题目：Segal-Shale-Weil Representations and Universal Fourier Transforms
报告人：Jing-Song Huang (HKUST)
时间：2020/10/27 20:00-21:00 (Beijing Time)
Zoom ID: 517 680 7232 Passcode: 453060
报告摘要：
The Fourier transform decomposes a function (typically a function of time or a
signal) into its constituent frequencies. It has been widely used in science and
engineering. Still, it plays a significant role in current development of mathematics,
for instance, in the recent progress of spherical packing problem as it can
simultaneously diagonalize the translations and make periodic structure easier to
understand.
The Fourier transform is the unique unitary intertwiner for the Segal-Shale-Weil
representation. It arises from an element of (the metaplectic cover of)
the symplectic group Sp(2n,R). Similar to the existence of the Casmir element
corresponding to the Laplacian operator for any reductive Lie algebra, the Fourier
element exists for any reductive Lie group and it defines an intertwiner for all unitary
representations.
We will demonstrate this Fourier element is interesting for understanding the
structure and classification of irreducible unitary representations of real reductive
Lie groups.
报告人简介：
Jing-Song Huang is currently a Chair Professor of Mathematics at the Hong Kong
University of Science and Technology. He received bachelor's degree from Beijing
University in 1984 and Ph D at MIT in 1989 under direction of David A. Vogan, Jr. He
is a recipient of the State Science Award (2002) and the Crouch Senior Research
Award (2004).
欢迎参加！
邀请人：白占强, 董超平