Analytic Techniques in Combinatorics (ANACOMB)

Hellenic Foundation for Research and Innovation (H.F.R.I.)

Project Number: HFRI-FM20-02717

This research project is devoted to the study of classical problems in combinatorics. Its novelty lies in the fact that it is based on methods from analysis. The interaction between the two fields—analysis and combinatorics—is a relatively recent trend which has been promoted by some of the best analysts of our time. It has already led to several advances, and it is expected to become more mainstream in the future, especially after the engagement of theoretical computer science in this interaction.  Specific research goals include: 

• the density polynomial Hales–Jewett conjecture; 

• bounds for the density Hales–Jewett theorem; 

• concentration estimates for functions of finite exchangeable random arrays; 

• euclidean Ramsey theory; 

• indivisibility and oscillation-stability.