学术报告（一）
报告题目：On asymptotic behavior of principal eigenvalues for elliptic operators
报告人：楼元 教授
报告时间：2025年3月26日（星期三）15:30-16:30
报告地点：卓越楼810会议室
Abstract：The study on the qualitative properties of principal eigenvalues for second order elliptic operators has a long history. In recent years there are some growing interest in investigating the asymptotic behaviors of such principal eigenvalues with small diffusion or large advection rates. In this talk we will give a brief review and discuss some recent works along this line. This talk is mainly based on joint works with Shuang Liu (Beijing Institute of Technology) and Maolin Zhou （Nankai University).
报告人简介：上海交通大学数学科学学院讲席教授、院长。1991-1995年就读于美国明尼苏达大学数学系，获博士学位；美国国家数学科学研究所（1995-1996年）和芝加哥大学（1996 -1998年）博士后；1998-2021年任教于俄亥俄州立大学数学系，曾任美国数学生物研究所副所长。研究兴趣是反应扩散方程及在生物学中的应用，发表学术论文150余篇，部分研究成果发表在Comm. Pure Appl. Math、 Memoirs AMS等期刊。目前担任J. Differential Equations、J. Math. Biol.、SIAM J. Appl. Math.等期刊编委以及DCDS-B期刊的共同主编，中国工业与应用数学学会会刊CSIAM Transactions on Life Sciences执行编辑。
学术报告（二）
报告题目：Solitons、breathers and lump solutions of the coupled (2+1)-dimensional Fokas system
报告人：虞国富 教授
报告时间：2025年3月26日（星期三）16:30-17:30
报告地点：卓越楼810会议室
Abstract：In this talk, we apply Hirota's bilinear method in conjunction with the Kadomtsev-Petviashvili hierarchy reduction technique to construct solitons, breathers and lump solutions of the coupled (2+1)-dimensional Fokas system. We derive three types of breather solutions by different choices of parameters, including Akhmediev breather, Kuznetsov-Ma breather and general one along some oblique line. By introducing two judicious differential operators in the dimension reduction procedure, we obtain rational solutions in terms of Schur polynomials. Three different kinds of fundamental lumps including bright lumps, dark lumps and bi-model lumps are investigated. We show that the arrangement patterns of fundamental lumps are determined by the irreducible parameters. Pattern formation of higher-order lump solutions at large times is described analytically by root structures of the Yablonskii-Vorob'ev polynomials. Finally, we propose a multi-component Fokas system and present multi-soliton and multi-breather solutions.
报告人简介：2007年6月博士毕业于中国科学院数学与系统科学研究院; 加拿大蒙特利尔大学博士后。现为上海交通大学数学科学学院教授、博士生导师，数学科学学院副院长。主要从事孤立子与可积系统、特殊函数、正交多项式方面的研究。在数学物理领域学术刊物上发表SCI论文40余篇。主持国家自然科学基金、上海市晨光计划、上海交通大学晨星青年学者奖励计划等多项研究课题。
