Columbia does send you something in the mail verifying that they recieved your AADSAS report. Then they will send you via regular mail an interview invite. But it takes a while . . . .
I sbmitted AADSAS on May 21, 2004
they recieved it on June 8, 2004
they sent me the interview invite on Aug. 15 or so.
So just be patient. they do seem to be more on the ball with admissions than a lot of other schools, so hopefully you will hear something soon.