Branch was born in New York to a Colombian social worker mother and a mechanical engineer father, both amateur musicians who encouraged her to play. When she was ten, the family moved to Wilmette, where Branch later attended New Trier High School and participated in its big-band program. But it took hearing a high-school friend’s copy of Ornette Coleman’s 1959 album The Shape of Jazz to Come to decide her future. “I totally flipped out and thought that record was brand new!” Branch says. She later attended New England Conservatory on and off until graduation, touring with a ska-punk band based out of Chicago during her off semesters and soaking up as much improvising as she could from free-jazz regulars Josh Abrams and then-Chicagoan Matana Roberts.

What makes Branch unique is her facility with both the mellifluous bebop lines of Clifford Brown, and the abstract, gestural improvisation favored by German trumpeter Axel Dörner. Often spotted wearing big hats cocked to the side, her striking appearance seems to take its cues from her two-aesthetics-at-once musicality.

“She totally sucker punches you when you first meet her,” says Fred Lonberg-Holm, the veteran Chicago cellist who tapped her for his own Lightbox Orchestra. “It’s such a weird, specialized muscle [trumpeters] have to have. So it’s really unusual to find a trumpeter who does what she does, let alone in a young woman.”

Despite her age, Branch has the working schedule of someone who has spent years networking. Her main projects include the trio Princess, Princess; the quartet Block and Tackle; the trio Battlecats; the trio Sherpa; and yet another trio that, on Thursdays at the Humboldt Park restaurant Treat, only plays Thelonious Monk songs. In addition, Branch books a new creative-music series at Pilsen’s Skylark on Mondays as well as jazz at Enemy and Heaven Gallery, runs her own live-sound-recording business (where most of her income comes from) and helps organize a Midwest artistic residency program called Harold Arts.

As a woman, Branch is in the odd position of being an outsider in a community of outsiders. “The other day I was playing at the [Hungry] Brain and as I was walking onstage, an audience member said, ‘Hey, watch out for his trumpet!’ ” Branch says. “I’m thinking, But this is my trumpet!” she recalls, amused by his assumption that a woman couldn’t possibly claim its ownership. Then she proceeded to throw down. But Branch insists the boys’-club reputation of jazz was more affecting early on. “Before I really knew what I was doing and had self-confidence, it probably impacted me more,” she says. “Especially playing bebop in high school, it’s almost a macho thing. Frankly, I think a lot of guys don’t like that, either.”

“Of recent arrivals, she’s one of the most interesting improvisers I’m lucky enough to play with,” Lonberg-Holm says. “She’s still young and sorting it out. But as she progresses and gets more sophisticated, she’s gonna really do some damage.”

Jaimie Branch weaves new traditions Monday 3 at Gallery 37.