In harmonic analysis, the pointwise convergence problem for the solution to the Schrödinger equation, sometimes called Carleson's problem, has recently drawn enormous attention and progress has been significant. There are also a number of natural variations of the classical problem. Cho, Lee and Vargas took a wider perspective and sought to understand the effect of varying the paths of convergence; along lines generated by a given fractal set, and along a tangential curve. I will introduce the new ideas in our recent work that allowed us to extend the results obtained by Cho--Lee--Vargas from the standard Schrödinger equation to the fractional Schrödinger equation. Part of the talk is based on collaborative work with Chu-hee Cho from Seoul National University.

Note: This seminar will be held as a Zoom online seminar.