Haochen Cheng 程昊辰

I am currently a third-year PhD student at Northwestern University, Department of Mathematics. My advisor is Ananth Shankar.

I am organizing the graduate algebraic geometry/arithmetic geometry/number theory seminar in Northwestern: GAGA_NU.

Email: haochencheng2028@u.northwestern.edu

Here is my CV.

I work in arithmetic geometry and number theory. Explicitly, I am mainly working on abelian varieties and Shimura varieties in positive or mixed characteristics, with possible intuition coming from complex geometry. I am also interested in non-abelian Hodge theory, (integral) p-adic Hodge theory and Galois representation, etc.

I am currently focusing on the relation between the positivity of Hodge bundles and local systems.

Haochen Cheng
Sacred Valley, Peru, 2026

Papers and Preprints:

  1. Non-liftability of Families of Abelian Varieties with Small l-adic Local System. Submitted.
  2. A rigidity result of family of abelian varieties of positive charactersitic. In preparation.

Random notes I wrote:

  1. A proof of Chebotarev density theorem over function fields: Chebotarev
  2. An introduction to Higgs semistable bundles over curves, this also appears as the appendix of Non-liftability of Families of Abelian Varieties with Small l-adic Local System: Semistable Higgs.
  3. An introduction to semistable reductions, semistable representations, etc (in progress):Semistable.
Miscellaneous

Summer 2026 Reading Seminar: Isocrystals.

I like to take photos sometime: Photos.