Where does ubuntu 14.04 drop core files?

By default, the Ubuntu kernel is configured to use apport to log coredumps. You can override this by overwriting /proc/sys/kernel/core_pattern, check the "Naming of core dump files" section in man core for details. For example:

echo '/tmp/core.%e.%p.%t' | sudo tee /proc/sys/kernel/core_pattern

Apport writes core dumps to /var/crash/_path_to_program.userid.crash, BUT it will only do so for applications installed from the main ubuntu apt repositories.

More info on apport: https://wiki.ubuntu.com/Apport

I think this is a more Linux kernel thing than a specific Ubuntu thing. Check out

cat /proc/sys/kernel/core_pattern

Check out the core file man page