  Degenerating the action of the elliptic Hall algebra on the Fock space, we
give a combinatorial formula for the Shalika germs of tamely ramified regular
semisimple elements $\gamma$ of $GL_n$ over a nonarchimedean local field. As a
byproduct, we compute the weight polynomials of affine Springer fibers in type
A and orbital integrals of tamely ramified regular semisimple elements. We
conjecture that the Shalika germs of $\gamma$ correspond to residues of torus
localization weights of a certain quasi-coherent sheaf $\mathcal{F}_\gamma$ on
the Hilbert scheme of points on $\mathbb{A}^2$, thereby finding a geometric
interpretation for them. As corollaries, we obtain the polynomiality in $q$ of
point-counts of compactified Jacobians of planar curves, as well as a virtual
version of the Cherednik-Danilenko conjecture on their Betti numbers. Our
results also provide further evidence for the ORS conjecture relating
compactified Jacobians and HOMFLY-PT invariants of algebraic knots.
