Charmless three-body $B$ meson decays at LHCb

Multi-body $b$-hadron decays to charmless final states, are a particularly interesting place to search for violation of $C\!P$ symmetry, due to the difference in weak and strong phases in competing decay amplitudes to many charmless final states. Furthermore, the weak phase accessible in certain loop-domiated $B_{(s)}^0 \rightarrow K_{\rm S}^0 h^+h^-$ decays is expected, in the Standard Model, to be similar to that of tree-dominated $b \rightarrow c\bar{c}s$ decays. Here measurements of the branching fractions of the $B_{(s)}^0 \rightarrow K_{\rm S}^0 h^+h^-$ decays are presented, which are the most precise measurements of these quantities to-date. Furthermore, an amplitude analysis of the $B^0 \rightarrow K_{\rm S}^0 \pi^+\pi^-$ decay is also presented, where $C\!P$ violation is observed in the $\overline{B}^0 \rightarrow K^{*}(892)^{-}\pi^{+}$ decay with a significance of approximately $6\sigma$.