/home/p/demo/demo/papers is for example a place where we sometimes work on joint papers.
All members of the lab are registered in the Unix password group "demolab". (type "groups" to know which groups you are a member of)
All files and directories here should be owned by the group demolab. By default it's likely that files created by you are owned by another group instead (i.e. "grad"). You can change by entering newgrp demolab; umask 002 so that new files you create will be owned by demolab and writable by others in the group.
Better yet, after doing some work there, go to the top directory where you've been working and type "makedemo". All files you created within the subtree will become demo owned and group writable.