Complex & Algebraic Geometry · 数学

Yan He贺岩

Assistant Professor (Jiangshi) by special appointment (Quanzhitepin), also a faculty postdoc (Shizi Bohou) · School of Mathematics & Information Science, Guangzhou University

I work in complex and algebraic geometry — the analytic side of it. My research centers on the Ohsawa–Takegoshi extension theorem and pluripotential theory, with separate interests in Nevanlinna theory and hyperbolicity. I also build things: small, sharp software systems that let me work the way I want to.

Research

The optimal constant, and what geometry hides inside it

The Ohsawa–Takegoshi extension theorem is one of the central analytic tools of modern complex and algebraic geometry: it guarantees that a holomorphic function defined on a subvariety extends to the whole space, with explicit control. The size of the constant in that control is not a technicality — it ties directly to Bergman kernel estimates, the Suita conjecture, Skoda's division theorem, and the existence of sections in algebraic geometry.

Extension with controlled L² norm — the constant C is where the geometry lives.

Using the Berndtsson–Lempert method together with geodesics in the space of Kähler metrics and the Ross–Witt Nyström correspondence, I work toward understanding and computing this optimal constant — and toward turning that understanding into new proofs of Skoda's division theorem and new effective criteria around the existence of holomorphic sections of KX + L (the Fujita-conjecture circle of problems).

A separate line of work runs through value distribution theory: developing a Nevanlinna-theoretic notion of hyperbolicity, and asking whether it is equivalent to Kobayashi hyperbolicity.

Selected Publications

Papers

preprint
Yan He, Johannes Testorf, Xu Wang · arXiv:2311.03840
2021
Nevanlinna and algebraic hyperbolicity
Yan He, Min Ru · International Journal of Mathematics
2021
Nevanlinna theory through the Brownian motion
Xianjing Dong, Yan He, Min Ru · Science China Mathematics
2021
A generalized subspace theorem for closed subschemes in subgeneral position
Journal of Number Theory

Current work in preparation: optimal constants in the Ohsawa–Takegoshi theorem via Berndtsson–Lempert, and partial Bergman kernel estimates on compact Riemann surfaces.

Path

Where I've been

2026 —
Assistant Professor
Guangzhou University · School of Mathematics & Information Science
2022 – 2025
Postdoctoral Researcher
Norwegian University of Science and Technology (NTNU), Trondheim · with Xu Wang
2016 – 2021
Ph.D. in Mathematics
University of Houston · advisor Min Ru
2012 – 2016
B.S. in Mathematics
Renmin University of China, Beijing
AI & Building

I build the tools I work with

Alongside the mathematics, I design and build software — usually small, sharp systems that get language models to do real, reliable work instead of demos. The instinct is the same one I bring to a proof: find the actual structure, then make it clean.

Flagship · 2026

A Modular Framework for AI-Assisted Math Research

A document system that makes the dependency structure of mathematics explicit: every lemma, computation, or definition is a node in a directed acyclic graph, with machine-readable links to its context, prerequisites, and consequents. Numbered, individually-annotated proof steps let me tell an AI collaborator exactly which step is unclear — and any subtopic can be promoted to a self-contained subproject, anchored to its parent. The design borrows a principle from scheme theory: there is no absolute object, only an object over its base.

github.com/dazhima/math-ai-framework →

complex geometry L² methods Nevanlinna theory AI agents knowledge systems automation self-hosting
Star Signs, Exactly

星座的數學基礎 · The mathematics behind star signs

Everyone knows their sun sign. Fewer know that it — and the ascendant, the sign rising on the eastern horizon at the moment of birth — is fixed entirely by elementary geometry, and that the whole problem linearises under stereographic projection. Two great circles on the sphere become two circles in the complex plane, each satisfying r² − |c|² = 1; their intersection is a pair of antipodal points, v₁·conj(v₂) = −1; and a single inequality decides which of the two is rising.

What falls out is not folklore. Above latitude 66.56° the ascendant stops circling the ecliptic once a day and merely oscillates — a winding number dropping from 1 to 0 — and there the closed form used by standard astrology software returns the descending point about 21.5% of the time.

Derivation + interactive tool · 2026

A complete derivation, and a globe you can check it against

Eight sections, from the definition of stereographic projection to a real birth time and place — with the counterexamples that killed the wrong routes kept in rather than tidied away. The companion tool draws the same objects four ways: a draggable 3D Earth, the north and south projections, and the Mercator map (which is exactly the logarithm of the north projection). It prints every intermediate value from Julian day to rising sign, and runs two invariants live on screen, so nothing has to be taken on trust.

推導 · Read the derivation →  ·  互動地球儀 · Interactive globe →

Others

Other things I keep here

Contact

Get in touch

Office
Room 222, 行政西楼后座 · School of Mathematics & Information Science, Guangzhou University · University Town, Panyu, Guangzhou

Open to collaboration in complex/algebraic geometry, students interested in several complex variables, and conversations about AI-assisted research workflows.