报告题目：The logarithmic Sobolev inequality for a submanifold i…

报 告 人：易承扬

时 间：2021年6月21日（周一）下午14:40-15:40

地 点：线上会议（会议号请联系程亮老师获取）

简 介：In 2019-2020, Simon Brendle proved several geometric inequalities. Inspired by this, we prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. This extends a recent result of S. Brendle with Euclidean setting. This is a joint work with Yu Zheng.

报告题目：Eigenvalue and heat kernel estimates on the canonical …

报 告 人：朱萌

时 间：2021年6月21日（周一）下午13:30-14:30

地 点：线上会议（会议号请联系程亮老师获取）

简 介：Let M be an m dimensional closed Kaehler manifold. We will present certain eigenvalue and heat kernel estimates for the Hodge Laplacian acting on smooth sections of the canonical bundle of M, i.e., (m,0)-forms. The main results only rely on the bound of the Ricci curvature, and the volume and diameter of M, instead of the bound of the whole curvature tensor in the general p-form case. This is a joint work with Zhiqin Lu and Qi S. Zhang.

报告题目：Fast Network Community Detection with Profile-Pseudo L…

报 告 人：张菁菲

时 间：2021年6月18日（周五）上午9:30

地 点：腾讯会议（会议号请联系胡建伟老师获取）

简 介：The stochastic block model is one of the most studied network models for community detection and fitting its likelihood function on large-scale networks is known to be challenging. One prominent work that overcomes this computational challenge is Amini et al. (2013), which proposed a fast pseudo-likelihood approach for fitting stochastic block models to large sparse networks. However, this approach does not have convergence guarantee, and may not be well suited for small and medium scale networks. In this article, we propose a novel likelihood-based approach that decouples row and column labels in the likelihood function, enabling a fast alternating maximization. This new method is computationally efficient, performs well for both small- and large-scale networks, and has provable convergence guarantee. We show that our method provides strongly consistent estimates of communities in a stochastic block model.