The Analysis and PDE Seminar will take place on Monday, December 5, in room 740, Evans Hall, from 4:10-5:00 pm.

Speaker: Casey Jao

Title: Mass-critical inverse Strichartz theorems for 1d Schr\”{o}dinger operators

Abstract: I will discuss refined Strichartz estimates at $L^2$ regularity for a family of Schrödinger equations in one space dimension. Existing results rely on sophisticated Fourier analysis in spacetime and are limited to the translation-invariant equation $i\partial_t u = -\tfrac{1}{2} \Delta u$. Motivated by applications to mass-critical NLS, I will describe a physical space approach that applies in the presence of potentials including (but not limited to) the harmonic oscillator. This is joint work with Rowan Killip and Monica Visan.