报告题目1：Hierarchical free-energy machine for strongly coupled combinatorial optimization problems

报告人：高炜教授，河海大学

报告时间：9月15日（周二）18:30-19:30

报告地点：腾讯会议：631-116-919

报告摘要：Free-energy machine (FEM) is a prevalent combinatorial optimization algorithm in terms of statistical physics techniques, which utilizes gradient calculation strategies to minimize the variational mean-field free energy, thereby obtaining the ground state of combinatorial optimization problems (COPs). However, traditional FEM is ineffective for strongly coupled COPs, failing to deeply characterize the complex interrelationships between variables. To overcome this limitation, we propose a hierarchical FEM. The basic idea is to fix one variable, design an energy function to characterize the remaining variables, and then hierarchically obtain optimization strategies corresponding to the fixed parameter values. The final optimization result is integrated in terms of specific COP expression. This work addresses the approximation of vulnerable graph parameters such as toughness, isolated toughness, binding number, scattering number, integrity, and rupture degree, which are classic examples of strongly coupled COPs. We present optimization strategies based on replica symmetry breaking, along with their respective explicit gradient calculation formulas.

报告人简介：高炜，河海大学数学学院教授。主要从事图论、人工智能、化学数学、非线性偏微分方程的研究。2012年6月于苏州大学数学系获得博士学位，在攻读硕士、博士学位期间多次以研究助理身份访问香港城市大学数学系，从事统计学习理论研究。先后在南京大学数学系，土耳其哈来大学数学系从事博士后工作，并顺利出站。累计发表论文300余篇，引用7000+，累计进入高被引论文50+，H指数45，2020年入选科睿唯安高被引科学家（跨学科），入选2021-2025爱思唯尔中国高被引学者（数学），从2019年开始入选斯坦福大学全球前2%科学家。

报告题目2：The vertex-arboricity of IC-planar graphs

报告人：王阳博士，浙江财经大学

报告时间：9月15日（周二）19:30-20:30

报告地点：腾讯会议：631-116-919

报告摘要：A graph is IC-planar if it can be drawn in the plane so that each edge crosses at most one edge and every vertex is incident with at most one crossing edge. In this talk, we show that the vertex set of an IC-planar graph can be partitioned into three forests, which strengthens the known result that the vertex set of a planar graph can be partitioned into three forests.

报告人简介：王阳，博士，毕业于浙江师范大学，现为浙江财经大学数据科学学院讲师。主要从事图的染色和划分相关问题研究。在《J. Graph Theory》、《Discrete Math.》、《Czechoslovak Math. J.》、《数学进展》等国内外杂志上发表论文9篇。

邀请人：数学研究所