From NYTimes.com:

MICHAËL ATTIAS AND RENKU +2 (Saturday) Mr. Attias, a saxophonist, develops compositional fragments into compact expeditions in Renku, a working trio with the bassist John Hébert and the drummer Satoshi Takeishi. Here he adds two alert interlopers, the trumpeter Kirk Knuffke and the pianist Russ Lossing. At 9 and 10:30 p.m., Cornelia Street Café, 29 Cornelia Street, West Village , (212) 989-9319, corneliastreetcafe.com; cover, $10, with a $6 minimum. (Chinen)

PETER EVANS QUINTET (Tuesday) Peter Evans, best recognized for his role in the upstart free-bop quartet Mostly Other People Do the Killing, is a trumpeter with an expressive command of timbre and tone. He’s also a bandleader of emerging promise, as he’ll seek to demonstrate here. Sharing the bill is the adventurous pianist Craig Taborn, performing a solo set. At 9:30 p.m., Le Poisson Rouge, 158 Bleecker Street, near Thompson Street, Greenwich Village , (212) 505-3474, lepoissonrouge.com; $10. (Chinen)

MARY HALVORSON QUINTET (Thursday) Mary Halvorson, an engagingly prickly guitarist of increasing prominence in new-music circles, recently expanded her sharp working trio, adding the trumpeter Jonathan Finlayson and the alto saxophonist Jon Irabagon. She presents that full group here, along with new material obliquely inspired by the palette of Benny Golson’s music for the 1950s-era Jazz Messengers. At 8 p.m., Roulette, 20 Greene Street, at Grand Street, SoHo , (212) 219-8242, roulette.org; $15; $10 for students; free for members. (Chinen)

GIUSEPPI LOGAN / EDGE (Tuesday) Mr. Logan is an alto saxophonist whose promising start, on the mid-1960s free-jazz scene, was curtailed by a mysterious silence. (In one prominent accounting of the era, he was said to have vanished.) His return is now officially at hand, courtesy of an uncompromising new release on the Tompkins Square label, which he celebrates here. Opening the bill — on a program organized by Mr. Logan’s old label, ESP-Disk — is Edge, a quartet led by the violinist Jason Kao Hwang. At 10 p.m., Bowery Poetry Club, 308 Bowery, between Houston and Bleecker Streets , live.espdisk.com; bowerypoetry.com; $10. (Chinen)

MALABY-SANCHEZ-RAINEY (Saturday) A collective that treads a middle ground between lyricism and abstraction, this trio consists of Tony Malaby on tenor saxophone, Angelica Sanchez on piano and Tom Rainey on drums. At 9 and 10:30 p.m., Jazz Gallery, 290 Hudson Street, at Spring Street, South Village , (212) 242-1063, jazzgallery.org; $20; $10 for students. (Chinen)