Derived Categories in Algebraic Geometry: slides of the talks

September 5-9, 2011,
Laboratory of Algebraic Geometry,
Steklov Math Institute,

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Alexei Bondal (Steklov Institute)
Orthogonal decompositions of sl(n) and mutually unbiased bases

Henning Krause (Bielefeld University)
Stratifying triangulated categories, part I

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.

David Favero (University of Vienna)
Generation time and algebraic cycles

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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Laboratory of Algebraic Geometry and its Applications