Sándor Kovács (University of Washington, Seattle): The role of singularities in the classification of complex projective manifolds

Abstract:
One of the interesting features of higher-dimensional complex geometry is that the classification of smooth projective manifolds requires the study of singular algebraic varieties. Indeed, even for the complete understanding of smooth complex surfaces, the investigation of singularities is inevitable. I will talk about this, or more precisely, why the study of singularities is necessary and how this helps in the minimal model program and in the moduli theory of higher dimensional varieties. The latter is a fairly young, dynamically developing area, where there is still a lot to do.