CP Violation and Mixing in Multi-body $D$ decays

We present recent LHCb results and future prospects for CP violation and mixing measurements in multi-body charm decays. The complex amplitude structure of multi-body decays provides unique sensitivity to CP violation localised in certain phase space regions. A model-independent search in the phase space of D->pi+pi-pi+pi- and D->K+K-pi+pi- decays showed no evidence for localised CP violation. If one assumes the no CP violation hypothesis, the probability of getting the observed results is 9.1% and 41%, respectively. The model-independent determination of gamma from B->DK requires external input to account for the interference of D0 and D0bar amplitudes to the same final state. Previously this input could only be obtained at the charm threshold, but recently it has been proposed that D mixing can provide complimentary information. For the example of D->K+pi-pi+pi- decays, it is shown that charm mixing can be used to considerably improve current constraints on the coherence factor and average strong phase difference, with existing data.