讲座人简介：

刘绵涛，男，2025年12月博士毕业于法国巴黎第七大学，导师为国际著名代数学家Bernhard Keller 教授，研究方向为代数表示论，曾在德国黑森林数学所，法国斯特拉斯堡大学，中国科学技术大学，清华大学等机构访问交流。

讲座简介：

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.