The Brascamp-Lieb Inequality on Compact Lie Groups and its Extinction on Homogeneous Lie Groups
数学专题报告
报告题目(Title)：The Brascamp-Lieb Inequality on Compact Lie Groups and its Extinction on Homogeneous Lie Groups
报告人(Speaker)：Ji Li教授 (Macquarie University, Australia)
地点(Place)：后主楼1124
时间(Time)：2026年4月4日（周六）15:30-16:30
邀请人(Inviter)：杨大春
报告摘要
The Brascamp-Lieb inequalities are well-understood on Euclidean spaces and abelian groups, but the non-abelian setting introduces profound algebraic and geometric obstructions.
In this talk, based on joint work with Michael G. Cowling and Chong-Wei Liang, we investigate these inequalities on locally compact groups, highlighting a striking dichotomy between compact and homogeneous Lie groups.
For compact Lie groups, we establish a necessary and sufficient condition for the finiteness of the Brascamp-Lieb constant. By decoupling the group into its semisimple and central torus components, we show this finiteness condition remarkably only requires testing on Lie ideals, and we provide an explicit formula for the constant. Conversely, on homogeneous Lie groups such as the Heisenberg group, we prove an extinction theorem: the non-commutative twisting of the group forces all such geometric inequalities to trivially reduce to multilinear H\"older inequalities.
This is talk based on: Michael G. Cowling, Ji Li and Chong-Wei Liang, The Brascamp-Lieb inequality on compact Lie groups and its extinction on homogeneous Lie groups, arXiv:2602.10647
