  Interferences between different emitters in the multi-parton shower is the
building block of QCD jet physics in vacuum. The presence of a hot medium made
of quarks and gluons is expected to alter this interference pattern. To study
such effects, we derive the gluon emission spectrum off an "asymptotic quark"
traversing a hot and dense QCD medium at first order in the medium density. The
resulting induced gluon distribution gets modified when the new interference
terms between the initial and final quark are included. We comment on the
possible phenomenological consequences of this new contribution for jet
observables in heavy-ion collisions.
