back in germany he returned to the ruhr university at bochum where, supervised by zehnder, he undertook research on v i arnol'd's fixed-point conjecture for symplectic maps.

How would the previous sentence be correctly capitalized?
Back in Germany he returned to the Ruhr University at Bochum where, supervised by Zehnder, he undertook research on V I Arnol'd's fixed-point conjecture for symplectic maps.