Working seminar on Fourier-Mukai transforms

Fall 2018

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

Tentative Schedule: also availabe on Google calendar

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