The non-linear Brascamp-Lieb inequality
报告题目(Title)：The non-linear Brascamp-Lieb inequality
报告人(Speaker)：Stefan Buschenhenke （德国基尔大学）
地点(Place)：后主楼 1124
时间(Time)：2019年9月9日 下午14:00-15:00
邀请人(Inviter)：薛庆营
报告摘要
We prove a nonlinear variant of the general Brascamp-Lieb inequality. Instances of this inequality are quite prevalent in analysis, and we illustrate this with substantial applications in the theory of oscil-latory integrals, abstract harmonic analysis and partial differential equa-tions. Our proof consists of running an efficient, or ”tight”, induction on scales argument, which uses the existence of Gaussian near-extremisers to the underlying linear Brascamp-Lieb inequality (Lieb’s theorem) in a fundamental way. A key ingredient is an effiective version of Lieb’s theorem, which we establish via a careful analysis of near-minimisers of weighted sums of exponential functions.
This is joint work with Jon Bennett, Neal Bez, Michael Cowling and Taryn Flock.
主讲人简介
Stefan Buschenhenke 博士于2014年4月毕业于德国基尔大学。先后在西班牙数学研究所、德国基尔大学、英国伯明翰大学做博士后；其研究兴趣是调和分析四大猜想方面的问题，如限制性定理和与曲面相关的极大函数等，目前与众多著名调和分析专家如A. Vargas, D. Mueller, J. Bennett, M. Cowling，I. Ikoromov等有深入广泛的合作。
