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.
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 L² 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.
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 L² 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.
Current work in preparation: optimal constants in the Ohsawa–Takegoshi theorem via Berndtsson–Lempert, and partial Bergman kernel estimates on compact Riemann surfaces.
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.
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.
A local-first assistant that reads Chinese academic and administrative forms, reuses durable facts, and produces copy-paste fill sheets — turning a recurring tax of academic life into a few clicks.
An AI agent node on a home VM that collects messages from WeChat, WeCom, and email, then syncs them to my working machine for downstream processing.
A real-time feed that turns live match commentary into plain-English explanation — speech-to-text into a streaming language model.
A private network layer that routes my machines through my own infrastructure, plus a reverse-tunnel setup that turns a second laptop into an on-demand remote-compute node.
Open to collaboration in complex/algebraic geometry, students interested in several complex variables, and conversations about AI-assisted research workflows.