On his 1987 Owl album, Homage to John Coltrane, Dave Liebman cites the dedicatee as “the decisive influence on my artistic life,” and nothing could be more obvious. Liebman’s busy, vital, and complex improvising stems not just from Coltrane’s technique (as is the case with so many saxophonists of the past 25 years); it also taps into the maelstrom of emotional intensity from which Coltrane’s epic improvisations sprang. Like Trane, Liebman has gone from the tenor sax to the soprano; in fact, he now relies exclusively on the straight horn, and he is widely considered one of the three or four best soprano players in jazz. But Liebman has carved out his own turf with a lighter, rounder, less nasal sound than Coltrane’s, and by trusting his own instincts. After he worked with Miles Davis, his Open Sky trio of the early 70s produced some stunning performances, while some of his projects in the 80s have been considerably less intriguing: the important thing is that Liebman (like Trane) continues to hunt for new ideas, and occasionally even new forms, without abandoning his own quite personal and influential concept. In Chicago, he’ll jam with locals both familiar and new to him; the familiar include bassist Kelly Sill, drummer Joel Spencer, and saxist Brad Wheeler, while the new face belongs to pianist Jim Trompeter, who regularly plays keyboards with (of all people) the Miami Sound Machine. Sunday, 9 PM, Green Mill, 4802 N. Broadway; 878-5552.