When you submit your application, you will receive a confirmation notice, which means that your application has been received. There are also two ways to check on your application.
The first is to use the tracking number given to you when you submitted the application online. If this shows you have materials missing that you are sure you've submitted, please contact the GSAS Admissions Office directly, as they receive all materials first before sending them to departments.
GSAS Admissions can be reached by calling (212) 854-6729, or emailing gsas-admissions@columbia.edu.