As soon as he shows up on the covers of America’s three national jazz magazines, which could be in the next couple months, British singer-songwriter-pianist Jamie Cullum should reap the rewards of his genre-blending approach to jazz and pop. That is, he’ll become a lightning rod in the ongoing debate about the commercialization of jazz–and he’ll love it. This brash, elfin 24-year-old has a jack-in-the-box energy: even as he tries to turn his young listeners on to Herbie Hancock, he punctuates his performances with piano-bench acrobatics a la Elton John. On Cullum’s major-label debut, Twentysomething (Verve), Radiohead’s “High and Dry” rubs elbows with Broadway classics by Cole Porter and Lerner and Loewe, Jimi Hendrix’s “Wind Cries Mary,” and his own attractively callow originals. Perhaps the title track of Twentysomething best sums up his iPod-generation aesthetic: it’s a postcollege youth anthem (“I could work for the poor, though I’m hungry for fame / We all seem so different but we’re just the same”) that uses the melody from Charles Mingus’s “Haitian Fight Song” as its bass line, opens up for a jazz piano solo, and breaks for a bossa nova interlude. In a recent radio interview, Cullum expressed a belief that jazz can be the real rock ‘n’ roll, a fresh source of the energy and excitement that rock so often fails to provide. The sales figures for Twentysomething–one million and climbing in Britain alone (it was released just a few days ago in the States)–suggest that his message has found an audience. Gabriel Mann opens. Thursday, May 20, 9 PM, Martyrs’, 3855 N. Lincoln; 773-404-9494.