for this workshop
Additive combinatorics and its applications
American Institute of Mathematics, San Jose, California
Ben Green, Shachar Lovett, Olof Sisask, and Madhur Tulsiani
This workshop, sponsored by AIM and the NSF, will be devoted to additive combinatorics and its applications in mathematics and computer science. One of the chief concerns of additive combinatorics is the classification of sets or functions that are only approximately algebraically structured, and results in this direction have turned out to be useful in diverse parts of mathematics and theoretical computer science, for instance in finding linear structures in various sets of integers and in property testing. Conversely, the need for stronger results to cater for applications has driven the development of additive combinatorics. The aim of this workshop is to gather researchers from all sides of these developments in order to tackle some of the area's fundamental problems.
The main topics for the workshop are:
- New applications for additive combinatorics in number theory and algorithm design and analysis
- The polynomial Freiman-Ruzsa conjecture, one of the central open problems in additive combinatorics
- The new polynomial method of Croot-Lev-Pach and Ellenberg-Gijswijt; Understanding its power and limitations, and how to overcome them.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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