Cluster additive functions and Ringel’s conjectures
报告题目：Cluster additive functions and Ringel’s conjectures
报告专家：曹培根 （香港大学）
报告时间：2023年6月29日15：30-16：30
报告地点：西南中心501
报告摘要：
Let A be a symmetrizable generalized Cartan matrix of size r. A cluster-additive function associated to A is a map from Z times [1,r] to Z satisfying certain mesh type relations. Such functions were introduced by Ringel, which are closely related with additive functions in representation theory. In the case that the Cartan matrix is of finite type, Ringel conjectured that cluster additive functions admit some certain periodicity and any cluster additive function is a non-negative linear combination of cluster-hammock functions, which are a class of “elementary cluster additive functions”.
In this talk, we will give some link between cluster additive functions and cluster algebras. Ringel’s conjectures are easy consequences of our results. This talk is based on a work in progress with Antoine de St. Germain and Prof. Jiang-Hua Lu.
专家简介：
曹培根，博士毕业于浙江大学，主要从事丛代数方面的研究工作。特别地，因解决了丛代数中的分母向量的正性猜想和丛代数的唯一性猜想于2021年获钟家庆数学奖。
邀请人：付昌建