Around spin Hurwitz numbers

We present a review of the spin Hurwitz numbers, which count ramified coverings with structures. It is known that they are related to characters Sergeev group and Q Schur functions. This allows one put whole story into context matrix models integrable hierarchies. The generating functions numbers $$\tau ^\pm $$ hypergeometric -functions BKP hierarchy; we their fermionic realization. cut-and-join equation in form heat written down. explain, how special d-soliton KdV Veselov–Novikov hierarchies generate $$H^\pm \left( \Gamma ^b_d \right) ^b_d,\Delta . well-known Kontsevich integral as -function neutral fermion vacuum expectation values (few different ones). also explain rewrite certain (including one) using relations between projective