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Orbital geometry - from matrices to Lie groups

发布日期:2018年03月01日

题 目:Orbital geometry - from matrices to Lie groups

报告人:譚天祐 (Tin-Yau Tam )

时 间:2018年3月9日 下午2:10-3:00

地 点:良乡校区理学楼305

报告摘要:

The celebrated Toeplitz-Hausdorff theorem asserts that the classical numerical range of a square complex matrix is a  convex set. Schur-Horn Theorem asserts that the set of the diagonals of Hermitian matrices of a prescribed eigenvalues is the convex hull of the orbit of the eigenvalues under the action of the symmetric groups. These results are about unitary orbit of a matrix.  Among interesting generalizations, we will focus our discussion on those in the context of Lie structure, more precisely, compact connected Lie groups and semisimple Lie algebras. Some results on convexity and star-shapedness will be presented.

报告人简介:

譚天祐(Tin-Yau Tam )出生于中国香港, 1986年毕业于香港大学数学系, 获得理学博士学位. 1998年被聘为美国奥本(Auburn University)大学数学与统计系教授, 2012年被聘为奥本(Auburn University)大学数学与统计系主任. 譚天祐教授是Alabama Journal of Mathematics杂志主编, Linear and Multilinear Algebra, Electronic Journal of Linear Algebra, Special Matrices, Proyecciones, Revista de Matematica 等杂志编委. 他的研究方向包括Linear Algebra/Matrix Theory and Applications, Multilinear Algebra, Lie group and Lie Algebra, Numerical Ranges and Radii等等.