The US pianist Brad Mehldau once observed that if you create new music with enough conviction in your own backyard, people start peering over the fence, whether they have any idea what you're up to or not. The evidence is particularly strong in the case of Alexander Hawkins, the 30-year-old Oxford-based piano improviser and composer who brought his new quintet to the Vortex for the London launch of their album All There, Ever Out. Hawkins' awesomely complex, extensively composed contemporary jazz is clearly the product of a computer-like musical mind, but that kiss of death –"cerebral" – can never be planted on his work. It sounds like all the future jazz you might imagine without ever being able to conceive of the details, but it also joyously invokes the past (Thelonious Monk, Elmo Hope, Steve Lacy); improvisers are pushed into corners from which only vaulting acts of spontaneous imagination will offer ways out.

The group mixed material from the new CD with swaths of Hawkins' new pieces. A Monk-like opener full of twists and slam-stops found Shabaka Hutchings snorting a clipped bass-clarinet motif against percussively snapping bass parts and bursts of lurching swing. Hawkins and guitarist Otto Fischer introduced a quiet melody over bowed bass, which Hutchings joined in a high whisper. An increasingly abstract three-way improv intensified between them, a jazz-swing bass-walk sprang up, and Hawkins launched into a mesmerising solo of explosive chordwork and mercurial Cecil Tayloresque runs in this passage (and in the subsequent dedication to bebop pianist Hope).

Both sets were equally eventful. The slow-climbing theme simply called Number Three, and So Very Know was among the second half's most memorable episodes: a meditation in delicate cymbal-edge sounds, glistening piano chords and bass-clarinet sighs, dedicated to recently deceased London drummer Tony Marsh.