  It is the aim of this paper to discuss the impact of nuclear fusion on the
EOS. This is a timely subject given the expected availability of increasingly
exotic beams at rare isotope facilities\,\cite{balantekin2014}. In practice, we
focus on $^{48}$Ca+$^{48}$Ca fusion. We employ three different approaches to
calculate fusion cross-sections for a set of energy density functionals with
systematically varying nuclear matter properties. Fusion calculations are
performed using frozen densities, using a dynamic microscopic method based on
density-constrained time-dependent Hartree-Fock (DC-TDHF) approach, as well as
direct TDHF study of above barrier cross-sections. For these studies, we employ
a family of Skyrme parametrizations with systematically varied nuclear matter
properties. We find a slight preference for forces which deliver a slope of
symmetry energy of $L\approx 50$\,MeV that corresponds to a neutron-skin
thickness of $^{48}$Ca of $R_\mathrm{skin}\!=\!(0.180\!-\!0.210)$\,fm.
