How to remove alu seat post from carbon frame?
What you need is some way to grip or gain purchase on the post so you can apply a force to, then apply the usual methods to free the post from the frame.

Possible means of gripping the post I can think of:


Old quill stem inserted into stem and tightened
Star fangled nut inserted into seatpost, with a long bolt threaded into it.


GCN has a video showing how to use hot water to free up the post. It seems that a substantial amount of force is still needed to pull the post out though.