Taking over the city’s major dance venues for five weeks, Festival in New York whittles down the dozens of contemporary works that Dance Reflections, Van Cleef & Arpels’s deep-pocketed dance wing, has sponsored since the pandemic to 16 shows. The choreographers include American icons Merce Cunningham, Trisha Brown, and Lucinda Childs as well as their Western European heirs. As some of these relative youngsters rarely visit, the festival wisely features not their latest but their most groundbreaking or most loved pieces. With The Dog Days Are Over, Jan Martens presents a sweaty, disco-inflected yet still mathematically harrowing version of Lucinda Childs’s pristine patternmaking. The word “polka” may be shorthand for “ridiculous dance,” but even the wretched techno music Alessandro Sciarroni uses in Save the Last Dance for Me cannot dent the pleasure in witnessing a dying Bolognese version, exclusive to men, of the whirly ballroom dance. The old, unspoken homoerotism sidles up to the new, loudly declared queerness to double the romance. As for frequent fliers to New York, Soa Ratsifandrihana’s and Noé Soulier’s capacity to combine the conceptually fascinating with the kinetically gratifying makes them worth seeing any number of times. —Apollinaire Scherr