关于举行数学学院2024年海外优青论坛的通知

论坛报告一: Stable invariant Hermitian random matrices and the rate of convergence

报  告  人: 张纪元博士鲁汶大学

报告时间: 2023年12月26日（星期二）上午10:20-10:55

报告地点: 37号楼3A02报告厅

报告摘要：We consider random matrix ensembles on the Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary group. The latter property entails that the eigenvectors are Haar distributed and, therefore, factorise from the eigenvalue statistics. We prove a classification for stable matrix ensembles of this kind of matrices with the help of the classification of the multivariate stable distributions and the harmonic analysis on symmetric matrix spaces. They can be classified by the stability parameter and the spectral measure, apart from a scaling and a shift. Moreover, we address the question how these ensembles can be generated from the knowledge of the first two quantities. We consider a sum of a specific construction of identically and independently distributed random matrices that are based on Haar distributed unitary matrices and stable random vectors. For this construction, we derive the rate of convergence in the supremum norm and show that this rate is optimal.

报告人介绍：张纪元，博士，2021年博士毕业于澳大利亚墨尔本大学数学与统计学院，同年留校任研究助理。2022年就职于比利时鲁汶大学任博士后至今。研究方向是随机矩阵理论及相关应用，论文发表在Adv. Math. Constr. Approximation, Lett. Math. Phys.等高质量数学物理期刊上。

论坛报告二: 基于混合相理论的两相流数学模型及其实际应用

报  告  人: 乔阳阳博士卡尔斯鲁厄理工大学

报告时间: 2023年12月26日（星期二）上午10:55-11:30

报告地点: 37号楼3A02报告厅

报告摘要：The purpose of this presentation is to show a generalized two-phase flow model based on a mixture theory and especially how it can be utilized for two realistic problems in the aspects of biology and applied geosciences.

报告人介绍：乔阳阳，博士。现受德国亥姆霍兹联合会资助在卡尔斯鲁厄理工大学从事地热开采数学模型方面的研究工作。主要研究内容包括数学模型开发与应用、数值算法不稳定性问题。开发了多套数值模拟软件，并应用于石油天然气采收，生物流动现象、锂离子电池系统、二氧化碳储存泄漏问题以及地热开采等问题。以第一和通讯作者在权威期刊M3AS、SIAM Math Analysis、Transp. Porous Media、Adv. Water Resources、SPE Journal发表论文十余篇。

欢迎广大师生前往！

数学学院

2023年12月25日