关于举行四川师范大学朱世辉教授和复旦大学张仑教授学术报告会的通知

报告题目1：Blow-up Energy Thresholds for the Hartree Equation with a Focusing Subcritical Perturbation

报  告  人：朱世辉  教授 (四川师范大学)

报告时间：2021年4月21日（星期三）下午15:00-16:00                

报告地点：腾讯会议，会议号：778 556 134

报告题目2：Asymptotics of the Pearcey determinant

报  告  人：张仑  教授 (复旦大学)

报告时间：2021年4月21日（星期三）下午16:00-17:00                

报告地点：腾讯会议，会议号：778 556 134

邀  请  人：凌黎明  教授

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数学学院

2021年4月19日

报告摘要 1：

This paper assesses the blow-up solutions for the Schrödinger equation with a Hartree-type nonlinearity together with a power-type subcritical perturbation. The precisely sharp energy thresholds for blow-up and global existence are obtained by analyzing potentially valid structures for associated functionals. This work joint with Tian Shuai, Yang Ying, Zhou Rui.

报告摘要 2：

The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a variety of statistical physics models beyond matrix models as well. In this talk, we are concerned with the Fredholm determinant , where  and  stands for the trace class operator acting on  with the Pearcey kernel. We obtain asymptotics of this determinant as , which is also interpreted as large gap asymptotics in the context of random matrix theory. It comes out that the Pearcey determinant exhibits a significantly different asymptotic behavior for and, which suggests a transition will occur as the parameter  varies. This talk is based on two recent joint works with Dan Dai and Shuai-Xia Xu.

报告人简介：

朱世辉，四川师范大学数学科学学院教授，博士生导师，四川省学术和技术带头人后备人选。已主持国家自然科学基金项目3项，教育部博士点基金项目（新教师），四川省杰出青年基金。主要从事非线性Schrodinger方程爆破解动力学性质研究，已在《J. Differential Equations》、《J. Mathematical Physics》、《J. Dynamics and Differential Equations》、《Dynamics of PDE》、《Nonlinear Differential Equations and Applications》、《中国科学》等国内外专业学术刊物上发表论文20余篇, 并多次被国内外专家引用，SCI他引180余次，包括国际著名学者 G. Fibich的专著（《The Nonlinear Schrodinger Equation: Singular Solutions and Optical Collapse》，Springer, 2015）等, 2篇论文入选ESI高被引。

张仑，复旦大学数学科学学院教授，博士生导师。研究方向为随机矩阵理论，Riemann-Hilbert方法与渐进分析，特殊函数与正交多项式等。迄今已在Comm. Pure Appl. Math.，Comm. Math. Phys.，Numer. Math.，SIAM J. Math. Anal.等国际重要学术期刊发表学术论文30余篇。主持包括优秀青年基金在内的多项国家自然科学基金，上海市东方学者、东方学者跟踪计划获得者。