Stability and the structure of the derived category of coherent
sheaves on irreducible curves of genus one 
-- Bernd Kreussler

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The talk has two parts. Part
I: relative Fourier-Mukai transforms on singular genus one fibrations are
studied, math.AG/4010349. Part II: the bounded derived category of coherent
sheaves over an irreducible singular curve of genus one is studied,
math.AG/0503496. We describe all spherical objects, all indecomposable objects
and the group of exact autoequivalences of this category. The main tool are
Harder-Narasimhan filtrations in the sense of Bridgeland.