These notifications are what you see when you click the bell in the upper right. This new system replaces the one I made live two weeks ago. Whenever somebody actively *edits* (using the web interface) any file in any project you collaborate on, a notification will get created or updated. If a person *comments* on any file in any project you collaborate on (using the chat interface to the right), then not only does the notification get updated, there is also a little red counter on top of the bell and also in the title of the SageMathCloud tab. In particular, people will now be much more likely to see the chats you make on files.
NOTE: I have not yet enabled any sort of daily email notification summary, but that is planned.
Some technical details: Why did this take all week? It's because the technology that makes it work behind the scenes is something that was fairly difficult for me to figure out how to implement. I implemented a way to create an object that can be used simultaneously by many clients and supports realtime synchronization.... but is stored by the distributed Cassandra database instead of a file in a project. Any changes to that object get synchronized around very quickly. It's similar to how synchronized text editing (with several people at once) works, but I rethought differential synchronization carefully, and also figured out how to synchronize using an eventually consistent database. This will be useful for implementing a lot other things in SageMathCloud that operate at a different level than "one single project". For example, I plan to add functions so you can access these same "synchronized databases" from Python processes -- then you'll be able to have sage worksheets (say) running on several different projects, but all saving their data to some common synchronized place (backed by the database). Another application will be a listing of the last 100 (say) files you've opened, with easy ways to store extra info about them. It will also be easy to make account and project settings more realtime, so when you change something, it automatically takes effect and is also synchronized across other browser tabs you may have open. If you're into modern Single Page App web development, this might remind you of Angular or React or Hoodie or Firebase -- what I did this week is probably kind of like some of the sync functionality of those frameworks, but I use Cassandra (instead of MongoDB, say) and differential synchronization.
I BSD-licensed the differential synchronization code that I wrote as part of the above.