22/01/2020, 10:00 — 11:00 — Sala P3.31, Pavilhão de Matemática
Emilio Franco, CAMGSD (IST, U. Lisboa)
The Fourier-Mukai transform (II)
We will resume our study of integral functors and Fourier-Mukai transforms focusing on the case of abelian varieties.
Projecto FCT UIDB/04459/2020.
15/01/2020, 10:00 — 11:00 — Sala P3.31, Pavilhão de Matemática
Emilio Franco, CAMGSD, Instituto Superior Técnico, Universidade de Lisboa
The Fourier-Mukai transform (I)
In this session we will introduce integral functors between the derived categories of sheaves of two schemes. A Fourier-Mukai transform is an integral functor that gives rise to a derived equivalence. We shall see some cases when this occur and explore the properties of this transform.
Projecto FCT UIDB/04459/2020.
20/11/2019, 15:00 — 16:00 — Sala P3.31, Pavilhão de Matemática
Emilio Franco, CAMGSD (IST, U. Lisboa)
The derived category of coherent sheaves II
In our journey towards homological mirror symmetry, we will resume our study of the derived category of coherent sheaves focusing on the functors involved in the definition of Fourier-Mukai transforms: push-forward, pull-back and tensor product. We will describe the associated derived functors and some relations among them, namely the projection formula and base change theorems.
Ver também
IMSHS_20_Nov_2019.pdf
Projecto FCT UID/MAT/04459/2019.
13/11/2019, 15:00 — 16:00 — Sala P3.31, Pavilhão de Matemática
Tom Sutherland, Faculdade de Ciências, Universidade de Lisboa
The derived category of coherent sheaves
Motivated by its role in homological mirror symmetry, this talk will introduce the derived category of coherent sheaves on a smooth projective variety. We will see that many of the typical operations on coherent sheaves can be lifted to derived functors, respecting the triangulated structure of the derived category. This paves the way for the systematic study of these functors as Fourier-Mukai transforms.
Projecto FCT UID/MAT/04459/2019.
06/11/2019, 15:00 — 16:00 — Sala P4.35, Pavilhão de Matemática
Emilio Franco, CAMGSD, Instituto Superior Técnico
Introduction to Mirror Symmetry on the Hitchin System
This will be an introductory talk for the Working Seminar on Mirror Symmetry on the Hitchin System. During this minicourse, organized by T. Sutherland and myself, we aim to understand Mirror Symmetry on Higgs moduli spaces as a classical limit of the Geometric Langlands program. In this talk I will briefly describe the geometrical objects involved in this program and provide a motivation for it coming from mathematical physics. The structure of the working seminar will also be discussed.
Projecto FCT UID/MAT/04459/2019.