## Deformation Theory and Moduli in Algebraic Geometry | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

July 23, 2007 to August 03, 2007 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Organized By: Max Lieblich (Princeton), Martin Olsson (Berkeley), Brian
Osserman (Davis), Ravi Vakil (Stanford) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

This workshop is intended to introduce to graduate students the main ideas of deformation theory and moduli spaces in algebraic geometry. We hope to illuminate the general theory through extensive discussions of concrete examples and applications. The intended audience is the graduate student with a strong interest in algebraic geometry, having at least some familiarity with the language of schemes, and ideally comfortable with the content of Hartshorne's book Algebraic Geometry.The workshop will be anchored by three lecture series on different aspects of the subject, as well as student projects aimed at furthering an understanding of the lectures and pursuing more advanced topics. The lecture series are: - Moduli spaces: functors, algebraic spaces, stacks, algebraic stacks (Lieblich).
- Deformations (a): tangent and obstruction spaces (Olsson).
- Deformations (b): representability and Schlessinger's criterion (Osserman).
Accompanying the lectures will be a collection of tightly integrated exercises. A large portion of the workshop will be devoted to these exercises, with the students expected to work on them during the daily group work time, as well as in the evenings. In addition, students will be expected to give short presentation on background material, which will be arranged in advance. Exercises are now posted online. Lectures are now online in the form of notes by volunteers, some official notes, and streaming videos.
• Information on the
background material which we expect participants
to be familiar with, as well as topics for the background
lectures.
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||