报告一
题目：代数连通度和谱半径在多智能体系统一致性研究中的应用
报告人：张胜贵 教授（西北工业大学）
报告时间：12月4号下午2：00--3：00
腾讯会议：609-244-573
或点击链接入会：https://meeting.tencent.com/dm/8vovDvt60igI
摘要：本报告主要介绍图的代数连通度和拉普拉斯谱半径在多智能体系统一致性问题研究中的重要应用。网络拓扑的代数连通度和谱半径决定了一致性协议的收敛速度：代数连通度越大，一阶系统的一致性收敛速度越快；代数连通度越大、谱半径越小，二阶系统的一致性收敛速度越快。网络拓扑也决定了多智能体系统达成一致时的通信量：对周期通信和事件触发的一致性协议，代数连通度越大、谱半径越小，智能体间的通信频率可以更低，系统达成一致需要的通信量更少。本报告研究了多智能体系统网络拓扑的冗余边识别问题和以减少系统通信量为目标的网络拓扑优化问题，并通过仿真实验验证了拓扑优化的效果。
报告二
题目：The perturbation on spectral radius of uniform hypergraphs
报告人：王力工 教授（西北工业大学）
报告时间：12月4号下午3：00--4：00
腾讯会议：609-244-573
或点击链接入会：https://meeting.tencent.com/dm/8vovDvt60igI
摘要：In this talk, we study how the spectral radius (resp., signless Laplacian spectral radius) changes when a connected uniform hypergraph is perturbed by subdividing an edge. We extend the results of Hoffman and Smith from connected graphs to connected uniform hypergraphs. Moreover, we also investigate how the Laplacian spectral radius behaves when an odd-bipartite uniform hypergraph is perturbed by subdividing an edge. As applications, we determine the unique unicyclic hypergraph with the largest signless Laplacian spectral radius, and also determine the unique unicyclic even uniform hypergraph with the largest Laplacian spectral radius. This is a joint work with Peng Xiao.
报告三
题目：Some new results on Lagrangians of hypergraphs
报告人：史永堂 教授（南开大学）
报告时间：12月4号下午4：00--5：00
腾讯会议：609-244-573
或点击链接入会：https://meeting.tencent.com/dm/8vovDvt60igI
摘要：A well-known conjecture of Frankl and F\{u}redi states that the $r$-graph with $m$ edges formed by taking the first $m$ sets in the colex ordering of $\mathbb N^{(r)}$ has the largest Lagrangian of all $r$-graphs with $m$ edges. The conjecture was settled when $r=3$ for sufficiently large $m$. For $r\ge 4$, Gruslys, Letzter and Morrison [Hypergraph Lagrangians I: The Frankl-F\{u}redi conjecture is false, Adv. Math., 365(2020), 107063] confirmed the conjecture when $m$ belongs to the principal range $\left[\binom{t-1}{r},\binom{t}{r}-\binom{t-2}{r-2}\right]$ for sufficiently large $t$, and found an infinite family of counterexamples for $ r \ge 4$ and $m=\binom{t}{r}-\binom{t-2}{r-2}+s$, where $r\le s\le\alpha_r\binom{t-2}{r-2}$ for some constant $\alpha_r$. In this talk, we will present some more maximisers of the Lagrangian outside the principal range. Joint work with Ran Gu, Hui Lei and Yuejian Peng.
