Singularity categories via higher McKay quivers with potential

报告题目：Singularity categories via higher McKay quivers with potential

报告人：刘钧旸 研究员 东京大学

报告时间：9月6日  16:00-18:00

报告地点：明理楼C302B

报告人简介：

刘钧旸，现为日本学术振兴会（JSPS）外国人特别研究员。2024年获清华大学博士学位，并于2021年至2023年在巴黎西岱大学开展博士研究。研究兴趣包括Calabi-Yau结构、三角范畴、Ginzburg微分分次代数、丛范畴与奇点范畴。近年来主要围绕Amiot猜想、Calabi-Yau结构及奇点范畴等问题开展研究，相关成果发表于Advances in Mathematics、Selecta Mathematica等国际知名数学期刊。

报告内容摘要:

In 2018, Kalck and Yang showed that the singularity categories associated with 3-dimensional Gorenstein quotient singularities are triangle equivalent (up to direct summands) to small cluster categories associated with McKay quivers with potential. We introduce higher McKay quivers with potential and generalize Kalck and Yang's theorem to arbitrary dimensions. The singularity categories we consider occur as the stable categories of categories of Cohen-Macaulay modules. We refine our description of the singularity categories by showing that these categories of Cohen-Macaulay modules are equivalent to Higgs categories in the sense of Wu. Moreover, we describe the singularity categories in the non-Gorenstein case.

承办单位：理学院、人工智能研究院

科学技术发展研究院