EVOLVING MUSIC (Monday) The next installment of this avant-garde series will feature two trios, each with a strong identity. First up at 7:30 p.m. is Flow Trio, with Louie Belogenis on tenor saxophone, Joe Morris on bass and Charles Downs on drums; the group has a stark but rewarding new album, “Rejuvenation” (ESP-Disk). At 9 the smartly blustery trombonist Ray Anderson leads a trio of his own, with bass and drums. The Local 269, 269 East Houston Street, at Suffolk Street, Lower East Side , (212) 254-5420, myspace.com/rucmanyc; $10 per set, $15 for the night; students $7 per set, $12 for the night (Chinen)20090625
TOMAS FUJIWARA AND THE HOOK UP (Saturday) Mr. Fujiwara’s alert drumming has propelled some excellent ensembles on the new-music landscape. Here he presents his own open-ended compositions for a band with Jonathan Finlayson on trumpet, Brian Settles on tenor saxophone, Mary Halvorson on guitar and Danton Boller on bass. At 9 p.m., Jalopy Theater, 315 Columbia Street, Red Hook, Brooklyn , (718) 395-3214, jalopy.biz; $15. (Chinen)20090625
? MARY HALVORSON (Sunday) Last year the guitarist Mary Halvorson released “Dragon’s Head” (Firehouse 12), a brambly but engaging debut featuring her own compositions for a trio with the bassist John Hebert and the drummer Ches Smith. Ms. Halvorson draws again from that material here, but she’ll also perform newer music for quintet, enlisting the trumpeter Jonathan Finlayson and the alto saxophonist Jon Irabagon. At 7 p.m., Joe’s Pub, at the Public Theater, 425 Lafayette Street, at Astor Place, East Village , (212) 598-7100, joespub.com; $12 in advance, $15 at the door, with a two-drink or $12 food minimum. (Chinen)20090625
ETHAN IVERSON AND TIM BERNE (Friday) Mr. Iverson, the pianist in the Bad Plus, has worked memorably with the alto saxophonist Tim Berne: last year they both appeared on “Buffalo Collision” (Screwgun), a self-titled debut by a collective, free-improvising quartet. Here they appear in mano-a-mano format, presumably with all the tension and cooperation that term implies. At 10 p.m., the Stone, Avenue C and Second Street, East Village , thestonenyc.com; $10. (Chinen)20090625
TONY MALABY’S APPARITIONS (Monday) Rhythm and texture are often equal priorities for the tenor saxophonist Tony Malaby, but that would seem especially true in this band, which includes two venturesome drummers — Tom Rainey and John Hollenbeck — along with a bassist, Drew Gress. At 8:30 p.m., Cornelia Street Café, 29 Cornelia Street, West Village , (212) 989-9319, corneliastreetcafe.com; cover, $10, with a one-drink minimum. (Chinen)20090625
ANDY MILNE AND BENOIT DELBECQ (Sunday) Mr. Milne and Mr. Delbecq are resourcefully contemporary pianists, both drawn to quixotic interrogations of harmony and timbre. They team up here, on two pianos, to revisit themes from a strangely beautiful new album, “Where Is Pannonica?” (Songlines). At 4:30 and 6:30 p.m., Klavierhaus, 211 West 58th Street, Manhattan , (718) 732-2276, gomediapr.com; $15, reservations suggested. (Chinen)20090625
? NEW TRUMPET UNDERGROUND 2009 (Friday through Sunday) An off-season production of the Festival of New Trumpet Music, this weekend series gathers eight trumpeter-bandleaders under a progressive banner. Highlights include a set by Old Idea, a Chicago group led by the cornetist Josh Berman, which just released its self-titled Delmark debut (Friday at 10 p.m.); a commissioned premiere by Nadje Noordhuis, an Australian-born trumpeter with a strong, pristine sound (Saturday at 9); and the Russ Johnson Quartet, a steady fixture on the New York scene (Sunday at 9:30). For a full schedule, visit fontmusic.net. Cornelia Street Café, 29 Cornelia Street, West Village , (212) 989-9319, corneliastreetcafe.com; $10 per set, or $15 per night. (Chinen)20090625
BEN PEROWSKY QUARTET (Saturday) Mr. Perowsky, an aggressive but nimble drummer, draws here from a very good forthcoming album, “Esopus Opus” (Skirl), with several reliable partners: the saxophonist and clarinetist Chris Speed, the accordionist Ted Reichman and the bassist Trevor Dunn. An earlier set, at 8 p.m., will feature the maniacally creative percussionist Cyro Baptista, improvising alone. At 10 p.m., the Stone, Avenue C and Second Street, East Village , thestonenyc.com; cover, $10 per set. (Chinen)20090625
MARC RIBOT (Tuesday) Mr. Ribot is a vagabond poet on solo electric guitar, as he proved a handful of years ago with the album “Saints” (Atlantic). He draws partly from the same repertory here, though probably with a few surprises thrown in. At 8 p.m., the Stone, Avenue C and Second Street, East Village , thestonenyc.com; cover, $10. (Chinen)20090625
SEX MOB (Friday) The members of this downtown institution have lately been engaged in various other pursuits, but their sound is as raucous, and their rapport as rambunctious, as ever. Steven Bernstein plays slide trumpet and leads the charge, though equal weight is pulled by Briggan Krauss on alto saxophone, Tony Scherr on bass and guitar and Kenny Wollesen on drums. At 10 p.m., 55 Bar, 55 Christopher Street, West Village , (212) 929-9883, 55bar.com; cover, $10. (Chinen)