi’an Jiaotong University, and various other places. All errors are my own.

  • Topics in Number Theory: L-Functions and Modular Forms Spring 2022 by Prof. Claire Burrin
  • Computations in Algebra and Number Theory Spring 2022 by Prof. David Loeffler
  • Algebraic Geometry I Fall 2022 by Emil Jacobson and Felix Sefzig
  • O-minimality and Diophantine Applications Fall 2022 by Prof. Emmanuel Kowalski
  • Modular Forms Spring 2022 by Prof. Sarah Zerbes
  • Elliptic Functions and Elliptic Curves Spring 2022 by Dr. Markus Schwagenscheidt
  • Algebraic Topology Ⅱ Spring 2022 by Prof. Paul Biran
  • Algebraic Topology Ⅰ Fall 2021 by Prof. Will Merry
  • Commutative Algebra Fall 2021 by Prof. Emmanuel Kowalski
  • Riemannian Geometry: Chapter 0 Spring 2021 by Prof. 王立周 (Lizhou Wang)
  • Notes on Complex Analysis (MATH 205B) Spring 2020 by Prof. Dan-Virgil Voiculescu
  • Functional Analysis Fall 2019 by Prof. 杨家青 (Jiaqing Yang)


Other documents

  • LaTeX version of ``Modular curves and modular forms’’ by Fred Diamond and John Im
  • LaTeX version of Serre’s 2001 letter to Carole Hamer