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

More notes will be added over time.

Write-ups

• p-Adic families of automorphic forms (notes from my talk at the Y-RANT VIII, September 2026)
• Theta operators on (p-adic) automorphic forms and applications (notes from my talk at the Oxford Junior Number Theory Seminar, May 2026)
• Automorphic forms as bridge and gap (notes from my talk at the London Junior Number Theory Seminar, March 2026)
• Local geometry of the eigencurve (notes from my short talk at Y-RANT VII, August 2025)
• O-minimality and Diophantine applications (notes from my talk at the London Junior Number Theory Seminar, January 2025)
• Geometry and algebra of (B, N)-pairs (notes from my talk at a study group on Bruhat–Tits buildings)
• Automorphic forms on adele groups (my master’s thesis — still full of errors, so available on request)
• The Ax–Grothendieck theorem (a topic that captivated me)
• The class number formula and beyond (a semester project supervised by Dr. Claire Burrin)

Notes

My handwritten notes from various lecture series are available on request, as the files are too large to be stored here. They come from many wonderful courses I attended in London (LSGNT / LTCC / TCC), at ETH Zürich, UC Berkeley, Xi’an Jiaotong University, and elsewhere. I am deeply grateful to all the lecturers; any errors are, of course, 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 Dr. 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 (unfortunately, I lost the original source files and can no longer update these notes)
• Functional Analysis Fall 2019 by Prof. 杨家青 (Jiaqing Yang)

Other documents

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

Please let me know if you spot any typos or errors!