[COMING UP ON TOMORROW] MATH Lecture Series - KӒHLER-EINSTEIN METRICS WITH LARGE SYMMETRY

[ICTP Math Section]

*MATH Lecture Series*

*Date and Venue*: Every Wednesday, 11:00-13:00 - ICTP Leonardo Building 
- /!! This Wednesday in the Lagrange Lecture Hall !!/

Wed, 16 September: Lecture 1 - Budinich Lecture Hall
Wed, 23 September: Lecture 2 - Euler Lecture Hall
*Wed, 30 September: Lecture 3 - Lagrange Lecture Hall*
Wed, 7 October: Lecture 4 - Lagrange Lecture Hall

/Each lecture will be one hour in duration, with additional time 
allocated for questions and discussion./

*Speaker: *Xiaohua Zhu (Capital Normal University, China)
*
*
*Title:* KӒHLER-EINSTEIN METRICS WITH LARGE SYMMETRY

*Abstract:*
In 2004, Wang and I found a priori C°-estimates for certain real 
Monge-Ampère equations to study Kähler-Einstein metrics on toric 
manifolds. This method was later generalized by many people to study 
Kähler-Einstein metrics or Kähler-Ricci solitons on G-manifolds, 
horosymmetric manifolds, spherical varieties etc. Recently, Tian and I 
found a local version of the Wang-Zhu’s estimate to study the 
degeneration of Kähler-Ricci flow on such manifolds. This method can be 
also used to construct complete Kähler-Ricci solitons on certain 
non-compact toric manifolds. In this series of lectures, we will give 
four lectures related to the above works as follows.

Lecture 1: Kähler-Einstein metrics on toric manifolds
Lecture 2: Complete Kähler-Ricci solitons on non-compact toric manifolds
Lecture 3: Some fundamental results and volume monotonicity on 
Kähler-Ricci flow on Fano manifolds
Lecture 4: Degeneration of Kähler-Ricci flow on Fano G-manifolds

*References:*
[1] X. Wang and X.H. Zhu, Kähler-Ricci solitons on toric manifolds with 
positive first Chern class, Adv. Math., 188 (2004), 87-103.
[2] T. Delcroix, Kähler-Einstein metrics on group compactifications, 
Geom. Funct. Anal., 27 (2017), 78-129.
[3] N. Sesum and G. Tian, Bounding scalar curvature and diameter along 
the Kähler-Ricci flow (after Perelman), J. Inst. Math, Jussiu, 7 (2008), 
575-587.
[4] J. Ye and X.H. Zhu, Weighted volume comparison and monotonicity for 
Lp-bound of Bakry-Emery Ricci curvature, arXiv:2604.17367.
[5] G. Tian and X.H. Zhu, Horosymmetric limits of Kähler-Ricci flow on 
Fano G-manifolds, J. Eur. Math. Soc., doi.org/10.417/JEMS/153, 
arXiv:2209.05029.


All are welcome to join.

Indico: https://indico.ictp.it/event/11524/

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