| 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. |
