White to move! How should white proceed?
Wow. I found the first move really quick, but it is puzzling out the best defenses that is the key here. The point is that the black rook at h8 is hanging, and if you keep the threats against the king active, then that rook can't move. It takes a grandmaster to keep this all from spinning out of control over the board- hats off to Kogan! In any case- the first move is 1.Rc8!
1.Rc8+ Qc8 (forced)
The point is that the black queen is deflected allowing white to capture at b4:
Threat here is that white is going to play Nd4 attacking the knight at f5 which is all that preventing Qe7 with mate. Black has to find a way to get other protection on that square, but it isn't easy to find. The best I can see is the following line:
2.........Rb8 3.Qa3! Qc2 4.b3!
The idea of black's last two moves is to put the queen on b4 (via c3) or c5 after Rc8, to block the white queen's access to e7. Best I see is...
The idea is to drive the queen away from guarding the d4 square.
5......Qb4 6.Qb4! Rb4 and finally 7.Bh8 leaving white up a full piece, the bishop taken at b4 at move 2. There are other lines I haven't shown, but the most critical is the one where black tries to save the rook at h8:
1.Rc8 Qc8 2.Qb4 Rb8 3.Qa3 Rh7 4.Nd4! Qb7 5.Nf5 Qb4 6.Qb4 Rb4 7.Nd6+ Kf8 8.b3 and white has two pieces for a rook, and the knight at d6 is a monster knight- totally winning.