Celebrated in America, where he now resides, he is being showcased at the Barbican, in London, where audiences are joining the club of those who regard his passionate eclecticism as one of classical music's most hopeful routes to the future.
He'll use anything to hand - for him a laptop is as much a musical instrument as a violin or cello - and when I meet him he is immersed in two parallel tasks: writing a cello concerto, and "something" for the Kronos Quartet to perform with the Inuit singer Tanya Tagaq.
But what he most wants to talk about is a project that will shortly consume all his energies: composing a score for Francis Ford Coppola's forthcoming film of Mircea Eliade's philosophical novella Youth without Youth. A mediocre book, he says, but a wonderful script.
The project sprang from Coppola's 20-year ambition to make a film based on the life of Robert Moses, the official who tore down half of New York in the Fifties to free up space for brand-new highways. The film, to be called "Megalopolis", also drew on the Catiline conspiracy in ancient Rome.
"It would be set in New York in the near future, but it would also reflect Rome in its decadence," Golijov explains. "It would be an epic, with an intermission, like an opera. But Francis's father had been a composer, and had written some of the music in The Godfather and Apocalypse Now, and Francis didn't want to use a Hollywood composer.
"He asked around, heard my stuff and liked it, and sent me a beautiful handwritten letter. And we agreed that I would write a symphony for 'Megalopolis', previous to the shoot. If it worked for him, he would take his cues from it: the symphony would dictate the rhythm of the film, which is something almost unheard of these days."
The project was abandoned when Coppola didn't get the backing. But he remained fascinated by a character in "Megalopolis" who had the power to freeze time, and he found a novel based on the same idea. Youth without Youth is about the nature of time and consciousness. "My immediate response was that I must make something haunting," says Golijov. "And I wanted to do so with just a zither, but unfortunately The Third Man already exists. However, I think we will end up doing something similar."
The Barbican programme began with a night of premieres led by Golijov's new song-cycle, Ayre, performed by his muse, the soprano Dawn Upshaw. This piece is an electrifying meld of Christian, Jewish and Arab songs from medieval Spain, plus two he wrote himself. Instrumentation ranges from oud to klezmer clarinet to many varieties of percussion. Ayre is, Golijov admits, autobiographical: "It's the piece that is closest to who I am. A Jew raised in a Catholic country, who moved to Jerusalem, where he was mesmerised by the Arab culture. The songs deal with the matters that are the most important in life: love and the possibility of the existence of God."
Golijov's first inspiration was the music of the Argentinian composer Astor Piazzolla. After the military junta took power, he left for Jerusalem, and later studied under the composers George Crumb and Oliver Knussen. What put Golijov on the map was an invitation from the conductor Helmuth Rilling to compose a Passion for Latin America. "I said, 'No, I'm Jewish - I can't write that', and he said, 'You can simply do your reaction to the Passion.'" La Pasion segun San Marcos, with its black Jesus, will be sung at the next Barbican concert, later this month.
Golijov wanted to focus on the contrast between the church hierarchy and people in the time of Jesus, who was a low-rank priest. "For me the parallel with my own country lay in the way the archbishop of Buenos Aires blessed the weapons of [General] Videla, and in the way low-rank priests who worked in the slums were being 'disappeared' and killed."
'La Pasion Segun San Marcos', Barbican, London EC2 (020 7638 8891) 24 February. 'Ayre' is on Deutsche GrammophonReuse content