Research

Yuji Odaka’s research lies at the interface of algebraic geometry and complex differential geometry, centered on Kähler–Einstein or related canonical metrics and related topics. In particular, he has developed foundational aspects of K-stability, clarifying its connections with birational geometry, moduli theory, singularities, and Arakelov geometry, and proposed the framework of (K-)moduli for K-polystable varieties. In the Fano setting, he contributed to the development of K-stability theory, including the introduction of the delta invariant (stability threshold) with K.Fujita, and the construction of compact moduli spaces of K-polystable Fano varieties (based on joint work with C.Spotti, S.Sun). He has also studied degenerations and compactifications of moduli spaces of Calabi-Yau and hyperkähler varieties, relating Gromov-Hausdorff limits to Satake- and Morgan-Shalen-type compactifications (with Y.Oshima), as well as arithmetic aspects of canonical metrics through the introduction of K-modular height, a generalization of the Faltings height. His later work includes that on bubbling of Kahler-Einstein metrics, construction of compactified moduli of Sasaki-Einstein manifolds (or Calabi-Yau cones), and a new (hyper)Kahler geometric approach to Kaledin's conjecture on symplectic singularities (with Y.Namikawa).