Calabi-Yau structures
on derived and singularity categories
of symmetric orders
报告专家：刘钧旸 博士后（东京大学）
报告时间：2月4日（周三）10:30-11:30
报告地点：四川大学数学学院东409
报告摘要：
This is a report on recent work in collaboration with Norihiro Hanihara (arXiv:2512.03836). We develop a differential graded enhancement of Amiot's construction of Calabi-Yau structures on Verdier quotients. Using this framework, we establish the existence of a right Calabi-Yau structure on the dg singularity category associated with a symmetric order. Combining this with a structure theorem in collaboration with Bernhard Keller, we establish a triangle equivalence between the singularity category with a cluster-tilting object and the cluster category associated with a Calabi-Yau dg algebra. We also construct a left Calabi-Yau structure on the bounded dg derived category of a symmetric order, which is a non-commutative analogue of a result by Brav-Dyckerhoff.
专家简介：
刘钧旸，博士毕业于巴黎西岱大学，目前受日本JSPS研究资助在日本东京大学从事博士后研究工作。研究方向为代数表示论,相关工作发表于J Algebra, C.R. Math. Acad. Sci. Paris等知名数学期刊。
邀请人：付昌建
