Is it possible to identify who deleted my shared folder? My Mac, in my workplace, can be accessed from other Mac systems (file sharing is enabled, and it has no password set).

I've found out there are 2 folders were deleted (missing from my desktop). 

How can I check who was connected to my system or who was access my desktop remotely, so that I can identify who deleted my folder?
Regrettably Mac OS X does not log file access and changes by default. The user responsible for deleting the two folders is unlikely to be identifiable through your Mac's log files.

There are records kept of file changes in .fseventsd but these are at a block level, rather than the folder and file level.

Third party file recovery tools may still be able to recover your two lost folders.