ELSV-type formula for the monotone Hurwitz numbers

Hurwitz numbers enumerate factorization of permutations into the product of a given number of transpositions. Monotone Hurwitz numbers enumerate similar factorizations satisfying certain monotonicity condition. The classical now ELSV formula expresses Hurwitz numbers as intersection numbers on moduli spaces of complex curves. We announce an analogue of this formula in the monotone case. Its derivation is based on the topological recursion for these numbers obtained earlier by Do, Dyer, and Mathews