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Professor Figalli, fresh from his 2018 Fields Medal, discusses his initial disbelief at getting the award, his work that led to it, including seminal work in optimal transport. He also touches on some new work in free boundary problems, in particular studying interface in phase transitions. New developments in mathematics mean a chance of major progress in the field. He also touches upon his new role as ambassador for mathematics – in his home of Switzerland, birth country of Italy, as well as the world.

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