Last Update 2019/04/22
My main area of interest lies in algebraic geometry. More specifically, I have been working on birational geometry of algebraic varieties, which focuses on classification of algebraic varieties under birational equivalence. In particular, I am interested in topics related to Minimal Model Program (e.g., existence of good minimal models, non-vanishing conjecture, abundance conjecture, minimal log discrepancies) and properties of minimal varieties and Fano varieties (e.g., boundedness properties, birationality problems, positivities). Most of my work are related to boundedness of Fano varieties and I showed that K-semistable Fano varieties with degree bounded from below form a bounded family. Recently with my collaborators, we established the optimal Noether inequality for threefolds of general type.
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