Cluster theory through derived categories and self-injective algebras

簇倾斜理论和高维Auslander-Reiten理论中的一个重要问题是在代数的派生范畴中刻画所有的d簇倾斜子范畴。本年度的研究通过对衍生类群倾与淤积关系的研究，对这一问题进行了研究。某些类型的淤积物，称为d-淤积物，已知会产生群集倾斜的子类别。研究的重点是了解在何种情况下，某种组合操作（称为突变）能够保持被淤积物的特性，以及簇倾斜突变操作与淤积物突变操作之间的关系。

An important problem in cluster-tilting theory and higher-dimensional Auslander-Reiten theory is to characterise all d-cluster-tilting subcategories in the derived category of an algebra. The research this year has studied this problem by studying the connection between cluster-tilting and silting in derived categories. Certain types of silting objects, called d-silting objects, are known to give rise to cluster-tilting subcategories. The research has focused on understanding under which circumstances a certain combinatorial operation, called mutation, preserves the property of being d-silting, and how the operation of cluster-tilting mutation relates to that of mutation of silting objects.