  We propose the interpolatory hybridizable discontinuous Galerkin
(Interpolatory HDG) method for a class of scalar parabolic semilinear PDEs. The
Interpolatory HDG method uses an interpolation procedure to efficiently and
accurately approximate the nonlinear term. This procedure avoids the numerical
quadrature typically required for the assembly of the global matrix at each
iteration in each time step, which is a computationally costly component of the
standard HDG method for nonlinear PDEs. Furthermore, the Interpolatory HDG
interpolation procedure yields simple explicit expressions for the nonlinear
term and Jacobian matrix, which leads to a simple unified implementation for a
variety of nonlinear PDEs. For a globally-Lipschitz nonlinearity, we prove that
the Interpolatory HDG method does not result in a reduction of the order of
convergence. We display 2D and 3D numerical experiments to demonstrate the
performance of the method.
