IST-OMU 1-day meeting on complex geometry is a small in-person workshop for researchers working in complex geometry and related fields. The meeting aims to foster active discussions and exchanges of recent developments among participants.
Date: January 22 and 23, 2026
Venue: Room 201 (Floor map) in Main building (Google map) at Ookayama campus, Institute of Science Tokyo (Access information)
10:00--11:00: Takahiro Aoi
11:30--12:30: Kiyoon Eum
Lunch
14:30--15:30: Satoshi Jinnouchi
16:00--17:00: Natsuo Miyatake
Social dinner (If you would like to attend the social dinner, please register via the “Social Dinner Registration Form” by January 20.)
Free discussion
Takahiro Aoi (National Institute of Technology, Wakayama College)
Title: Recent developments in the study of the microscopic stability thresholds
Abstract: Berman introduced the microscopic stability thresholds and uniform Gibbs stability in order to study Kähler-Einstein metrics on Fano manifolds. Berman proved that if a Fano manifold is uniformly Gibbs stable, then there exists a unique Kähler-Einstein metric. (His result is an analytic counterpart of the algebro-geometric result by Fujita-Odaka.) In this talk, I will talk about a generalization of Berman’s result to polarized manifolds. I will also talk about some recent developments in the study of coupled Kähler-Einstein metrics on Fano manifolds. This talk is partially based on the joint work with Satoshi Nakamura.
Kiyoon Eum (Korea Advanced Institute of Science and Technology)
Title: Asymptotic expansion of the variation of the Quillen metric and its moment map interpretation
Abstract: The Donaldson–Fujiki moment map picture interprets the scalar curvature of a Kähler metric as a moment map for the action of Hamiltonian diffeomorphisms on the space of compatible complex structures. We generalize this picture to other scalar curvature quantities using equivariant determinant line bundles. Interpreting the complexified orbit as varying Kähler potentials while keeping the complex structure fixed, these moment maps arise as variations of the log of the Quillen metric on determinant line bundles. This framework also naturally yields other GIT counterparts, such as log-norm functionals (~Mabuchi functional) and weights (~Futaki invariant).
Satoshi Jinnouchi (Osaka University)
Title: Admissible Hermitian-Yang-Mills metrics on log terminal Kähler-Einstein varieties
Abstract: In this talk, I introduce that the slope stability of reflexive sheaves over log terminal Kähler-Einstein varieties imply the existence of admissible Hermitian-Yang-Mills metrics with respect to singular Kähler-Einstein metrics. I will also explain the ideas of proof. A crucial ingredient is the strict positivity of singular Kähler-Einstein metrics in the sense of currents, which is proved by Chen-Chiu-Hallgren-T\hat{o}-Sz\'{e}kelyhidi. This talk is based onhttps://arxiv.org/abs/2511.20033 and https://arxiv.org/abs/2512.24161.
Natsuo Miyatake (Tohoku University)
Title: Comparison and Growth of Subharmonic Functions, and Complete Harmonic Metrics
Abstract: Holomorphic functions and subharmonic functions are among the most fundamental concepts in complex analysis and potential theory.In this talk, I introduce two functions, which I call entropy and free energy, associated with a semi-positive singular Hermitian metric $e^{-\varphi} h_\ast$ on the canonical bundle of a Riemann surface, that are expected to measure the size and growth of a subharmonic weight function $\varphi$, as well as the extent of domination $\varphi \ge \varphi'$ and $\sqrt{-1}\,\bar{\partial}\partial \varphi \ge \sqrt{-1}\,\bar{\partial}\partial \varphi'$ between two subharmonic weight functions $\varphi$ and $\varphi'$.They are defined by using complete harmonic metrics associated with holomorphic $r$-differentials, and their extension to more general subharmonic weight functions on the canonical bundle. Extending the maximum principle techniques for complete harmonic metrics developed by Dai--Li and Li--Mochizuki, I will provide several estimates for these functions. One of the developments I hope to see is that these functions will bring a new perspective to existing theories on the approximation of equilibrium weights, that is, the potential functions of equilibrium measures. I will explain that one of the goals in this direction is to quantitatively establish an entropy growth and free energy decay principle, in the sense introduced here, for non-equilibrium weights that approximate equilibrium weights.
Yoshinori Hashimoto (Osaka Metropolitan University)
Satoshi Nakamura (Institute of Science Tokyo)
Osaka Central Advanced Mathematical Institute (MEXT Promotion of Distinctive Joint Research Center Program JPMXP0723833165 and Osaka Metropolitan University Strategic Research Promotion Project: Development of International Research Hubs).