We first introduce the theoretical framework of Ollivier Ricci curvature and the curvature flow on graphs. Next, we briefly present several recent advances at the intersection of graph geometry and real-world problems. In particular, we introduce the Geometric Evolution Graph Convolutional Network (GEGCN), a novel framework that enhances graph representation learning through explicit modeling of geometric evolution on graph structures. Extensive experiments demonstrate that GEGCN achieves excellent performance on classification tasks across various benchmark datasets, including homophilic/heterophilic graphs, filtered graphs, and large-scale graphs.

The report is based on collaborative works with Ma Jicheng, Tian Yulu, Yang Yunyan and Zhao Juan.

报告人简介：赵亮，北京师范大学数学科学糖心视频 ，教授, 博士生导师。研究方向为非线性分析及其在交叉领域的应用，已在JMPA、CVPDE、JDE、PRE、Sci. China Math.等期刊发表论文30余篇，含多篇ESI高被引论文，出版专著或教材7部。