Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.[-]

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.[-]

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.[-]

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.[-]

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.[-]

We show that the ring of Siegel-Jacobi forms of bounded ratio between weight and index is not finitely generated. Our main tool is the theory of toroidal b-divisors and their relation to convex geometry. As a byproduct of our methods, we prove a conjecture of Kramer about the representation of all Siegel-Jacobi forms as sections of certain line bundles and we recover a formula due to Tai for the asymptotic dimension of the space of Siegel-Jacobi forms of given ratio between weight and index. This is joint work with José Burgos Gil, David Holmes and Robin de Jong.[-]

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.[-]