Abtract: We will talk about two uniqueness results: (1) On C^3, any complete asymptotically conical Ricci-flat Kahler metric with a smooth link at infinity must be the flat metric. (2) Zoll manifolds of type CP^n with entire Grauert tubes are biholomorphic/isometric to CP^n with its Fubini-Study metric. These two results are not directly related to each other but interestingly their proofs share parallel ideas and ingredients: (I) certain analytic compactification results, (II) connection between differential-geometric invariants (Conley-Zehnder index/Morse index) to certain algebra-geometric invariants (minimal log discrepancy/Fano index) and (III) some classification results from algebraic geometry. We will also discuss how the two results are related to some classical open problems in complex geometry. This talk is based on joint works with Zhengyi Zhou and Kyobeom Song respectively.

Brief biography: Dr. Chi Li is currently an associate professor at Rutgers University. He obtained Ph.D. degree from Princeton University in 2012 under the supervision of Prof. Gang Tian. He has worked at Stony Brook University and Purdue University. Dr. Chi Li’s main area of research is complex geometry. He received the Sloan Research Fellowship in 2017 and was an ICM2022 speaker at the session of Complex Algebraic Geometry.

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