in this research community

## Fourier restriction conjecture and related problems

American Institute of Mathematics, Pasadena, California

organized by

Dominique Maldague, Yumeng Ou, Po-Lam Yung, and Ruixiang Zhang

This research community, sponsored by AIM and the NSF, is for mathematicians studying Fourier restriction theory and related problems. Originating from a deep observation of Stein in 1967, the Fourier restriction conjecture predicts that if $S$ is a curved smooth submanifold of Euclidean space, then taking the Fourier transform and restricting to S extends to a bounded linear operator (from $L^p(\mathbb R^n)$ to $L^1(S)$, for certain $p$). This is somewhat unexpected since the Fourier transform of an $L^p$ function is a priori only almost everywhere defined and $S$ is a zero measure set in $\mathbb R^n$. This conjecture is deep and far-reaching and has surprising connections to PDE, number theory, incidence geometry, combinatorics and geometric measure theory.

Our research community hosts small working groups, occasional larger problem sessions and seminars, and periodic social events. Our main aim is to introduce earlier career mathematicians to the field and to the community, as well as to facilitate collaborations within the field.

If you are interested in joining our research community, please fill out this application form. Applications are open to all, and we especially encourage women, underrepresented minorities, and researchers from primarily undergraduate institutions to apply.

For more information, see the home page of this research community or email *research@aimath.org*