Hypergraph matching problems and multidimensional matrices

The talk aims to draw attention to the interplay between the hypergraph matching theory and the theory of diagonals in multidimensional matrices. We overview some classical or just nice results on existence and counting matchings in hypergraphs and see how the matrix approach works for them. In particular, we discuss matchings in d-partite d-graphs, the Ryser's conjecture and other generalizations of the Hall's theorem, upper bounds on the numbers of perfect matchings, and extremal cases for the existence of perfect matchings in hypergraphs known as space and divisibility barriers.