Title: Gradient estimate of harmonic function and eigenfunctions Speaker: Prof. Guoyi Xu (Tsinghua University) Time: 2018-11-16, 11:00-12:00 Place: N913 Abstract: Since Cheng-Yau proved the gradient estimate of harmonic functions in 1975, their method played important role in geometric analysis. Its philosophy was generalized to prove the lower bound of eigenvalues and parabolic Harnack estimate by Li-Yau, later to establish the Harnack estimate in Ricci flow by Hamilton, the fundamental gap theorem by Andrews and Clutterbuck. In this talk, we will firstly review the history of gradient estimate and its important application, then present our recent results in this direction. Some open questions will be posed in “accessible disguise”, basic PDE and Riemannian geometry is enough to understand most part of the talk. Attachment: