刘昱成 博士学术报告
Title: Stability conditions on cyclic categories
Speaker: Dr. Yucheng Liu（刘昱成）
Affiliation: Beijing international center for Mathematical research, Peking University（北京国际数学研究中心）
Time:14:00-15:00, Friday, 10th Feburary, 2023 (UTC+8, Beijing Time)
Venue: Room 1502, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing
（东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）
Abstract
The phenomenon [2] = [0] is ubiquitous in mathematics. In this talk, we will focus on triangulated categories with a Bott isomorphism β : [2]
id. We call such a triangulated category a cyclic category. On such categories, it is easy to see that there is no t-structures, hence no Bridgeland stability conditions either.
However, in 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 condition on a Z-graded triangulated categories.
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.
About the Speaker