After briefly recalling some computational aspects of blowing up and of
representation of resolution data common to a wide range of desingularization
algorithms (in the general case as well as in special cases like surfaces or
binomial varieties), we shall proceed to computational applications of
resolution of singularities in singularity theory and algebraic geometry, also
touching on relations to algebraic statistics and machine learning. Namely, we
explain how to compute the intersection form and dual graph of resolution for
surfaces, how to determine discrepancies, the log-canoncial threshold and the
topological Zeta-function on the basis of desingularization data. We shall also
briefly see how resolution data comes into play for Bernstein-Sato polynomials,
and we mention some settings in which desingularization algorithms can be used
for computational experiments. The latter is simply an invitation to the
readers to think themselves about experiments using existing software, whenever
it seems suitable for their own work.Comment: notes of a summer school talk; 16 pages; 1 figur