Our guide to dance performances happening this weekend and in the week ahead.

A.I.M. at the Joyce Theater (Oct. 15-16, 7:30 p.m.; Oct. 17-18, 8 p.m.; through Oct. 20). Kyle Abraham’s work combines artistic experimentation and identity exploration, with influences ranging from postmodern dance to the hip-hop and club scenes in Pittsburgh, where he grew up. This eclectic program reflects that spectrum: It includes “Solo Olos,” a 1976 dance by one of Abraham’s idols, Trisha Brown; “Show Pony,” a short, spiky solo that’s all attitude; and an ensemble piece by Keerati Jinakunwiphat, a company dancer. Abraham also introduces a new solo for himself, with live gospel choir, and on Tuesday only, the ballerina Misty Copeland performs a charged solo that Abraham recently created for her.

212-242-0800, joyce.org

AMERICAN BALLET THEATER at the David H. Koch Theater (Oct. 16, 6:30 p.m.; Oct. 17, 7:30 p.m.; through Oct. 27). Wednesday’s season-opening gala is composed of one classic and two new works. That classic is George Balanchine’s “Theme and Variations,” an elegant exercise in stamina that he made for Ballet Theater in 1947. The premieres come courtesy of Jessica Lang, who created a short, jazzy piece set to songs by Tony Bennett, and Twyla Tharp, with her first new work for this company in a decade. Tharp’s piece, “A Gathering of Ghosts,” honors the 20-year tenure of the principal dancer Herman Cornejo. On Thursday, the Balanchine and the Tharp are shown with Alexei Ratmansky’s fresh, joyful, recent ballet, “The Seasons.”

212-496-0600, abt.org

YANIRA CASTRO/A CANARY TORSI at New York Live Arts (Oct. 16-20, 7:30 p.m.). Since Castro, a Puerto Rican artist and choreographer, founded her interdisciplinary collective in 2009, a driving question has been how humans — performers and spectators alike — behave in situations together. Her latest piece on that theme, “Last Audience,” was inspired by Greek writings on democracy, the depiction of judgment and mercy in requiems and the political news of the day. Reservations are required for this performance, which is free and preceded at 6:30 p.m. by a meal with guest artists. The work itself unfolds as a communal ceremony performed with, not for, the audience.

212-691-6500, newyorklivearts.org