Working seminar on Fourier-Mukai transforms

Fall 2017

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

References:



Tentative Schedule: also availabe on Google calendar

Day Speaker Title References Room
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
Orlov's theorem
Huybrechts MATH-106
November 22 Aeran Intro to abelian varieties Polishchuk, Bartocci et al. MATH-106
November 29 Lucas Abelian Fourier-Mukai transform Polishchuk, Bartocci et al. MATH-106
December 13 ? Classification of semistable bundles on elliptic curves Polishchuk, Bartocci et al. MATH-106
Additional topics for next semester: