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

- Hyperplane Sections and Derived Categories
- Homological Projective Duality
- Homological Projective Duality for Grassmannians of Lines

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 |