Variable coefficient Lp local smoothing

I will discuss some recent work concerning variable coefficient extensions of Lp local smoothing estimates for the Schrodinger propagator. This can be thought of as a counterpart to a classical oscillatory integral operator bound of Bourgain (1991). Whilst Bourgain’s result relies on studying Kakeya sets of curves, our Lp local smoothing result relies on studying Nikodym sets of curves. An important observation of Wisewell (2005) is that the Nikodym theory is surprisingly different from the Kakeya theory. Our work aims to further investigate and exploit these differences. 

https://yale.zoom.us/j/91759982176?from=addon