Publons will serve you in-app notifications about a number of different things and all of those notifications can be seen in the Notifications page of your private dashboard. 

Every week we will send a summary of the notifications that have been created for you on profile to your primary email address.  This email can be turned off along with any other “Reminder” emails by deselecting the “Send me emails with reminders and tips on how to use Publons” option in your email preferences.