This is one of my biggest frustrations. What could be more important than telling a user that their task is ready to start? IMHO, nothing! So while there is a notification that others have pointed out, I have found this to be the least informative and most confusing notification, and it is "by design" which I found out after questioning it, thinking it was a bug.
The "Ready to Start" notification is not clear at all. The user gets a notification that the predecessor is done (which is in GIANT font and is also the least important piece of information in the notification which makes it really confusing to people who can't understand why they are getting it, and thusly wind up turning it off, so there's that problem), and then it shows at the bottom which tasks are ready to start. BUT the ready to start tasks listed don't say your name, it says which ROLES are ready to start working on which tasks. It also lists all the other tasks ready to start that often have nothing to do with the person getting the notification. And to top it off, If there are more than a couple of tasks that are ready to start, the notification doesn't have room to list them all, so you may get this notification and your task that is ready to start isn't even listed!!
Jill Ackerman