  The electromagnetic field distribution as well as the resonating frequency of
various modes in superconducting cavities used in particle accelerators for
example are sensitive to small geometry deformations. The occurring variations
are motivated by measurements of an available set of resonators from which we
propose to extract a small number of relevant and independent deformations by
using a truncated Karhunen-Lo\`eve expansion. The random deformations are used
in an expressive uncertainty quantification workflow to determine the
sensitivity of the eigenmodes. For the propagation of uncertainty, a stochastic
collocation method based on sparse grids is employed. It requires the repeated
solution of Maxwell's eigenvalue problem at predefined collocation points,
i.e., for cavities with perturbed geometry. The main contribution of the paper
is ensuring the consistency of the solution, i.e., matching the eigenpairs,
among the various eigenvalue problems at the stochastic collocation points. To
this end, a classical eigenvalue tracking technique is proposed that is based
on homotopies between collocation points and a Newton-based eigenvalue solver.
The approach can be efficiently parallelized while tracking the eigenpairs. In
this paper, we propose the application of isogeometric analysis since it allows
for the exact description of the geometrical domains with respect to common
computer-aided design kernels, for a straightforward and convenient way of
handling geometrical variations and smooth solutions.
