Stability conditions on triangulated categories and cyclic categories
报告题目：Stability conditions on triangulated categories and cyclic categories
报告专家：刘昱成（北京大学）
报告时间：2022年12月29日，15：00
报告地点：腾讯会议：882-7334-4303
报告摘要：
In the first half of this talk, we will give a general introduction to the theory of Bridgeland stability conditions on triangulated categories. In the second half of this talk, we will present a new notion of stability conditions on cyclic categories. Here a cyclic category is a triangulated category with a canonical Bott’s isomorphism β : [2] ≃[0] = id.
The phenomenon [2] = [0] is ubiquitous in mathematics. And it is easy to see that on cyclic categories, there is no t-structures, hence no Bridgeland stability conditions either.
However, in the second half of this talk, we will introduce a new notion of stability conditions on cyclic categories. Along this way, we will see a notion of Maslov index, which plays the same role as in Fukaya categories, i.e. when all the Maslov indexes vanish, we can lift our stability conditions on a Z/2Z-graded cyclic categories to the usual Bridgeland stability conditions on a Z-graded triangulated category.
I will present some examples of our stability conditions on the category of equivariant matrix factorizations, which also appeared in FJRW-theory. We will observe the phenomenon of chirality symmetry breaking in these examples, which might be of some physics interests.
专家简介：刘昱成，美国东北大学博士，现为北京大学国际数学研究中心博士后；研究方向为代数几何。
邀请人：李彦鹏
