Unity app won't start

I recently got a Mac Mini and an iPad to develop Unity3d apps. However, Unity applications crash immediately after launch.

Here's what I do: make an _empty_ project in Unity. Build it (non-development build, no stripping, no call optimisation - all default). Build it in xcode and run. The app launches on the iPad (shows the "Made with unity3d" splashscreen) and immediately exits. I sprinkled some logs in AppContoller.mm and found that it's the UnityInitApplication function that crashes....

Unity app won't start