IGAP COMPLEX DIFFERENTIAL GEOMETRY SEMINARS - Friday 12 May, at 14:15 (Reza Seyyedali and Romina M. Arroyo) - VENUE: IGAP Lecture room 205 (former Sissa Building in via Beirut 2)

[ICTP Math Section]

IGAP COMPLEX DIFFERENTIAL GEOMETRY SEMINARS


Friday, 12 May, at 14:15

Venue: IGAP lecture room 205 (former SISSA building, via Beirut 2 - Trieste)
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14:00 -15:00 - Reza Seyyedali (IPM, Teheran, Iran)

Some a priori estimate for constant scalar curvature Kahler metrics

Abstract: The problem of existence of constant scalar curvature Kahler 
metrics (cscK) on compact Kahler manifolds has been studied for many 
years. In the case of complex one dimension, the answer is provided by 
the uniformization theorem. It states that any compact Riemann surface 
admits a metric of constant Gaussian curvature. One way to prove this 
fact is to solve a semi linear elliptic equation.
In higher dimensions, cscK metrics satisfy a fully nonlinear fourth 
order elliptic equation. It is extremely difficult to deal with such 
equations partially due to lack of maximum principle.
In a recent breakthrough, Chen and Cheng proved some important a priori 
estimates for cscK metrics. More generally they showed that in a given 
Kahler class, the set of metrics with uniform bounded scalar curvature 
and bounded relative entropy is compact in C^{\infty} topology.  In a 
joint work with Z. Lu, we generalized their results. Mainly, we replace 
the uniform boundedness assumption on scalar curvature with some L^p 
boundedness.


15:15 - 16:15 - Romina M. Arroyo (FAMAF & CIEM - Universidad Nacional de 
Cordoba, Argentina)

Invariant SKT structures on nilmanifolds

Abstract: A very active research field in complex geometry arises from 
imposing Hermitian metrics with special properties. One of the most 
studied cases is the one of "strong Kähler with torsion" (SKT for short) 
geometry.
In this talk, we will introduce SKT Hermitian manifolds, with a 
particular emphasis on invariant SKT structures on Lie groups. After 
that, we will discuss the existence of invariant SKT structures on 
nilmanifolds. More precisely, we will prove that an invariant SKT 
structure on a nilmanifold forces the nilmanifold to be at most 2-step 
nilpotent and we will provide examples of invariant SKT structures on 
2-step nilmanifolds in arbitrary dimensions.
This talk is based on a joint work with Marina Nicolini.

All are welcome to attend

https://indico.ictp.it/event/10361/

-- 
Koutou Mabilo
ICTP Mathematics Group
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