Associate Professor Zhou Zhengyi and His Collaborator Publish Significant Findings in Top Journal Inventiones Mathematicae

On October 7, 2025, Associate Professor Zhou Zhengyi, from AMSS and his collaborator Professor Chi Li of Rutgers University in the United States, published their latest research findings online in Inventiones Mathematicae, one of the top four mathematics journals, under the title "Kähler compactification of ℂⁿ and Reeb dynamics.

The study points out that let X be a smooth Kähler manifold, and assume Y⊂X is a smooth divisor, with X\Y being biholomorphic to ℂⁿ. They prove that (X,Y) is biholomorphic to (ℙⁿ,ℙⁿ⁻¹). They then investigate certain Kähler orbifold compactifications of ℂⁿ and, as an application, further prove that on ℂ³, the flat metric is the unique asymptotically conical, Ricci-flat Kähler metric whose metric cone at infinity has a smooth link. As a key technical tool, the study utilizes S¹-equivariant positive symplectic homology to derive a new characterization of the minimal discrepancy of isolated Fano cone singularities. This research represents a significant advancement in interdisciplinary fields such as complex geometry and symplectic geometry, achieving breakthroughs in both theoretical innovation and technical contribution.

Zhou Zhengyi's research focuses on symplectic topology and contact topology. He primarily uses the theory of pseudoholomorphic curves, especially symplectic field theory, to study rigid phenomena in symplectic and contact topology, particularly issues related to symplectic fillings and symplectic cobordisms. His main work includes proving the conjecture by Wolf Prize winner Eliashberg on the non-existence of Liouville fillings for real projective spaces; constructing the first non-topological obstruction to the existence of Weinstein fillings; collaborating to construct a series of contact invariants in rational symplectic field theory; collaborating to construct tight but non-symplectically fillable contact structures on high-dimensional standard spheres; and collaborating to solve the high-dimensional generalized Bishop conjecture.