April 11: Quick Introduction: Derived categories,
April 18: Derived functors, Serre duality, Grothendieck-Ver\ dier duality, Fourier-Mukai formalism. (Essentially no proofs, depending on the audience.)
April 25: Theorem of Bondal-Orlov: Varieties with ample (anti-)canonical bundle are determined by their deriv\ ed category Semi-orthogonal decompositions, exceptional collections
May 9: Semi-orthogonal decompositions, exceptional collections
June 6: Kuznetsov's category, fractional CY categories Categories of graded matrix factorizations (Orlov's description of Kuznetsov's category)
June 13: Categories of graded matrix factorizations (Orlov's description of Kuznetsov's category)
June 20:
July 4:
July 11:
D. Huybrechts: Fourier-Mukai transforms in algebraic geometry. Oxford Mathematical Monographs. 2006.
C. Weibel: An Introduction to Homological Algebra. Cambridge. 1994
tbc