Zhelun Chen

Welcome to my personal homepage. (Last update: 10 Dec 2025)

My name is Zhélún Chén (simplified Chinese: 陈哲伦). I am pursuing a doctoral degree under the supervision of Robin de Jong (since Oct 2022) and David Holmes (since Dec 2023). The PhD project is funded by a CSC-Leiden University Scholarship.

Research interests:

Arakelov Geometry (geometric aspects of the Beilinson–Bloch height pairing)
Hodge Theory (mixed Hodge structures of biextension type and their variations)

I am particularly interested in the limiting behaviour of the archimedean height pairing of (homologically trivial) algebraic cycles on a degenerating family of complex varieties.

Seminars in Leiden and Utrecht

Email: zl.chen1729@gmail.com

Master's Thesis: Silverman–Tate's height inequality: generalizations and applications, supervised under Prof. Walter Gubler, Jan 2022

I work out the proof of Silverman–Tate's height inequality, and generalize it slightly with Debam Biswas. As applications I discuss rudiments of unlikely intersections, a very special case of the André–Oort conjecture, and a new height inequality by Gao–Habegger, which in turn implies the geometric Bogomolov conjecture in characteristics zero. Updated version available upon request.

Bachelor's Thesis: Satz von Kronecker–Weber und Aspekte von Kroneckers Jugendtraum, supervised under Prof. Claus Scheiderer, Sep 2018

Following the text "Algebraic Numbers" (MR0340212) by Ribenboim, I work out the proof of the Kronecker-Weber theorem without using Class Field Theory. Then I discuss very briefly a higher dimensional analogue of the theorem using torsion points of a CM elliptic curve, after elaborating on the proof of the group law on elliptic curve as done in Washington's book on elliptic curves (MR2404461).