This autumn, New York is bursting with dance. Ayodele Casel, one of the city’s preëminent tap dancers and choreographers, will have her first full-evening show at the Joyce (Sept. 24-29), a collaboration with the Latin-jazz composer and bandleader Arturo O’Farrill. (Tap is enjoying a welcome resurgence, with women leading the way.) Casel and four other dancers will share the stage with O’Farrill’s band, tapping to a range of music styles, from rumba to bomba (a thrillingly percussive style from Puerto Rico) and, of course, Latin jazz. “It’s a family affair,” Casel says, “rooted in the need to communicate everything human.”
The most recognizable element in Merce Cunningham’s “Summerspace,” from 1958, is its design. A Pointillist backdrop, by Robert Rauschenberg, glows with yellow, orange, red, blue, purple, and green dots; the…