Zhelun Chen

Welcome to my personal homepage.

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 interested in how degenerations in geometry influence degenerations in arithmetic. Specifically, I like to consider the asymptotic behaviour of archimedean height pairings for algebraic cycles in degenerating families of complex varieties. This provides another instance of the principle that "limits of archimedean invariants are controlled by their non-archimedean counterparts" (see Boucksom).

Seminars in Leiden and Utrecht; Intercity Number Theory Seminar (NL)

Email: zl.chen1729@gmail.com

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