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Studies of the $\Delta$ baryon resonance and the $K_0^\ast(700)$ and$a_0(980)$ meson resonances using $N_f=2+1$ lattice QCD for pion masses near200 MeV are presented. The $s$-wave scattering lengths for both the $I=1/2$ $N\pi$ and $I=3/2$ $N \pi$ channels and properties of the $\Delta$ resonance areidentified from the finite-volume energy levels of the lattice simulation. Theimportance of a three-quark $\Delta$-operator in the $N\pi$ system andtetraquark operators in the mesonic systems is investigated.

Lattice QCD studies of the $\Delta$ baryon resonance and the  $K_0^\ast(700)$ and $a_0(980)$ meson resonances: the role of exotic operators  in determining the finite-volume spectrum