## 東京名古屋代数セミナー

担当者 阿部 紀行、Aaron Chan、Erik Darpoe、伊山 修、中村 力、中岡 宏行、高橋 亮 http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2020年10月27日(火)

16:30-18:00   オンライン開催
オンライン開催の詳細は上記URLをご覧ください。

Positive cluster complex and $\tau$-tilting complex (Japanese)
[ 講演概要 ]
In cluster algebra theory, cluster complexes are actively studied as simplicial complexes, which represent the structure of a seed and its mutations. In this talk, I will discuss a certain subcomplex, called positive cluster complex, of a cluster complex. This is a subcomplex whose vertex set consists of all cluster variables except for those in the initial seed. I will also introduce another simplicial complex in this talk - the tau-tilting complex, which has vertices given by all indecomposable tau-rigid modules, and simplices given by basic tau-rigid modules. In the case of a cluster-tilted algebra, it turns out that a tau-tilting complex corresponds to some positive cluster complex. Due to this fact, we can investigate the structure of a tau-tilting complex of tau-tilting finite type by using the tools of cluster algebra theory. This is joint work with Haruhisa Enomoto.