GitLab

Use a cookie for storing authentication token instead of sessions (sessions can't reliably have their expiration time extended without globally modifying the php ini file)
Rename $u_user to $this_user for better clarity
Change all uses of $_SESSION['user'] to the existing '$this_user' variable (and reduces the risk of stale user data being used for stuff)
Remove sessions altogether, since they're no longer being used for anything (they can be added back if anyone really wants them for something, but be aware that you'll have to recreate your session in auth.php, not just create it at login, since the PHP session is likely to expire a long time before the user's authentication token)

in user profiles/info, because this area is bound to expand soon.

This uses jQuery, which is available under an MIT license, so should be OK to use.
Otherwise, I'm happy if someone wants to rewrite it without the jQuery dep.