Befitting his reputation for being difficult to categorize, Julian Lage offered a diverse set at One Longfellow Square on Sunday that was rooted in jazz but touched by rock, country and world music. Songs from the 28-year-old California native’s new album, “Arclight,” figured prominently.

“Presley,” a playful cross-genre piece, was an early standout as the guitarist displayed his technical range during passages that had him alternately finger picking, hard picking and hand hammering the strings of his Telecaster electric guitar. Kenny Wollesen also varied his approach on this rock-tinged piece, employing both brushes and hands on his drum kit. This number, like many during the 90-minute performance, featured a wide dynamic range, moving from delicate whispers of sound to thunderous power chords.

“Activate” was a full-on jazz excursion, with a fast-walking bass line by Jorge Roeder underpinning torrents of notes from the leader. Lage pushed his band mates forward until they became a surging unit intent on taking the music as fast and as far as they could.

A Middle Eastern rhythm took the band’s “Prospero” in a slightly more meditative direction, with the leader’s scalar extrapolations riding on top.

Lage, a former child prodigy, noted that he first played Portland at the age of 12. A youthful enthusiasm remains a part of his stage presence. He often smiled broadly as he leaned into his solos or admired those of his band mates.

Roeder offered several rich solos, including some double-stop work on his upright bass that hearkened back to the avant-garde era of the 1960s. He and the others later took things to the edge of collective improvisation on a piece called “Stop Go Start,” earning shouts of approval from the attentive crowd as they worked through the tumult toward a higher musical plain.

Because of a shared eclecticism and particular fondness for musical Americana, Lage is sometimes compared to guitar veteran Bill Frisell. Lage’s “Ryland” suggested their affinity through an appreciation for a soulful, countrified melody. The younger musician, however, added a snap at the end of his lines that repeatedly freshened the piece, offsetting its lyricism with a charge of energy.

The encore brought things back to a more traditional concept, as the guitarist led the threesome in a slow, sweet version of the classic “I’ll Be Seeing You,” perhaps suggesting he’ll be back this way again.

Steve Feeney is a freelance writer who lives in Portland.

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