Sergei Rachmaninoff did indeed visit Madison, though long before your time. The great Russian composer and pianist played on campus as part of the seventh Concert Series in 1926–27. The concert was sponsored by the Wisconsin Union Theater but did not take place in the Union or Union Theater, since neither was built then.
Rachmaninoff first toured the United States in 1909, debuting his Piano Concerto No. 3. Although the successful tour made him a popular figure in America, he loathed the experience and declined offers of future concerts and several lucrative contracts. After the Russian Revolution, he decided that audiences in the United States might provide the solution to his financial concerns. He arrived in New York in 1918 and played 40 concerts in four months. From then until his death in 1943, Rachmaninoff traveled the United States as a touring pianist to support himself and his family. His busy concert career took a toll on his productivity as a composer, however, and an even bigger obstacle was homesickness.
During the years you attended UW-Madison, several outstanding pianists performed in the Union Theater, including Rudolf Serkin, Robert Casadesus, Vladimir Horowitz, Myra Hess and Artur Rubinstein. You can find a short summary of the Concert Series history and complete listing of Concert Series artists online.