Abstract:  Since the recent resolution of Carleson’s $\varepsilon^2$ -conjecture in the plane by Jaye, Tolsa, and Villa, and in higher dimensions by Fleschler, Tolsa, and Villa, it is known that the tangent points of certain domains are characterized via qualitative control on a certain spherical spectral function. In this talk, we will discuss a quantitative version of this conjecture - we will give a characterization of higher-dimensional, higher-regularity domains via quantitative conditions on the same spherical spectral function. This is joint work with Max Engelstein and Tatiana Toro.

 

Host: Ben Foster