The Exchange Quiver of Cluster Algebras and the Exchange
Quiver of Root Systems
报告专家：行田康晃（The University of Tokyo）
报告时间：2023年9月4日（星期一）16：00-17：00
报告地点：数学学院东409
报告摘要：In 2002, Fomin and Zelevinsky classified cluster algebras of finite type by using Dynkin root systems. In the proof of this classification, they established a bijection between cluster variables and almost positive roots, demonstrating that it induces a graph isomorphism between the exchange graph of clusters and that of c-clusters. This graph isomorphism now plays a crucial role in connecting cluster algebra theory with Lie theory.
In recent times, the exchange graph of clusters (and c-clusters, respectively) has been given a "natural" orientation in cluster algebra theory (and Lie theory). In this presentation, I will demonstrate that these orientations are preserved by the graph isomorphism provided by Fomin and Zelevinsky.
专家简介：行田康晃，东京大学数理科学研究院特別研究员PD，主要从事丛代数方面的研究，目前在 Annals of Combinatorics, Annales de l’institut Fourier, IMRN, SIGMA等国际重要期刊上发表论文数篇。
邀请人：付昌建
![[lecture]行田康晃-01.png](http://tianyuan.scu.edu.cn/upload/default/20230827/%5Blecture%5D%E8%A1%8C%E7%94%B0%E5%BA%B7%E6%99%83-01.png "[lecture]行田康晃-01.png")