报告题目：Topics on variational problems of quantum many-body systems

报告人：郭玉劲

报告时间：2023年08月18日（周五）15:00-18:30

报告地点：数学楼315会议室

报告摘要：The variational problems are often used to model the ground states of quantum many-body systems, including ultracold Bose gases, ultracold Fermi gases, pseudo-relativistic boson stars, and so on. The interactions among atoms represents a major difficulty in mathematically understanding such quantum systems. The investigations on the corresponding variational problems can be traced back as early as the celebrated works of P.L. Lions and E. Lieb around 1980s. In this series of talks, we shall first introduce the fundamental main results of several typical variational problems. We then discuss how to analyze the limiting behavior of the variational problem arising in ultracold Bose gases. The variational problems in the rotational case is finally analyzed.

报告人简介：郭玉劲，教授，博士生导师，华中师范大学数学与统计学学院副经理，先后主持中国科学院“百人计划”、国家自然科学基金优秀青年科学基金、国家杰出青年科学基金等项目。2007年获得加拿大英属哥伦比亚大学博士学位，2007年至2012年先后工作于美国明尼苏达大学、加拿大康科迪亚大学，随后工作于中国科学院武汉物理与数学研究所，2019年初至今工作于华中师范大学。主要从事变分理论及其在非线性偏微分方程、数学物理等领域的应用研究，围绕微机电系统MEMS方程、质量临界约束变分理论、量子多体系统涡旋现象等课题做出过一系列原创性研究。相关成果在美国数学会出版一部英文研究专著，在Comm. Pure Appl. Math.、Arch. Ration. Mech. Anal.、Trans. Amer. Math. Soc.、J. Math. Pure Appl.等数学权威期刊上发表论文40余篇。