  In this paper, we develop an adaptive multiresolution discontinuous Galerkin
(DG) scheme for scalar hyperbolic conservation laws in multidimensions.
Compared with previous work for linear hyperbolic equations
\cite{guo2016transport, guo2017adaptive}, a class of interpolatory
multiwavelets are applied to efficiently compute the nonlinear integrals over
elements and edges in DG schemes. The resulting algorithm, therefore can
achieve similar computational complexity as the sparse grid DG method for
smooth solutions. Theoretical and numerical studies are performed taking into
consideration of accuracy and stability with regard to the choice of the
interpolatory multiwavelets. Artificial viscosity is added to capture the shock
and only acts on the leaf elements taking advantages of the multiresolution
representation. Adaptivity is realized by auto error thresholding based on
hierarchical surplus. Accuracy and robustness are demonstrated by several
numerical tests.
