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His last album Imaginary Room (2012), including musicians like Lars Danielsson, Jacob Karlzon, Verneri Pohjola, Morten Lund and Marius Neset, have opened the most important music scenes for Bałdych, and he was invited to the biggest jazz festivals in Europe like the Montreux Jazz Festival in Switzerland and the London Jazz Festival.
In 2010 he produced a new project at the invitation of London Sinfonietta called One Day in which he set to music a Saturday edition of the Guardian newspaper, performed at London's Southbank Centre in the London Jazz Festival.