This seminar will focus on Fourier-Mukai transforms and their applications to classical algebraic geometry and the study of moduli spaces. We will start by introducing derived categories (no prior knowledge will be assumed), then we will define the Fourier-Mukai transform and discuss a few reasons why this is such a powerful tool. After this we will see some applications to the study of Abelian varieties.
This is intended as a friendly learning seminar; we will take the time to introduce the foundations and discuss examples. Everybody is welcome!
Speakers' meeting: September 22, 1pm, room MATH-103.
Schedule: Wednesday 2-3pm
First talk: October 11
|October 11||Philip||Introduction to derived categories||Huybrechts||MATH-106|
|October 18||Stefano||Triangulated categories||Huybrechts||MATH-106|
|October 25||Alessio||Derived Functors||Huybrechts||MATH-105|
|November 1||Oliver||The derived category of coherent sheaves||Huybrechts||MATH-106|
|November 8||Tom||Fourier-Mukai transform: definition and basic examples |
|November 22||Aeran||Intro to abelian varieties||Polishchuk, Bartocci et al.||MATH-106|
|November 30||Lucas||Abelian Fourier-Mukai transform||Polishchuk, Bartocci et al.||MATH-106|
|December 20||?||Classification of semistable bundles on elliptic curves||Polishchuk, Bartocci et al.||MATH-106|