He asked the three women to close their bodies into an even tighter circle, so that a bystander would want to know what they were talking about. He then told Coll, “You want to ease into that bubble one vertebra at a time.” They tried the sequence again a few times, and Coll’s approach to the circle became slinkier and more desperate, each phase of his rejection funnier and more pointed. Peck seemed satisfied, but his praise was understated: “Good. I like it. That was pretty good.”

As the dance unfolded it became a story about flirtation, with little valleys of power and crosscurrents of romantic innuendo: charming, fast, but punctuated by moments of poignant emotion. Early on, a group of three men executed a series of difficult lifts, with two collaborating to lift the third while all three rotated their bodies, again and again: They became a knot that was tying and untying itself. Peck, not quite satisfied, stepped into the dance to enact the lifts and turns himself, to see how they felt. “Try and be extra close,” he told them. “It can be like a Picasso painting. Limbs coming out of people in unusual ways.” They tried the movement again, and it got faster, bigger, messier. There was a feeling between Peck and the dancers of joyful collaboration.

Peck, like Robbins and Balanchine before him, has studied the dancers’ personalities deeply. Many of them were his classmates at the School of American Ballet, and they have been friends since they were teenagers. Peck knows their romantic lives, and he knows the private rituals they enact before they go onstage. He knows who is difficult and who is easy to work with, and whose gifts haven’t been sufficiently exploited. Craig Hall told me: “There’s no hierarchy in his ballets. There are principal dancers, and they’ll step out, but they go back into the group. It almost seems like it’s lonely to be by yourself. You want to go back into the herd. You’re comfortable and you’re stronger there.”

There’s a gesture from the third movement of the 2015 “Rodeo: Four Dance Episodes” — a dance set to music by Aaron Copland that is now part of the company’s repertoire — that encapsulates the way Peck leaves a bread-crumb trail of intimate knowledge of the dancers in his pieces. Peck created a pas de deux for Ramasar and Sara Mearns, who were once a couple but “maintained a really good professional relationship,” Peck said. He had been watching footage of migrating birds and wanted to capture the way two bodies moving at high speed, tantalizingly close to each other, could still maintain their independence. Mearns, Peck told me, is one of the strongest and most exacting dancers in the company, and Ramasar one of the few men who can comfortably match her. The choreography Peck created continuously shifts the literal and metaphorical balance of power between them. Mearns initiates moments of coupling, and sometimes supports Ramasar’s weight. It is a dance of equals. But then there is a moment — so subtle you could easily miss it — when Mearns lays her head on Ramasar’s chest, and almost imperceptibly, he flinches before wrapping his arms around her.

Most often in ballet, the male partner is the pillar on which the female dancer’s beauty is displayed. The male invites the female to dance, supports her as she balances en pointe, and takes her in his arms to lift her high above his head. Peck doesn’t reject these conventions outright, but he makes dances that reflect the moment he lives in, when power relations between men and women are constantly shifting, and gender and sexuality are more fluid. He watches the people around him, seeing how in the back of rehearsal, some of the women are joking around and lifting the men. “He realizes how strong people are,” Hall says, “and what you can do should not be boxed in by classifications.” Alastair Macaulay, The Times’s chief dance critic, told me that Peck makes refreshing use of the male corps de ballet, who are only occasionally featured on their own: “He makes them look motivated, aligned, passionate, as never before.”

Last October, for a performance of “The Times Are Racing,” Peck cast two men — Taylor Stanley and Daniel Applebaum — in its tender, sensual duet. It was widely seen as a statement of inclusion in a work that was already dealing with themes of resistance. But the idea of casting a same-sex pair didn’t begin in the abstract: Peck loved Stanley and Applebaum’s dancing in the piece, and he wanted two of his gay colleagues to be able to go onstage without any pretense, in just the same way he wanted all the dancers to feel comfortable in their sneakers.

One winter Sunday, I visited Peck and his fiancée, Patricia Delgado, in their apartment, a cheerful floor-through of a brownstone on the Upper West Side. They greeted me at the door wearing matching slippers, embraced me and offered me a warm drink. As Peck puttered around his kitchen, producing a mug from a large cabinet filled with colorful dishes, a slight guardedness I’d previously felt from him began to dissolve. He brought me a cup of peppermint tea, and we all sat together at a long wooden table. Delgado took up a needle and thread and a pair of pink silk pointe shoes and starting deftly sewing an elastic band. Mending shoes is a constant activity for ballerinas, and Delgado, laughing, told me, “If men had to do this, they wouldn’t be dancers.”