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).
Each series will consist of eight lectures, given daily Monday-Thursday. Each Friday will feature two 90-minute guest lectures. The speakers will be Brian Conrad, Paul Hacking, Jason Starr, and Ravi Vakil.

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.

Week 1 schedule
9:00-9:30Vakil LieblichStarr
10:30-11:00Break OlssonBreak
11:30-12:00Break Vakil
1:00-2:00LunchBBQ &
Afternoon Off
2:00-3:00BG #4 and #5BG #6BG #3BG #8
3:30-5:30BG #2BG #7BG #1Group Work

Note: In addition to the above, we will have a lecture by Ravi Vakil at 7:15 PM on Tuesday, July 24, in 60 Evans Hall on the Berkeley campus

Week 2 schedule
9:00-12:00Group Work
1:00-1:30Lieblich Hacking
2:30-3:00Olsson Break
3:30-4:00Tea Conrad
5:00-5:30Question and Answer