# Eiji Inoue

E-mail: eiji.inoue [at] riken.jp

I am a postdoc at

RIKEN iTHEMS from April 2021.

**CV** and

Papers & Talks
Research interest

: Geometry and Analysis

Current main interest

: Canonical metrics in Kähler geometry and K-moduli space.

**Keywords**: μ-cscK metric (including Kähler-Ricci soliton and extremal metric), μK-stability, optimal destabilizer (non-archimedean canonical metric) in 'μ-framework', moduli theory on Fano varieties

**Constant μ-scalar curvature Kähler metric (μ-cscK metric)** is a framework unifying cscK metric and Kähler-Ricci soliton, which I proposed in

arXiv:1902.00664.
The concept of μ-cscK metric possesses a natural parameter λ of freedom, which plays a role reminiscent of `temperature'.
Kähler-Ricci soliton appears when λ=2π (on a Fano manifold (X, -K_X)) and extremal metric appears in the limit λ=-∞.
The related μK-stability has a simple form especially when λ=0 for general polarization.
We may regard the parameter as a continuity path connecting Kähler-Ricci soliton and extremal metric on Fano manifolds, or connecting μ^0-cscK metric and extremal metric for general polarization.
There is also interesting phenomenon analogous to phase transition when λ tends to +∞.
I think μ-cscK metric is an attractive part in the extensive framework on

weighted cscK metric introduced by Abdellah Lahdili.

The latest papers and preprints

*The moduli space of Fano manifolds with Kähler-Ricci solitons*, Advances in Math. Volume 357, 1 Dec. 2019, Article 106841, available also at arXiv:1802.08128.
*Constant μ-scalar curvature Kähler metric - formulation and foundational results*, preprint arXiv:1902.00664.
*Equivariant calculus on μ-character and μK-stability of polarized schemes*, preprint arXiv:2004.06393.
*Entropies in μ-framework of canonical metrics and K-stability, I -- Archimedean aspect: Perelmna's W-entropy and μ-cscK metrics*, preprint arXiv:2101.11197.
*Entropies in μ-framework of canonical metrics and K-stability, II -- Non-archimedean aspect: non-archimedean μ-entropy and μK-semistability*, in preparation.

Schedules

Talks

- 20, July, 2021, Zoom,
*ZAG seminar*.
- Postponed, Princeton,
*Princeton-Tokyo workshop on Geometric Analysis*.
- Postponed, Aarhus,
*Aarhus Complex Geometry Workshop*.
- 2023-2024, Cambridge,
*TBA*.

I'll be there

Links

Advisors

Akito Futaki (2016 Apr.-2018 Mar.)
Shigeharu Takayama (2018 Apr. -2020 Sep.)
Yuji Odaka (2019 Apr. -2020 Mar. at Kyoto University)
Collaborators (ongoing)

Hokuto Konno
Masaki Taniguchi
Friends (Prof. Takayama's students)

Takahiro Inayama
Masataka Iwai
Genki Hosono
Takayuki Koike
Tomoyuki Hisamoto
Shin-ichi Matsumura