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22/01/2020, 10:00 — 11:00 — Room P3.31, Mathematics Building

Emilio Franco, *CAMGSD (IST, U. Lisboa)*

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The Fourier-Mukai transform (II)

We will resume our study of integral functors and Fourier-Mukai transforms focusing on the case of abelian varieties.

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15/01/2020, 10:00 — 11:00 — Room P3.31, Mathematics Building

Emilio Franco, *CAMGSD, Instituto Superior Técnico, Universidade de Lisboa*

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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.

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20/11/2019, 15:00 — 16:00 — Room P3.31, Mathematics Building

Emilio Franco, *CAMGSD (IST, U. Lisboa)*

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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.

#### See also

IMSHS_20_Nov_2019.pdf

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13/11/2019, 15:00 — 16:00 — Room P3.31, Mathematics Building

Tom Sutherland, *Faculdade de Ciências, Universidade de Lisboa*

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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.

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06/11/2019, 15:00 — 16:00 — Room P4.35, Mathematics Building

Emilio Franco, *CAMGSD, Instituto Superior Técnico*

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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.