Scientific Programme

Morning Lectures

The academic programme consists of a series of morning lectures, afternoon working groups and a few contributed talks.

We will have three series of lectures introducing the main subjects of the week. The goal of the lectures will be to communicate the fundamental motivating questions in each field, the tools used to address them, and the important results. We plan to have two lectures each morning. Prof. Viehweg (participation to be confirmed) will give one or two special lectures as a senior speaker.

Moduli I: Moduli of curves. Series of three lectures, by Prof. Farkas
Moduli II: Moduli of vector bundles. Series of three lectures, by Prof. Popa
Arcs in birational geometry.  Series of two to three lectures by Prof. Mustata

Moduli and positivity of push-forward sheaves. Two lectures by senior speaker Prof. Viehweg (to be confirmed)

The lectures are supposed to be of introductory nature; they will be geared towards an audience that has some background in algebraic geometry, but is not necessarily familiar with the subjects taught. We aim to convey enough material so that the participants can then, with a reasonable amount of work, read a current research paper or go to a research talk, and be able to get something useful out of it.

The lectures of Profs. Farkas and Popa will be coordinated and closely related. The interplay between the various moduli spaces will be discussed in detail. For instance, cycles on the moduli space of curves defined in terms of special vector bundles turn out to have very special properties from the point of view of the birational geometry.

Afternoon Working Groups

In the afternoon, the participants will break up into groups, and work with a mentor on problems that will give them a hands-on feel for the methods of the field. The afternoon groups will be related to the topics discussed in morning lectures. Participants choose their working group in advance when they are accepted for participation.

In these groups, the mentors explain ideas and set problems, which the participants then discuss, try to understand and work out. Throughout the afternoon, the mentors shall lecture for no more than 30-40 minutes total. In the remaining time, the participants will be discussing in smaller groups, work out examples and details of proofs, and present the results to each other. The mentor will be present to guide the discussion, help the subgroups and explain material that isn't clear. Ideally, the subgroups should be getting together in the evenings to continue the discussion, or to prepare a presentation for the next day.
We will also have a few contributed talks in the afternoon by participants whose research is related to our main topics.

The format of the academic program will be loosely modeled on two hugely successful weeks, the Snowbird conference in Algebraic   Geometry 2004, and the Graduate Student Warmup Week to the AMS Summer Research Institute in Algebraic Geometry that took place in 2005.

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