This project aims at systematically analyzing and studying the combinatorial statistics database FindStat with machine learning techniques. The two guiding open problems are longstanding questions in enumerative, bijective and algebraic combinatorics. They concern the famous q,t-Catalan numbers. The first is to find a combinatorial proof of their symmetry and the second is to find a combinatorial definition for general reflection groups. These two longstanding open problems are perfect candidates to be approached using machine learning techniques. A lot of research has been devoted to solutions and we expect machine learning combinatorial statistics and maps to provide genuinely new combinatorial insight.

An arrangement of finitely many linear hyperplanes is simplicial if all its regions are simplicial cones. From the geometric perspective, simpliciality imposes strong restrictions and it is widely believed that simplicial arrangements are rare. In contrast to the geometric side, computer experiments suggest an abundance of simplicial matroids! This project initiates a coherent study of simpliciality in arrangements and matroids with an emphasis on algebra, combinatorics, and geometry. The three main directions of research, Generation and Realization, Algebra and Convexity, and Matroidal and Simplicial Combinatorics are pursued in parallel.