local smoothing estimate for the Fourier integral operators satisfying cinematic conditions

Speaker: Prof. Changxing Miao,Institute of Applied Physics and Computational Mathematics, Beijing

Title: local smoothing estimate for the Fourier integral operators satisfying cinematic conditions
Time&Venue：2022.05.05 17:00-18:00 N913
Abstract: Local smoothing conjecture which was formulated by Sogge has close relationship with other significant conjectures such as Bocher-Riesz conjecture, restriction conjecture and  Kakeya conjecture,  and finds its extensive applications in Harmonic analysis and PDEs . In this talk, we will present the recent improvement of local smoothing estimate of a certain class of Fourier integral operators satisfying cinematic curvature conditions. The main ingredients in our proof are wave packet decomposition, the Bourgain-Guth argument and the polynomial method,   variable coefficient decoupling inequality and square function estimates.   This talk is based on a series of joint works with Chuanwei GAO, Bochen Liu and Yakun Xi.