Seminar: Stability of the Heisenberg Uncertainty Principle in some geometric settings

Thời gian: 14:00 đến 17:00 Ngày 13/08/2025

Địa điểm: Phòng C102, VIASM, 161 phố Huỳnh Thúc Kháng, Hà Nội

Báo cáo viên: Do Xuan Anh, University of Connecticut.

Tóm tắt: This talk provides an overview of recent advancements in the study of stability results for functional and geometric inequalities, with a particular focus on the Heisenberg Uncertainty Principle (HUP). A key component of deriving such stability results is the establishment of corresponding identities and Poincaré inequalities for Gaussian measures. While Poincaré inequalities for Gaussian measures are well-understood in Euclidean spaces, their counterparts in other settings remain unknown. In this talk, we introduce a Poincaré inequality for Gaussian measures on hyperbolic space, along with several variants that incorporate scaling parameters. These results allow us to establish L 2 -stability results for a general case of the HUP in the hyperbolic setting. If time permits, we also dicuss the sharp stability estimates for the second order HUP. This work is part of a joint collaboration with Guozhen Lu, Nguyen Lam, Debdip Ganguly, Joshua Flynn, and Lingxiao Zhang.