IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

We will present two results in complex geometry: (1) A Kähler compactification of $\mathbb{C}^n$ with a smooth divisor complement must be $\mathbb{P}^n$, which confirms a conjecture of Brenton and Morrow under the Kähler assumption; (2) Any complete asymptotically conical Calabi-Yau metric on $\mathbb{C}^3$ 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.