On the categorification of the cluster variety of triples of flags
组织者
演讲者
刘绵涛
时间
2026年03月26日 08:00 至 09:00
地点
Online
线上
Zoom 442 374 5045
(BIMSA)
摘要
The cluster variety of triples of flags (associated with a split simple Lie group of Dynkin type Delta) plays a key role in higher Teichmuller theory as developed by Fock-Goncharov, Jiarui Fei, Ian Le, ... and Goncharov--Shen. We refer to it as the basic triangle associated with Delta. For simply laced Delta, we construct and study a Higgs category, in the sense of Yilin Wu, which we expect to categorify the basic triangle. This category is a certain exact differential graded (=dg) category, in the sense of Xiaofa Chen, which is Frobenius and stably 2-Calabi-Yau. We show that it has indeed the expected cyclic group symmetry and that its derived category has the expected braid group symmetry. A key ingredient in our construction is a conjecture by Merlin Christ.