White to move! Win, lose, or draw? How should white proceed?
For example- after 1.Qe7, a move to the b-file by the king is met by 2.Qb7+ followed by 3.Kg2, and the black king must avoid the g8-a2 diagonal, so 1.....Kd4 is met by 2.Qd6+ followed by 3.Qb6, from which he can maneuver with checks to get to b7 and the king to g2.
I think 1.Qe7+ is the way to go- white wants one of two things- get the queen to b6 supporting the pawn's advance to a7 and protecting f2 for a move- or even better, getting the queen to b7, and then move the king to g2 protecting the f2 pawn. The position should eventually reduce to the latter state eventually, and black can't defeat this with any king moves, nor can I see any queen maneuvers that are fast enough to get to a draw by repetition.