Topic

Moduli Spaces

Moduli spaces are fundamental objects of algebraic geometry which have been at the center of interest since the beginnings of the subject. In a nutshell, moduli spaces are spaces whose points correspond in a natural way with geometric objects that one would like to study, such as Riemann surfaces, or vector bundles on a fixed space. Understanding the geometry of moduli spaces often helps to understand the geometric objects themselves, and many of the fundamental questions in the field lead to problems concerning the geometry of an associated moduli space. Moduli are, however, not only of interest to the algebraic geometer. They also play a role in other subjects, such as theoretical physics and cosmology where they appear in relation with mirror symmetry. Partially inspired by ideas coming from theoretical physics, recent years have seen great progress in the understanding of those spaces.

Arcs

Arcs were introduced to algebraic geometry by Nobel Laureate John Nash. The arc scheme of a complex variety is a higher order analogue of its tangent space, giving more refined information about the nature of the variety. It is of fundamental interest to understand how algebraic properties of arc schemes relate to geometric properties of the underlying variety. Interest in arcs was rekindled with the introduction of motivic integration into algebraic geometry. Today, arcs are used to better understand the singularities that appear in the Minimal Model Program. The use of arcs for the description of invariants of singular varieties, and for the study of birational maps are two major topics of current research.

Aim of the school

The goal of this summer school is to introduce a large range of Ph.D. students and young researchers working in algebraic geometry and neighboring fields to exciting, important and extraordinarily active fields of current research. The summer school will also give the participants an opportunity to meet leading researchers in a relaxed setting, and to begin to establish working relationships with their fellows.

This summer school is generously supported by the Volkswagen Foundation   Volkswagen Logo