报告题目 (Title)：Topological Matter Protected by Momentum Space Crystallographic Groups（动量空间晶体群保护的拓扑物态）
报告人 (Speaker)：赵宇心 教授（香港大学）
报告时间 (Time)：2026年6月16日（周二）16:00-17:30
报告地点 (Place)：宝山校区G601
邀请人(Inviter)：胡晓 教授
主办部门：量子科技研究院/理学院物理系
报告摘要：
While crystallographic groups are typically considered in real space, momentum-space crystallographic groups (MCGs) have recently emerged as an active research area. This development is largely driven by the framework of projective crystal symmetry, where all non-symmorphic crystallographic groups arise from phase factors between real-space translations and point-group elements, according to Mackey’s representation theory. A key implication of non-symmorphic MCGs is that the momentum-space unit—traditionally regarded as a torus—can take the form of any compact flat manifold, known as the ten platycosms, which are the orbital spaces of the ten Bieberbach groups. For each platycosm, the topological classification, specifically the reduced K-group, is isomorphic to the second integral cohomology group of the corresponding Bieberbach group. We will further demonstrate that the cohomology groups of MCGs can exhaustively classify all Abelian crystalline topological insulators, as well as all twistings of point-group actions over the Brillouin torus. By establishing an isomorphism between the integral cohomology and a one-degree-lower cohomology with U(1)-valued functions over momentum space as coefficients, we can algebraically formulate a complete set of topological invariants for classifying Abelian crystalline topological insulators and algebraically represent all twistings of point-group actions.
