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American Institute of Mathematics, Palo Alto, California

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This workshop, sponsored by AIM and the NSF, 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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

The deadline to apply for support to participate in this workshop has passed.

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