Homological Projective Duality Seminar

Fall 2012

We will start with an introduction to derived categories and then we will move on to the recent work of Kuznetsov on Homological Projective Duality.

Speakers' meeting: October 2, 3:30pm, room 005.
Schedule: Every other Tuesday, 4-6pm
First talk: October 16, 4pm

References:
Some introductory material on derived categories:

Jean-Louis Verdier, Des Categories Derivees des Categories Abeliennes, Asterisque N.239 (1996)
Daniel Huybrechts, Fourier-Mukai Transforms in Algebraic Geometry, Oxford University Press (2006) (electronic version available with a SISSA IP address)
Claudio Bartocci, Ugo Bruzzo and Daniel Hernandez Ruiperez, Fourier-Mukai and Nahm transforms in geometry and Mathematical Physics, Birkäuser (2009)
Sergei Gelfand, Yuri Manin, Methods of Homological Algebra, Springer (2003)
Charles Weibel, An Introduction to Homological Algebra, Cambridge Univ. Press (1994)
Richard Thomas, Derived categories for the working mathematician
Andrei Caldararu, Derived categories of sheaves: a skimming
Thorsten Holm, Peter Jorgensen, Triangulated categories: definitions, properties, examples

The papers of Kuznetsov we will be looking at:

Tentative Schedule:

Day	Speaker	Title	References
October 16	Ada Boralevi	Triangulated Categories	Huybrechts, Verdier
October 30	Giangiacomo Sanna	Introduction to Derived Categories	Huybrechts, Verdier
November 23 4pm	Alice Rizzardo	Derived Functors and the Derived Category of Coherent sheaves	Huybrechts, Verdier
November 27	Fabio Tanturri	Semiorthogonal Decompositions A full exceptional collection on P^n	Huybrechts 8.27-8.29 Caldararu 3.1-3.2 HPD p.161ff.
December 11	Mattia Pedrini	Lefschetz Decompositions and statement of Homological Projective Duality	HPD p.174ff.
January 15	Giangiacomo Sanna	Homological Projective Duality - What, How and Who