作为Gorenstein环的推广，Auslande-型环是同调代数与代数表示论中的重要和热门研究对象，并且与许多同调猜想以及Cluster代数、倾斜代数密切联系。本项目将致力于研究Auslander-型环在相关的同调猜想及其在代数几何、代数表示论等领域的应用。通过研究Auslander-型环上某些特殊模类的同调性质、相对同调性质以及特殊Auslander-型代数上的对偶函子和特殊序列（比如说，几乎可裂序列）的存在性，为包括Gorenstein对称猜想在内的一些同调猜想的最终解决以及Auslander-型环类的应用研究提供理论支持。

Auslander-type rings, which can be considered as generalizations of Gorenstein rings, are important and hot reseach objects in homological algebra and representation theory of algebra. Moreover, they are closely related with many homological conjectures as well as Cluster algebra and tilting algebra. In this project, we will devote to studying applications of Auslander-type rings on related homological conjectures and their applications on algebric geometry among other reseach area. By studying homological and relative homological properties of module categories over Auslander-type rings as well as existence of dualize functors and special sequences (e.g. almost spilt sequence), we want to provide theoretical support to the final solution of Gorenstein Conjecture among others and applied reseach of Auslander-type rings.