Ralph Alessi Quartet (Friday) Ralph Alessi, an adventurous and crisply proficient trumpeter, has a recent album, “Cognitive Dissonance” (Cam Jazz), featuring the same excellent rhythm partners featured here, each a bandleader in his own right: the pianist Jason Moran, the bassist Drew Gress and the drummer Nasheet Waits. The band was brilliant at a one-nighter last summer, and there’s no reason to think it won’t be here. At 9 and 10:30 p.m., Jazz Gallery, 290 Hudson Street, at Spring Street, South Village, (212) 242-1063, jazzgallery.org; $20, or $10 for members. (Nate Chinen)
Aum Fidelity at the Stone (Sunday and Monday) The second half of June at the Stone has been organized by Steven Joerg, who runs Aum Fidelity, a small but righteous label devoted to experimental music. His programming naturally touches on some in-house label talent, like the free-jazz collective Other Dimensions in Music, which plays both sets on Sunday, the latter of which will feature Fay Victor on vocals. But it will also include events like a Monday-night large-ensemble workshop (at 7:15) and performance (at 9) led by the vibraphonist Karl Berger. For a full schedule, see thestonenyc.com. (Through June 30.) At 8 and 10 p.m., the Stone, Avenue C and Second Street, East Village; $10. (Chinen)
Peter Evans Trio (Sunday) Peter Evans is a trumpeter with a dizzying command of timbre and texture, and he isn’t afraid to clobber you with it. He appears here in a trio with the bassist Moppa Elliott, his band mate in the delirious free-bop band Mostly Other People Do the Killing; the drummer is Kassa Overall. Mr. Evans also appears in an earlier set, at 8:30 p.m., led by the young guitarist Rafiq Bhatia. At 10 p.m., Cornelia Street Café, 29 Cornelia Street, Greenwich Village, (212) 989-9319, corneliastreetcafe.com; $10 cover, with a $10 minimum. (Chinen)
Vijay Iyer Sextet (Thursday) In his music for small ensembles, the pianist Vijay Iyer favors a surging, complex, mutant strain of postbop, steeped in portent and incident. This group is built around the core of his superb quartet with Rudresh Mahanthappa on alto saxophone, Stephan Crump on bass and Marcus Gilmore on drums. The additional firepower comes from Graham Haynes, a cornetist, and Mark Shim, a tenor saxophonist, and it won’t be wasted. Tickets are free, but reservations are recommended and can be made online; for details, see rivertorivernyc.com. At 7 p.m., Castle Clinton National Monument, Battery Park, 200 Rector Place, Lower Manhattan. (Nate Chinen)
Red Hook Jazz Festival (Saturday) Now in its fourth year, this scrappy Brooklyn festival gathers a handful of bands for a negligible price. The lineup includes the Ingrid Laubrock Quartet, Josh Sinton’s Holus-Bolus, the Jeff Davis Band, Renku and Stephane Wrembel’s Django Experiment. From 1 to 6 p.m., Urban Meadow, urbanmeadowbrooklyn.blogspot.com; $5; children free. (Chinen)
Craig Taborn (Friday) Craig Taborn, a busy sideman in New York’s left-of-center jazz vector, recently released his solo-piano debut, “Avenging Angel” (ECM), a brilliant and unpredictable study informed by contemporary classical music as well as several currents of improvisation. It’s a sit-up-and-take-notice statement, and not just because Mr. Taborn hasn’t released an album as a leader in years. At 7 p.m., Rubin Museum of Art, 150 West 17th Street, Chelsea, (212) 620-5000, rmanyc.org; $20; $16.20 for members; $5 student standby. (Chinen)
Henry Threadgill’s Zooid (Thursday) Mr. Threadgill, 67, has long been one of the most thrillingly elusive composers in and around the jazz idiom: a sly maestro of unconventional timbres, bristling counterpoint and tough but slippery rhythms. Zooid, his working band for the last decade, features tuba and trombone, along with drums, acoustic and bass guitars, and now cello. In two recent albums on Pi, this group has been tough and utterly itself; that’s even truer up close and in person. (Through June 25.) At 9 and 10:30 p.m., Jazz Gallery, 290 Hudson Street, at Spring Street, South Village, (212) 242-1063, jazzgallery.org; $25, or $15 for members. (Chinen)
Undead Jazzfest (Thursday) The messiest, most thrillingly unpredictable of our summer jazz festivals has expanded to Brooklyn this year, but first comes this opening night, centered around the usual three clubs in a tight radius of Greenwich Village. At Le Poisson Rouge, highlights include Tarbaby (at 9:30 p.m.) and David Torn’s Goldfinger (12:50 a.m.); across Bleecker Street at Kenny’s Castaways, look for Harris Eisenstadt’s Canada Day (7:40 p.m.) and a trio with Michael Blake on saxophones, Ben Allison on bass and Rudy Royston on drums (12:20 a.m.). Or stake out Sullivan Hall, which has the most consistently rewarding lineup, including sets by Paradoxical Frog (8:30 p.m.), the pianist Gerald Clayton (9:40 p.m.) and the Andrew D’Angelo Big Band (10:50 p.m.). After Thursday, the festival moves to Brooklyn; for a full schedule, see undeadjazz.com. (Chinen)
