Upon graduation, she commenced an eight-week tour of the United States, culminating on November 27, 1963, at Carnegie Hall in New York City.
In 1961, she participated in and won Le Premier Prix at the Concours International Marguerite Long-Jacques Тhibaud in Paris.
Mdivani has taught at institutions in Eastern Europe and the Middle East and has also served on the juries of international competitions.
Often, her programs were unusual; for example, on January 24, 1986, in the Great Hall of the Moscow Conservatory, Mdivani performed all five piano concertos of Sergei Prokofiev in one concert.
1; Stravinsky – Concerto for Piano and Wind Instruments; Solo repertoire: Works by Bach, Beethoven, Brahms, Busoni, Chopin, Debussy, Gubaidulina, Haydn, Hindemith, Kefadis, Liszt, Mendelssohn, Mussorgsky, Mozart, Ovchinnikov, Prokofiev, Rachmaninoff, Reger, Schnittke, Schubert, Schumann, Scriabin, Stravinsky, Taktakishvili, Tchaikovsky and many other composers.