*主持人：张通 研究员

*讲座内容简介：
Modular invariants of families of curves appear in various mathematical branches. Specially, in lower-dimensional topology, the modular invariant $\delta(f)$ is the sum of fractional Dehn twists coefficients. In this talk, I will present our work on the sharp lower bounds of modular invariants, which based on the lower bounds of fractional Dehn twists coefficients. This is a joint work with Prof. Sheng-Li Tan.

*主讲人简介：
刘小雷2012年博士毕业于华东师范大学，导师为谈胜利教授，他曾在香港科技大学，中国科学院数学与系统科学研究院从事博士后工作，现任大连理工大学数学科学学院副教授。