数学学科2025系列学术报告之三十二暨数学学科研究生学术论坛

　　报告一题目：An introduction to pluripotential theory

　　报告人：王伟

　　报告时间：12月10日（星期三）16:00-17:00

　　报告地点：理学院1-210

　　摘要：I will talk about some basic facts and motivations of pluripotential theory in several complex variables, and extension to several quaternionic/octonionic variables

　　报告人简介：王伟，浙江大学教授、博士生导师。主要从事多复变函数论和复流形理论的研究工作，在《J. Eur. Math. Soc.》《J. Math. Pures Appl.》《Trans. Am. Math. Soc.》《Math. Z.》等杂志发表学术论文60余篇，主持国家自然科学基金面上项目多项。

　　报告二题目：Infinite horizon LQ and overtaking optimal control problems for singular Volterra integral equations

　　报告人：周华成

　　报告时间：12月10日（星期三）16:00-17:00

　　报告地点：理学院1-301

　　摘要：This work is concerned with infinite horizon linear quadratic optimal control and overtaking optimal control problems for singular Volterra integral equations. The admissible control set under which the cost functional is well-defined is obtained. The characterization of the existence and uniqueness of the optimal control under proper conditions is explored by maximum principle type necessary conditions. By using this characterization, we show that the optimal control for linear quadratic optimal control of the fractional system cannot be obtained by linear feedback with a constant gain satisfying an algebraic Riccatic equation. When the cost functional is unbounded, the overtaking optimal control is studied, and both the existence and nonexistence of a solution for overtaking optimal control in various cases are established by characterizing the weight function.

　　报告人简介：周华成，中南大学教授，博士生导师。主要从事偏微分方程控制理论、随机控制系统、自抗扰理论、最优控制等理论研究；获中国科学院院长特别奖，入选国家高层次青年人才，主持国家自然科学基金项目3项；在《IEEE Tans. Automat. Control》《Automatica》《SIAM. J. Conttol Optim》《ESAIM Conttol Optim. Calc. Vat》《Systems Control Lett.》《J. Differential Equations》《J. Optim. Theory Appl.》等杂志发表学术论文。

　　报告三题目：On some nonlinear variational problems related to the critical Hartree equation

　　报告人：杨敏波

　　报告时间：12月10日（星期三）16:00-17:00

　　报告地点：理学院1-401

　　摘要： In this talk we will introduce several different variational models related to the critical Hartree equation. Firstly, we mainly focus on some variations of the classical Hardy-Littlewood-Sobolev inequality and its weighted case. Secondly, we will introduce the qualitative analysis of the critical Hartree equation and its applications in the study of the stability of a nonlocal version of Sobolev inequality and the asymptotic behavior of solutions of the nonlocal critical Hartree equations. This talk is based on several papers by Xiang Li, Fashun Gao, Vitaly Moroz, Weiwei Ye and Shuneng Zhao.

　　报告人简介：杨敏波，浙江师范大学数学科学学院院长，教授，博士生导师。主要从事非线性分析和椭圆型方程的研究工作，在《Calc. Var. Partial Differential Equations》《Math. Z.》《Commun. Anla. Geom.》《 J. Differential Equations》《Nonlinearity》 等杂志发表论文80余；主持国家自然科学基金面上项目、国际（地区）合作交流项目，浙江省自然科学基金重点项目等多项。

　　报告四题目：An introduction the the representations of quotient singularities

　　报告人：何济位

　　报告时间：12月11日（星期四）10:30-11:30

　　报告地点：理学院1-301

　　摘要：Let A be a regular algebra, and let G be a finite group which acts on A. Let A^G=\{a\in A| g(a)=a,\forall g\in G\} be the invariant subalgebra. In general, A^G is not a regular algebra. In this talk, I will give a brief survey of the representations of the singularities of A^G in terms of McKay correspondence.

　　报告人简介：何济位，杭州师范大学教授，博士生导师。主要从事非交换代数的研究工作，主持国家自然科学基金面上项目3项、青年项目1项，省部级科研项目4项；在《Trans. Am. Math. Soc.》《Math. Z.》《J. Noncomm. Geometry》《Israel J. Math.》《J. Algebra》等杂志发表学术论文。