We are investigating these reports of black screens. At this time I recommend the following steps. Please first disable background applications and then verify your game/files (Uplay or Steam). Please do not enable those applications for the rest of troubleshooting and please try the game in between steps.
If you have continued issues please perform the remaining steps in our PC crashing FAQ. The final step from that FAQ is to send in your system files. Please make sure background applications are still disabled if you get to that point and send us your files. They will help us to determine the cause of this issue.