题目:  Introduction to nonlinear Lie theory and higher structures 

报告人： 生云鹤（吉林大学） 

时间: 2016年3月11日 周五 下午16:00-17:30   

地点： 管理科研楼1611

摘要： Lie algebroids are generalizations of Lie algebras and tangent bundles. They are infinitesimal objects of Lie groupoids.
We call corresponding theory nonlinear Lie theory. Higher structures are mainly about Lie 2-algebras and Lie 2-groups. They are categorification of Lie algebras and Lie groups. In this talk, I will introduce some basic facts about Lie algebroids. In particular, I will talk about a Lie bialgebroid, whose double is not a Lie algebroid anymore (this is different from the case of Lie algebras), but a so called Courant algebroid. Then higher structures show up naturally. On the other hand, from graded geometry point of view, a Courant algebroid corresponds to a degree 2 symplectic NQ manifolds. Finally, I will talk about recent work on degree 3 symplectic NQ manifolds. A degree 2 symplectic NQ manifold gives rise to an LWX 2-algebroid(named after Liu-Weinstein-Xu), which is a categorified Courant algebroid.