for this workshop
Flag algebras and extremal combinatorics
at the
American Institute of Mathematics, Pasadena, California
organized by
Jozsef Balogh, Dingding Dong, Bernard Lidicky, and Annie Raymond
This workshop, sponsored by AIM and the NSF, will be devoted to further developing the method of flag algebras and its applications. Flag algebras, developed by Razborov in 2007, allows one to solve problems in combinatorics via streamlined calculations that combine elements from computer engineering and optimization. It led to many recent breakthroughs on long-standing open problems of Erdős, Sós, Turán, Gromov and Zarankiewicz, to name a few. The technique is versatile and can be applied in other settings than graphs and hypergraphs including permutations, oriented graphs, point sets, embedded graphs, and phylogenetic trees.
The main topics for this workshop are:
- Applications of flag algebras to topics in combinatorics, such as hypergraph Turán problems, rainbow Turán problems and Sidorenko's conjecture.
- Better understanding the strengths and limitations of flag algebras, e.g., to prove inequalities that generate all valid inequalities of a certain form and to find classes of problems that cannot be solved with the method.
- Obtaining proofs by flag algebras which are not using computers.
This event will be run as an AIM-style workshop. 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.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than May 13, 2025. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
