The District has the good fortune to be an annual gathering place for up-and-coming jazz talents from around the world. I speak, of course, of the Thelonious Monk Jazz Competition, which this year focuses on 14 outstanding young sax players. (That roster includes a D.C. native and favorite, altoist Braxton Cook.) The semifinals, held at the Museum of Natural History’s Baird Auditorium, will winnow the field down to three, who will compete the next night at the Kennedy Center’s Einsehower Theater. And what’s an international jazz competition without an all-star jazz gala immediately afterward?