Richard Chen See is setting up for a rehearsal at the Alvin Ailey American Dance Theater studio. Today, the company will be running through choreographer Paul Taylor’s fiery “Piazzolla Caldera” for the first time. Chen See danced in the very first performance of the piece for the Taylor Company in 1997, and he’s now staging it — and running the practices — for Alvin Ailey.

“It’s like learning a brand new language,” he says about “Caldera,” a work inspired by the music of the Argentine composer Astor Piazzolla. “The tango is a working-class dance, and the dancers have to interact with this Latin desire, but combine it with the clean precision of modern dance.”

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It’s also technically demanding: A male dancer glides across the room, two women hanging from his arms; one man suddenly flips another upside down and, while holding each other, the two begin doing a series of cartwheels; there’s a lot of violent tussling and intricate footwork and an almost desperate hunger in the performers’ interactions.

“That’s the great thing about tango,” says Chen See. “You can be totally in love or at odds and battling, sometimes at the same time.”

“Piazzolla Caldera” is just one of — count ‘em — four company premieres (three of them world debuts) that Alvin Ailey has planned this winter season. Also on deck: Ronald K. Brown’s Cuban-inflected “Open Door,” featuring music by Arturo O’Farrill and the Afro Latin Jazz Orchestra; “Untitled America: First Movement,” the first of a three-part series about the U.S. incarceration system created for the company by choreographer and MacArthur “Genius” Kyle Abraham; and “Awakening,” the first work choreographed by Robert Battle since joining Alvin Ailey as artistic director in 2011.

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“I have eclectic tastes,” says Battle in his office, talking about his reasoning behind the season’s ambitious programming. “It’s hard to distill into one sentence what my vision is, but I think of [company founder] Mr. Ailey’s generous spirit, the community he fostered, every day. And I know there are some things I do that ruffle feathers, but sometimes the things worth doing are the things that people don’t understand right away.” After all, he says, look at Stravinsky’s “Rite of Spring,” one of the most notorious — and important — ballets ever performed. “I just follow my gut and see where that leads.”

That spirit of adventure and experimentation is part of the company’s DNA. Started in 1958 by African-American choreographer Alvin Ailey, the multi-racial troupe combined elements of ballet, jazz and traditional African dance, and from the beginning confronted such issues as slavery, racism and injustice through movement. But their performances were also celebrations of black and minority cultures, such as an early work paying homage to the blues and Ailey’s Southern childhood in Depression-era Texas.

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The Alvin Ailey Dance Theater will be mounting a new production of that piece, “Blues Suite,” as well as another Ailey classic, “Cry,” created in 1971 for his muse, Judith Jamison. “It was a birthday gift for Ailey’s mother, and it was a real collaboration between him and Jamison,” says Battle. “It was one of the great partnerships in dance, and it’s something that will live on for a long, long time.” And for this production, the 72-year-old Jamison will be coming into the studio to coach the dancers herself.

“It’ll be one of those moments that you just wish you had been in that room to witness,” says Battle. “That’s definitely one of the highlights of the season.”

Alvin Ailey American Dance Theater will perform at New York City Center from December 2 – January 3. For tickets, go to the its website.

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