I had the privilege of studying music and playing in the band at Northern while Dennis Dafoe was directing there. Both he and Toby Rath were truly wonderful teachers and taught me so much in both the high school and college levels!
The piece played by the Vera is the Scherzo in B-flat Major, D. 593 No.1, by Schubert. I've been searching for it too, until I found it listed as "Schubert" in my cell ringtones!