Seminars

Higher groups in higher gauge theory

Author:    Publicsh date:2018-10-08    Clicks:
Title:Higher groups in higher gauge theorySpeaker:朱晨畅教授(哥廷根大学数学研究所,华中科技大学数学中心)Time:2018.10.08,4-5pmLocation: Center for Mathematical Sciences, Room 813Abstract:There has been much recent development on higher symmetries in topological orders as the study of topological phase of maters has become a very active field in condensed matter physics. In this talk, we wil...

Title:Higher groups in higher gauge theory

Speaker:朱晨畅教授(哥廷根大学数学研究所,华中科技大学数学中心)

Time:2018.10.08,4-5pm

Location: Center for Mathematical Sciences, Room 813


Abstract:

There has been much recent development on higher symmetries in topological orders as the study of topological phase of maters has become a very active field in condensed matter physics. In this talk, we will  carry out the mathematical foundation of a recent joint project with Tian Lan and Xiao-Gang Wen in the above direction. Higher groups are group objects in a higher category. In a very concise way, they can be realised as a simplicial object satisfying suitable Kan conditions. We will give a more explicit algebraic model to realise some of them. This model is between the target of Dold-Kan functor and the skeleton case. Then we discuss higher gauge theory for topological orders, classification of them in lower dimensions, and explicit realisations in special cases.