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Tin Yau Tam: So-Thompson’s conjectures on products of matrix exponentials and beyond

时间:2021-12-10来源:数学学院

报告时间:2021年12月11日(星期六)20:00-22:00

报告平台:腾讯会议 ID:338 491 626

:Tin Yau Tam 教授

工作单位University of Nevada, Reno

举办单位:数学学院

报告简介

In 1991 Wasin So and Robert C. Thompson conjectured two formulas of matrix exponential products.

Conjecture 1: For Hermitian matrices X,Y∈ Hn, there exist n by n unitary matrices U, V such that eX/2eY eX/2 = eUXU-1+V Y V-1

Conjecture 2: Let S, T be n by n complex symmetric matrices in a neighborhood of zero. Then there exist nbu n complex orthogonal matrices P,Q such that

eS/2eT eS/2 = eUSU>+V TV

The first conjecture was proved by So in 2004 and his proof makes use a result of Alexander A. Klyachko. We will discuss its generalization in the context of Lie group, which was obtained by Luyining Gan, Xuhua Liu and Tin-Yau Tam in 2021. The second conjecture remains open.

报告人简介

谭天祐(Tin-Yau Tam)教授于1986年获得香港大学博士学位。现任美国内华达大学里诺 分校(University of Nevada, Reno)数学与统计系终身教授、系主任,国际知名矩阵理论方面的 数学家。主要从事矩阵,多重线性代数,数值域和李群方面的研究。在《Proceedings of American Mathematical Society》、《SIAM Journal of Matrix Analysis and Applications》、 《Linear Algebra and Its Applications》、《Linear and Multilinear Algebra》、《Journal of London Mathematical Society》、《Bulletin of Canadian Mathematical Society》、《Pacific Journal of Mathematics》、《Journal of Japan Mathematical Society》和《Journal of Lie Theory》等国际学术期刊上发表主要学术论文一百余篇。担任国际学术期刊《Linear and Multilinear Algebra》, 《Electronic Journal of Linear Algebra》,《Special Matrices》的编委,《Alabama Journal of Mathematics》的主编,美国《Mathematical Reviews》及德国《Zentralblatt Math》 的评论员;曾被邀请共同撰写《Handbook of Linear Algebra》;多次组织国际学术会议。

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