Create a zip-up hoodie design that members of Facebook's Notifications team will feel happy to wear to work and around town frequently.
Use icons, images or text that are related to Facebook notifications. Ideas include Facebook's F icon, the globe for notifications with a count for new notifications, a mobile phone, an envelope for email. Maybe also the word "Notifications".
Also, consider using some line chart that shows an arrow going up and to the right since the Notifications team is part of Facebook's Growth team - the Growth team is responsible for ensuring that Facebook's monthly active users and daily active users continues growing.
You don't have to use all the ideas listed above. They're there just to suggest some ideas.
Also, feel free to experiment with putting things on different parts of the hoodie (chest, sleeves, back, etc.).
Finally, I've attached an image of a logo that people liked. This logo worked well because: 1) it incorporates important elements of growth (line chart which depicts user growth that is up and to the right, global reach of FB and bars in the G that show more growth) and 2) it's simple and clean.