Constant Scalar Curvature Metrics in Sasaki and Kahler Geometry

University Of New Mexico, Albuquerque NM

Investigators

Abstract

This award supports participation of US based researchers in a one week long international conference in pure mathematics to be held at the CIRM (France), Jan 15, 2018 - Jan 19, 2018. The title of the conference is "Constant Scalar Curvature Metrics in Sasaki and Kahler Geometry." The conference aims at presenting and further developing the latest achievements in the Yau-Tian-Donaldson conjecture, which is one of the most fundamental conjectures in complex geometry. The conjecture is at the intersection of two different domains that have deep impact in pure mathematics and modern physics: differential geometry and algebraic geometry. The goal of the meeting is to gather some of the world experts in the several aspects of the Y-T-D conjecture and have them exchange ideas among themselves as well as interact with junior researchers with fresh ideas so as to make progress in the solution of the most general version of the conjecture. The conference will serve as a learning opportunity as well as a way to help make connections and open the way to mathematical collaborations. The participants will come from diverse backgrounds and countries and the organizing committee will promote attendance of underrepresented groups in the mathematical sciences. Since the conjecture of Yau-Tian-Donaldson stating the equivalence between the existence of Kahler-Einstein and K-polystability has been proved in 2012, Kahler geometers are turning to the extension of this conjecture to existence of constant scalar curvature (csc) Kahler/Sasaki metrics. This extension is far from being a trivial question since the csc equation is by far more difficult (non-linear 4th order PDE). Nevertheless, this topic is now booming and in the last few years many related results have been proved. The determination of the organizers is to make the conference an opportunity to present and further develop the latest achievements of the subject and to promote interaction between researchers of the domain. The topics of the conference lie at the crossroads of the following research fields: complex/CR geometry, symplectic/contact geometry, complex algebraic geometry, Geometric Invariant Theory and algebraic stability, moduli spaces, complex analysis, geometric quantization, heat kernels asymptotics, geometric flows and partial differential equations, mathematical physics. Consequently, one can hope that the techniques developed and the unveiled relations will have an impact on other areas of Geometry, as the study of Einstein metrics, special holonomy geometries, moduli spaces of Kahler metrics and moduli of algebraic varieties, just to name a few. The stimulating interaction of the different sub-fields above has always been fruitful in the past and it is natural to hope that some of these sub-fields can benefit from the advances on the Yau-Tian-Donaldson conjecture in a long range. The website of the conference is located at: http://scientific-events.weebly.com/1750.html