This is a continuation of the 2017 Working seminar on Fourier-Mukai transforms. We will be learning about applications of Fourier-Mukai transforms to the general theory of derived categories and to classical algebraic geometry (and maybe to physics!).

This is intended as a friendly learning seminar; we will take the time to introduce the foundations and discuss examples. Everybody is welcome!

**Schedule:** Thursday 11am-12pm

**First talk:** November 22

**References: **

- Daniel Huybrechts, Fourier-Mukai Transforms in Algebraic Geometry, Oxford University Press (2006)
- Claudio Bartocci, Ugo Bruzzo and Daniel Hernandez Ruiperez,
*Fourier-Mukai and Nahm transforms in geometry and Mathematical Physics*, Birkäuser (2009) - Alexander Polishchuk,
*Abelian Varieties, Theta Functions and the Fourier Transform*, Cambridge University Press (2003) - Jean-Louis Verdier,
*Des Categories Derivees des Categories Abeliennes*, Asterisque N.239 (1996) - 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

Day | Speaker | Title | References | Room |
---|---|---|---|---|

November 22 | Aeran | The classification of semi-stable bundles on elliptic curves, I | Hein-Ploog Bartocci-Bruzzo-Hernandez Ruiperez | CHAD-ROTB |

November 29 | Philip | The classification of semi-stable bundles on elliptic curves, II | Hein-Ploog Bartocci-Bruzzo-Hernandez Ruiperez | CHAD-ROTB |

December 6 | Felix | The derived category of projective space | Huybrechts | CHAD-ROTB |

December 13 | Tom | Embedding the moduli space of stable bundles on a curve into the moduli space of its Jacobian | Hein-Ploog, Stability of Picard sheaves Bartocci-Bruzzo-Hernandez Ruiperez | CHAD-ROTB |