我们建议研究Fano簇的几何。Fano簇是代数几何中的核心研究对象，是分类理论中代数簇的三大类之一。我们对Fano簇的了解在这十年中经历了飞速的发展。其中尤其重要的工作有Voisin关于Fano簇有理性及稳定有理性判别准则的工作，Birkar关于带有奇点的Fano簇的有限性的工作，以及Tian和Chen-Donaldson-Sun关于Fano簇K-stability的突破等。这些工作连接了代数几何中多个核心领域如Chow群，奇点理论，极小模型理论，Kahler-Einstein度量理论等等。这显示了Fano簇丰富的几何结构与在代数几何中的核心地位。在这个领域中仍然有很多重要的公开问题，如能否构造非单有理的有理联通簇？一般的维数为四的三次超曲面是否为有理的？是否能找到Fano簇K-stability的代数判别方法等等。鉴于这个领域的重要性我们期望对它进行深入的研究。

We propose to study the geometry of Fano varieties. Fano variety is one of the most important and well-studied varieties in algebraic geometry. Great progress has been made in this subject in the past decade, such as Voisin's work on stable-rationality of Fano varieties, Birkar's solution of BAB conjecture, which is about the boundedness of singular Fano varieties, Tian and Chen-Donaldson-Sun's breakthrough on K-stability of Fano varieties and the existence of Kahler-Einstein metrics, etc. These works connect different branches of algebraic geometry, such as Chow groups, theory of singularities, the minimal model program, Kahler-Einstein metrics, etc and manifest rich structure of Fano varieties and its importance in algebraic geometry. There are still many interesting and important open problems in this field. We can only mention a few: does there exist a rationally connected variety which is not unirational? How to prove that a generic cubic fourfold is not rational and is the rationality of a cubic fourfold related to its Hodge structure? Can we find an algebraic criterion of K-stability of Fano varieties? We like to take this opportunity to study these problems.