Czifra Domonkos: Linear programming bounds for geometric problems

We introduce a general linear programming method to bound the density of sets avoiding certain "patterns". For example, sets in \R^d containing no segments of length 1, or sets on the sphere \S^d containing no orthogonal vectors. In the latter case we apply our method to improve upon the best existing bound in the literature. The method also involves the search for certain "witness" sets, for which we developed an efficient algorithm, using Monte Carlo Tree Search, and using ML to evaluate states.
Joint work with Mate Matolcsi, Daniel Varga and Pal Zsamboki.