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Seminar
FIELD Math:Geometry
DATE January 06 (Thu), 2022
TIME 19:00-21:00
PLACE Online
SPEAKER Delcroix, Thibaut
HOST Park, Kyeong-Dong
INSTITUTE Universit? de Montpellier
TITLE Existence of canonical Kahler metrics on spherical varieties: Lecture 2. Differential geometric aspects: horosymmetric varieties
ABSTRACT Existence of canonical K?hler metrics on complex manifolds is one of the major problems in analytic and algebraic complex geometry. In this series of lectures, I will present various results regarding this question, on the class of spherical varieties. I will explain why and how these varieties are more tractable both from the differential geometry and the algebraic geometry viewpoint. A short and biased historical review of examples will serve as a motivation to study this particular class, but I will also try to highlight how this study may yield useful insight for the study of more general varieties, and hint at various significant obstacles still to be lifted for spherical varieties.

The plan of the lecture will roughly be as follows:
Lecture 1 - Overview of canonical metrics on spherical varieties (short historical review, combinatorial criterions, examples and counter-examples) January 5 (Wednesday), 19:00-21:00 (KST)

main references:
Examples of K-unstable Fano manifolds https://arxiv.org/abs/1911.08300
The Yau?Tian?Donaldson conjecture for cohomogeneity one manifolds https://arxiv.org/abs/2011.07135

Lecture 2 - Differential geometric aspects: horosymmetric varieties (complex Monge?Amp?re equations and variational approach on horosymmetric varieties) January 6 (Thursday) 19:00-21:00 (KST)

main references:
K?hler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functional https://doi.org/10.1515/crelle-2018-0040
Coupled complex Monge?Amp?re equations on Fano horosymmetric manifolds, with Jakob Hultgren https://doi.org/10.1016/j.matpur.2020.12.002

Lecture 3 - Algebro-geometric aspects (test configurations and non-Archimedean functionals on spherical varieties) January 7 (Friday) 19:00-21:00 (KST)

main references:
K-Stability of Fano spherical varieties https://doi.org/10.24033/asens.2430
Uniform K-stability of polarized spherical varieties, with an appendix by Yuji Odaka https://arxiv.org/abs/2009.06463

https://sites.google.com/view/eag-seminar

LINK: https://zoom.us/j/2906238932
Meeting ID: 290 623 8932
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