Curvature, diameter and eigenvalues of amply regular graphs

发布时间：2024-03-12 作者：浏览次数：

Speaker:	刘世平教授	DateTime:	2024年3月16日（周六）下午14：30-15：30
Brief Introduction to Speaker: 刘世平，中国科技大学教授，博士生导师，2002年—2006年在山东大学数学基地班获理学学士学位，其间获潘承洞奖学金。2012年于德国莱比锡马普数学所和莱比锡大学获博士学位。2012—2013年在莱比锡马普数学所做博士后，2013年—2016年在英国杜伦大学任研究助理，2016年入选第七批国家级人才计划。主要研究兴趣集中在离散几何分析等领域，学术成果发表在Adv. Math.，Crelle's Journal，Ann. Henri Poincaré, Calc. Var. PDE等主流学术期刊上		Place:	六号楼二楼报告厅
Abstract:Bounding the diameter of a distance-regular graph in terms of its intersection numbers is a very important problem. Recently, there are strong interests to bound the diamter via a small initial part of the intersection array (see, e.g., Neumaier-Penjić, Combinatorica 2022). For that purpose, we consider the diameter and eigenvalue estimates of a more general class of graphs called amply regular graphs. In this talk, we elaborate the point that the local regularity conditions in the definition of an amply regular graph play a role very similar to curvature. In differential geometry, a general principle is that the information about curvature at every point leads to diameter and eigenvalue bounds. We will discuss sharp diameter and eigenvalue bounds for amply regular graphs derived from estimating the Lin-Lu-Yau curvature of each edge. This talk is based on joint works with Xintian Li, Xueping Huang, and Qing Xia.

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