Date: Thursday 14th March 2013 br Speaker: Daniel Greb (Bochum) br Title: Compact moduli spaces for slope-semistable sheaves br br Abstract: While the variation of moduli spaces of H-slopeGieseker-semistable sheaves on surfaces under change of the ample polarisation H is well-understood, research on the corresponding question in the case of higher-dimensional base manifolds revealed a number of pathologies. After presenting these, I will discuss recent joint work with Matei Toma (Nancy), which resolves some of these pathologies by looking at curves instead of divisors. This naturally leads to the question whether higher-dimensional analogues of the Donaldson-Uhlenbeck compactification exists, and I will discuss our construction of such a compactification.