  We consider the problem of the R-matrix of the quantum toroidal algebra
$U_{q,t}(\ddot{\mathfrak{gl}}_1)$ in the Fock representation. Using the
connection between the R-matrix $R(u)$ ($u$ being the spectral parameter) and
the theory of Macdonald operators we obtain explicit formulas for $R(u)$ in the
operator and matrix forms. These formulas are expressed in terms of the
eigenvalues of a certain Macdonald operator which completely describe the
functional dependence of $R(u)$ on the spectral parameter $u$. We then consider
the geometric R-matrix (obtained from the theory of K-theoretic stable bases on
moduli spaces of framed sheaves), which is expected to coincide with $R(u)$ and
thus gives another approach to the study of the poles of the R-matrix as a
function of u.
