The War Room - The People Window
You get to the People Subscreen by pressing this button:
The left panel continues to accept and display chat for the Gathering you are presently in; the right panel shows a list of people in your currently selected Gathering. Clicking on a person's name brings up their publically available profile information.
You can press the button to bring up the Page Dialog. You can page anyone - not just the people in your currently selected Gathering.