IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
9:15am|Remote Access
Topic: Kähler Compactification of ℂn and Reeb Dynamics
Speaker: Zhengyi Zhou
Affiliation: Chinese Academy of Mathematics and Systems Science
Date: January 17, 2025
We will present two results in complex geometry: (1) A Kähler compactification of ℂn with a smooth divisor complement must be ℙn, which confirms a conjecture of Brenton and Morrow under the Kähler assumption; (2) Any complete asymptotically conical Calabi-Yau metric on ℂ3 with a smooth link must be flat, confirming a modified version of Tian’s conjecture regarding the recognition of the flat metric among Calabi-Yau metrics in dimension 3. Both proofs rely on relating the minimal discrepancy number of a Fano cone singularity to its Reeb dynamics of the conic contact form. This is a joint work with Chi Li.