### Derived Categories in Algebraic Geometry: slides of the talks

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For a compactly generated triangulated category, there is a notion of stratification
based on the action of a graded commutative noetherian ring. I will explain this concept
and its applications. Then I will present examples where such a stratification has been
established. This is a report on a joint project with Dave Benson and Srikanth Iyengar.

Generation time was introduced by A. Bondal and M. Van den Bergh in
order to demonstrate saturatedness of the derived category of a smooth
proper variety. The notion was developed further by R. Rouquier and
D. Orlov where they study the minimal generation time and the set of
all generation times as a categorical invariant. I will summarize
results in a recent preprint with M. Ballard and L. Katzarkov
connecting generation time to the existence of algebraic cycles on a
smooth variety.

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