Abstract
In the nineties Shokurov introduced the technique of complements to investigate adjunction. After a brief introduction I will discuss how this technique shows the possible configurations of multiple fibers on elliptic surfaces of Kodaira dimension less or equal to zero.

Location:
Room I-105, Department of Mathematics and Statistics, University of La Frontera.

Abstract
The group law of the Jacobian of a genus 2 curve is governed by the linear system of cubics on this curve: This is a classical property, already used in cryptography. I will present an application of this interpretation to the construction of a birational model of the generalized Kummer variety of this Jacobian.

Location:
Manuel López Ramírez Auditorium, Department of Mathematics and Statistics, University of La Frontera.

Abstract
I will consider in this talk so called Enriques manifolds of IHS-type, which are non simply connected manifolds whose universal cover is an irreducible holomorphic symplectic (IHS) manifold and as such they are natural generalizations of Enriques surfaces. The goal of the talk is to prove the Morrison-Kawamata cone conjecture for certain such manifolds when the degree of the cover is prime by using the analogous result (established by Amerik-Verbitsky) for their universal cover. If time permits I will also show the cone conjecture for the known examples having non-prime degree. This is a joint work with Gianluca Pacienza.

Location:
Manuel López Ramírez Auditorium, Department of Mathematics and Statistics, University of La Frontera.

Abstract
There are several constructions in different mathematical contexts to obtain families of mirror-symmetric objects, meaning they correspond through mirror symmetry. Among these, we are particularly interested in Batyrev’s duality and the Berglund-Hübsch-Krawitz construction. In this talk, I will explain how these two constructions allow us to obtain families of mirror-symmetric Calabi-Yau varieties and how a new construction, which generalizes both, can be introduced: the construction with good pairs. This is joint work with Michela Artebani and Robin Guilbot.

Location:
Manuel López Ramírez Auditorium, Department of Mathematics and Statistics, University of La Frontera.

Abstract
In this talk, I will introduce the mapping class group (MCG) of a topological surface. After discussing some general properties of MCGs, I will focus on the class of large mapping class groups. Part of this talk will be devoted to mentioning some fundamental results in their development. I will conclude my presentation by giving a brief overview of the fascinating topic of the large-scale geometry of these groups.

Location:
Manuel López Ramírez Auditorium, Department of Mathematics and Statistics, University of La Frontera