Sharp local smoothing estimates for Fourier integral operators
报告题目(Title)：Sharp local smoothing estimates for Fourier integral operators
报告人(Speaker)：Christopher D. Sogge 教授（Johns Hopkins University, USA）
地点(Place)：后主楼 1124
时间(Time)： 2019年1月15日 15:00 - 16:00
邀请人(Inviter)：徐桂香
报告摘要
We present joint work with D. Beltran and J. Hickman on sharp local smoothing estimates for general Fourier integral operators. Local smoothing bounds imply major estimates in harmonic analysis, including Bochner-Riesz estimates, oscillatory integral estimates and bounds for the size of Besicovitch sets and related problems involving Kakeya maximal functions. Our work gives a sharp resolution to the most general form of the local smoothing problem formulated by the speaker in the early 1990s. We rely on decoupling estimates of Bourgain and Demeter.
主讲人简介
Chris Sogge教授1982年本科毕业于芝加哥大学，1985年博士毕业于普林斯顿大学，师从E.M.Stein教授，是调和分析领域Stein学派重要代表人物，是杰出的调和分析与偏微分方程专家，Chris Sogge教授在Fourier积分算子理论、限制性定理、波动方程Strichartz估计及流形上Laplacian算子特征函数估计等领域做出一系列杰出的学术成果，出版专著《Lectures on Nonlinear Wave Equations》、《Fourier Integrals in Classical Analysis》、《Hangzhou Lectures on Eigenfunctions of the Laplacian》。已发表100余篇学术论文，其中十余篇学术论文发表在Acta. Math., Ann. Math., J. Amer. Math. Soc., Invent. Math.顶级期刊。Chris Sogge教授获得如下学术荣誉：
1985 NSF Postdoctoral Fellowship, 1985
1988 Sloan Fellowship, Presidential Young Investigator Award
1994 Invited speaker, International Congress of Mathematicians, Zurich
2005 Guggenheim Fellow
2007 Johns Hopkins Diversity Recognition Award
2012-13 Simons Fellow
2013 Fellow, American Mathematical Society
2014 Professor of the Year, JHU Mathematics Department
