Organizers: Alan Chang (Washington University of St. Louis), Zane Li (North Carolina State University), Po-Lam Yung (Australian National University)
This research community, sponsored by AIM, is for mathematicians studying Fourier restriction theory and related problems. Our main aim is to introduce early career mathematicians to the field and to the community, as well as to facilitate collaborations within the field.
Previous organizers include: Dominique Maldague, Yumeng Ou, and Ruixiang Zhang.
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(NEW! July 17, 2025) We are sponsoring an event for online research group projects for graduate students/early career postdocs. The rough timeline will be that projects start in early September and groups ideally will meet online semi-regularly throughout the year. Successful applicants will receive a list of projects that they can rank their preferences and we will assist in formation of research groups paired with a designated mentor.
The proposed projects build upon our a stream of new results concerning Fourier restriction, Kakeya, square function and decoupling inequalities, by many forerunners in our field. They are of a varying level of difficulties and will likely benefit from a combination of geometric, combinatorial, and/or number theoretic ideas. Some of these questions will feature submanifolds of the frequency space with intermediate dimensions and co-dimensions. Some of them investigate the role of curvature, in particular when they degenerate. Some others will help one build a better understanding of the latest technology, and maybe improve upon them. Familiarity with induction on scales, orthogonality (e.g. along the lines of the high-low method), and transversality (such as Brascamp-Lieb and its perturbation) will be useful.
A brief description of goals, expectations and projects is available here.
If interested please apply here by August 29, 2025.
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Please sign up here if you are interested in joining the community. Members of this community will, among other things, have the opportunity to take part in online research projects, and receive communications from us about our activities. We welcome contributions from members of the community who could offer mentorship to more junior researchers in our field, or more generally run other initiatives that will help us grow into a better community.
If you have written a paper with other members of this community and have acknowledged AIM for their support, please let us know via this Google form so that we can report to AIM in due course.