In 1989, he traveled to the United States. That same year he won first prize in the Robert Casadesus International Piano Competition. After he won first prize in the Palm Beach International Piano Competition and first prize in the Hamamatsu International Piano Competition, he became a Laureate of the Queen Elisabeth Music Competition in 1991.
Babayan won first prize in the Scottish International Piano Competition and third prize at the Busoni International Piano Competition. He was a prize winner at the Esther Honens International Piano Competition.
His programming often includes Romantic composers such as Rachmaninoff, and modern works by composers such as Witold Lutosławski, György Ligeti, Carl Vine and Arvo Pärt. He is also recognized for his prominent interpretations of Johann Sebastian Bach. He frequently appears as a soloist with such orchestras as The National Orchestra of Belgium, The Cleveland Orchestra, The Italian Symphony Orchestra of Brescia & Bergamo, and the Czech State Philharmonic.
Babayan has collaborated with such conductors as Valery Gergiev, Yuri Temirkanov, Neeme Järvi, Hans Graf, David Robertson, Kazimierz Kord and Michael Christie. He has recorded with Deutsche Grammophon, the Connoisseur Society label, Discover Records and Pro Piano Records.
In 1996, Babayan founded the Sergei Babayan International Piano Academy at the Cleveland Institute of Music, where he is also an Artist-in-Residence. His students have included the pianists Grace Fong, now Director of Keyboard Studies at Chapman University Conservatory of Music; Mei-Hsuan Huang, Steinway Artist and Assistant Professor of Piano at Iowa State University; Ching-Yun Hu, winner of the 2008 Arthur Rubinstein Competition; Stanislav Khristenko, winner of Cleveland International Piano Competition and fourth prize winner at the 2013 Queen Elisabeth Competition, and Daniil Trifonov, Third Prize winner of 2010 International Chopin Piano Competition, First Prize winner of the 2011 Arthur Rubinstein Competition, and First Prize winner of the 2011 Tchaikovsky Competition.
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