In 2008, when the artistic director Peter Martins passed on hiring Alexei Ratmansky as New York City Ballet’s resident choreographer, it seemed a missed opportunity. The half dozen ballets that the Ukrainian has since created for the company have only confirmed how much he and the dancers belong together, with their shared musical wit and hunger for a challenge. Fifteen years on, the match has been sealed. For his inaugural work as New York City Ballet’s artist in residence, Ratmansky has chosen music by the suddenly ubiquitous composer Gustav Mahler—specifically, a funeral march to the tune of “Frère Jacques” that devolves into a carnivalesque dance number (from Symphony No. 1) and No. 5’s lushly romantic Adagietto. Don’t let the Gucci ads and biopics discourage you: Ratmansky will reveal colors and contradictions you have not heard in this music before. The premiere appears on a bill with City Ballet’s foundational choreographers—Balanchine, with his bubblegum-bright modernist ballet Symphony in Three Movements, and Robbins, with the affectingly hallucinatory Opus 19/The Dreamer. —Apollinaire Scherr