学术报告（甘盛文 2025.5.27）

摘 要 : Sogge made the local smoothing conjecture for wave equations in 1991. To study this problem, Wolff introduced the decoupling inequality in 2000. Later in 2014, Bourgain-Demeter proved the sharp decoupling inequality, and as a corollary, they proved a local smoothing estimate at the Stein-Tomas exponent p=2(n+1)/(n-1). In this talk, I will discuss how to improve this exponent. I will introduce several new techniques developed recently in harmonic analysis, for example, two-ends incidence estimate, refined decoupling and wave packet density.