#
Moduli Spaces of Properly Embedded Minimal Surfaces

June 6 to June 10, 2005
at the

American Institute of Mathematics,
San Jose, California

organized by

Michael Wolf,
David Hoffman,
and Matthias Weber

## Original Announcement

This workshop will be devoted
to advancing the understanding of properly embedded minimal surfaces
in three-space, a subject whose roots to go back to Euler and
Lagrange. New examples discovered in an
explosion of activity in the 1980's have gradually focused the subject on the
problem of classification. Recently, several new approaches and techniques
have been developed which together begin to suggest that it might be possible
to organize these examples into families, and indeed to describe the structure
of the space of properly embedded minimal surfaces. In particular, dramatic
advances have been made towards the goal of characterizing the classical
surfaces as the unique examples with fundamental properties, and new families
of examples have been found that were either unexpected or thought to be
unapproachable. This workshop will be tightly focused on a few specific
questions which are fundamental for this classification effort. These problems
are linked by a confluence of attention from mathematicians with different points
of view and by the prospect that real progress might be made by approaches
using several different methods simultaneously.
The main topics of the workshop are:

- Existence of new properly embedded minimal surfaces of
finite topology;
- The uniqueness question for classical minimal surfaces,
Scherk's surface and the Riemann example in particular;
- The existence question for properly embedded minimal surfaces with
infinite topology but no finite topology quotient;
- Deformations of properly embedded minimal surfaces and limits
of families of such surfaces.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.