Extremal Surfaces, Combinatorial and Geometric

The construction of "extremal" polyhedral surfaces may be thought of as a four-stage process:

First find a combinatorial scheme, analyze it topologically, realize it as a polyhedral surface in some Euclidean space, and finally find a realization in three-space.

At each of these steps, one faces surprisingly simple and basic open problems. In the lecture, I want to present old and new ideas, show examples, and discuss the key problems. This will lead us to talk about questions in combinatorial number theory, construct special matrices, and look at projections of high-dimensional polytopes.

Günter M. Ziegler, Technical University of Berlin

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