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). I am about to graduate and am actively seeking job opportunities.

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 degeneration in geometry is reflected 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).

Recently, I also got interested in the arithmetic and geometry of Ceresa cycles.

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

Email: zl.chen1729@gmail.com

PhD Thesis: Degeneration of the Archimedean Height Pairing, supervised by Prof. Robin de Jong and Prof. David Holmes, to appear

We study one-parameter variation of the local archimedean height pairing and the global Néron–Tate height pairing from a rather geometric perspective. The basic idea is to single out the line bundle that encapsulates the pairing; the variation problem then translates into an extension problem for this bundle. We investigate various aspects of this problem, including its Hodge-theoretic and intersection-theoretic ones. These line bundles and their extensions can be endowed with the structure of adelic line bundles, which provide finer information about the limiting behaviour of the height pairings.

Master's Thesis: Silverman–Tate's height inequality: generalizations and applications, supervised by 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 by 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).