Jazz's past and present will be celebrated this spring Jazz at Lincoln Center Orchestra: Trumpeter and roving ambassador for jazz Wynton Marsalis brings his nimble big band to town with a wealth of talent and tradition in tow. Expect sharp suits and even sharper tunes delivered by a band dedicated to bridging the gap between the music's history and its present. Walt Disney Concert Hall, April 20 www.laphil.com Ambrose Akinmusire: As if the weather weren't enough for Angelenos to gloat about, jazz fans got yet another reason when this trumpeter returned to his West Coast roots as an instructor at USC's Thornton School of Music. That means more opportunities to catch a unique, restless talent, including this residency, which should hint toward his next moves following his acclaimed Blue Note debut, "When the Heart Emerges Glistening." The Blue Whale, March 15-17. www.bluewhalemusic.com. Chick Corea: Whether leading the various incarnations of fusion innovators Return to Forever or continuing to explore duets with Gary Burton, this jazz piano great has hardly slowed down. This run of shows finds Corea exploring the trio form backed by Return to Forever bassist Stanley Clarke and Clarke's longtime drummer, Ronald Bruner Jr. Catalina Jazz Club, April 9-14. www.catalinajazzclub.com. Allen Ginsberg's "Kaddish": The connection between the Beat Generation and jazz is well established, and that thread will be further strengthened with this production staged by Hal Willner. The night will combine Ginsberg's poem with a film by Chloe Webb, projected paintings by Ralph Steadman and music composed and conducted by guitarist Bill Frisell, who leads a nine-piece band. Center for the Art of Performance at UCLA, Royce Hall. April 17 cap.ucla.edu/. Tribute to Miles: Jazz has been accused of celebrating its history at the expense of its present, but considering the particulars here, all such thoughts fall away. Produced by bassist and Davis collaborator Marcus Miller, this show features jazz royalty in fellow Davis sidemen Herbie Hancock and Wayne Shorter, joined by trumpeter Sean Jones and versatile drummer Vinnie Colaiuta. Walt Disney Concert Hall, April 23. www.laphil.com. SUMMER: Playboy Jazz Festival sets June 15-16 lineup Medeski Martin and Wood: Now in its second decade, this trio is often lumped into a "jam-band" ghetto, but within the organ group's thick bond to the almighty groove there are nods toward the interstellar explorations of Sun Ra, Cecil Taylor and other wonders of improvisation. John Medeski's lush solo piano album, "A Different Time," only underscores the group's ability to surprise. April 26 cap.ucla.edu/. Brad Mehldau Trio, the Bad Plus with Joshua Redman: An ambitious, expressive artist, Mehldau was in typically remarkable form on a pair of 2011 albums, and the Bad Plus have been pushing the boundaries of the piano trio for years with an irreverent mix of head-turning covers and originals. Here its sound will be fleshed out further with Redman's saxophone, a meeting that should yield fireworks. May 4 cap.ucla.edu/.