This chapter title is tough to nail down, there have been many songs (jazz and otherwise) called "Evolution," over the years. Sticking with a common theme with the chapter titles, I'm guessing that this is a reference to another John Coltrane compostion:
Evolution (1/4)
Evolution (2/4)
Evolution (3/4)
Evolution (4/4)
The only available recording of the song is from a 1965 concert that was released posthumously in 1971 as "John Coltrane Live in Seattle." It's an aggressive avant-garde composition, a good representation of Coltrane's late output before his death in 1967. If this is the song Ishizuka Shinichi had in mind it's an appropriate choice, foreshadowing a rocky road ahead for Dai.
In the flashback, Dai's teacher was playing at is Birdland, a famous jazz club in New York City. I'm not sure how old he's supposed to be, but my guess is that he was playing at the club's current location—opened in 1996—in Manhattan on W 44th between 8th and 9th Avenues.