The action center and its notifications are a very useful feature introduced in Windows 10: in particular, it allows also (by default) to be notified in real time of arriving messages/emails, push notifications from app (and even more) using a temporary popup window that appears on the right bottom of the screen.
However, especially when you are doing a presentation, this feature can be annoying! No problem: it is very easy to temporary switch off this feature for all the notifications or even only for the ones related to some app (e.g. Mail app).
Following screenshots show how it can be done from All Settings -> System -> Notifications & actions or from the settings page of a specific app (e.g. Mail app).
In general, you can definitively do it switching off the Get notification from apps and other senders option. However, very often, if you duplicate screen only while you are doing a presentation (connecting your PC/tablet to a projector, it will be sufficient to switch on the Hide notification when I’m duplicating my screen option.
Moreover note that tablet mode is not available when Extended these displays is set, so you need to choose the Duplicate these display option if you want to use that feature. In fact, in the previous setting it should not be clear from which possibly touch screen the O.S. should take inputs!!