主讲人:张根凯教授
瑞典哥德堡大学,Chalmers工业大学数学系主任教授。1991年瑞典Stockholm大学博士毕业,内蒙古大学83学士,复旦大学86年硕士。丹麦Odense大学博士后,澳大利亚悉尼New South Wales大学副研究员。2001获瑞典数学会的Wallenberg奖。曾在瑞典Mittag-Leffler研究所,德国Max-Planck研究所,英国剑桥Newton Institute,法国高等科学研究所IHES访问研究。中国科学院数学所现代分析创新团队海外成员,韩国高等研究所KIAS学者。
在有界对称域上的复分析和调和分析,李群表示,拟凸域上的Hankel算子作出杰出贡献。在国际一流数学杂志Journal of Functional Analysis, Duke Mathematics Journal, Advances in Mathematics, Journal of Geometric Analysis等发表多篇文章。
题目一:Cayley-Capelli identity and Radon transform. I
时间: 12月8日下午3:00-4:00理学实验楼312
Abstract: The classical Cayley-Capelli identity computes the action of the differential operator
$\det(\partial_x) $ on the functions $\det (x)^\lambda$ on the matrix space $M_{n, n}(\mathbb C)$. Here $\det(\partial_x)=\det(\partial_{ij})$ is the determinant of the matrix
differential operator $(\partial_{ij})$. In the first part of the talk I shall present some generalizations of the Capelli identity on some other matrix spaces and on certain Grassmannian manifolds.
题目二:Cayley-Capelli identity and Radon transform. II
时间:12月9日下午3:00-4:00理学实验楼312
Abstract:In the second part,weshall compute the eigenvalues of the Radon transform on Grassmannian manifolds and find inversion formula using the Capelli-type operators. (This is based on the joint work with S. Sahi.)
题目三:Lie group, discrete subgroups and their representations.
时间:12月10日3:00-4:00文清321课室
Abstract: A Lie group is a group with certain topological and smooth structures. The Euclidean space and the orthogonal groups are the simple examples. Many important geometric objects can be constructed by using quotient spaces of Lie groups; for example the torus can be viewed as the quotient space of the plane by its subgroupofIntegralpoints. Many geometric structures on quotient spaces can be studied by understanding the representations of the underlying groups. I shall focus on the Euclidean plane and the non-Euclidean Poincare unit disc and introduce some important research topicsand problems.
题目四:Complementary series representations of Hermitian Lie groups on the Shilov boundary of symmetric domains. I,
时间:12月11日11:00-12:00理学实验楼312
Abstract: In the first part of this talk I shall introduce the principal series representations of the symmetric group of classical bounded symmetric domains on the Shilov boundary. We find the corresponding complementary series representations both in the compact and non-compact picture.
题目五: Complementary series representations of Hermitian Lie groups on the Shilov boundary of symmetric domains. II.
时间:12月16日下午3:00-4:00理学实验楼312
Abstract:In the part II we shall study certain Hardy-Littlewood-Sobolev inequality and reflection positivity. (This is based partly on joint works in progress with T. Kobayashi and B. Orsted.)
主办单位:数学与信息科学学院
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