Analogies between moduli spaces of vector bundles and of flags (Q1372600)

This most enjoyable text is the main contents of a talk at the DMV (Deutsche Mathematiker Vereinigung). The point of departure is the analogy between vector bundles on Riemann surfaces and \(\mathbb{Z}\)-filtered vector spaces. There is a similar analogy between the moduli space of vector bundles and the moduli space of \(\mathbb{Z}\)-filtered vector spaces satisfying semi-stability conditions. This is illustrated by the problem of determining the singular cohomology of both kinds of spaces. The presentation is like a leisurely walk through the field, with highlights at the combinatorial problems appearing in the determination of the Poincaré series.