Mathematical Structures for Computable Topology and Geometry 26.05 - 31.05.2002 organized by Ralph Kopperman, Mike Smyth, Dieter Spreen Topological notions and methods have successfully been applied in various areas of computer science. Computerized geometrical constructions have many appli- cations in engineering. The seminar we propose will concentrate on mathematical structures underlying both computable topology and geometry. Due to the digital nature of most applications in computer science these structures have to be different from the mathematical structures which are classically used in applications of topology and geometry in physics and engineering and which are based on the continuum. The new areas of digital topology and digital geometry take into account that in computer applications we have to deal with discrete sets of pixels. A further aspect in which topological structures used in computer science differ from the classical ones is partiality. Classical spaces contain only the ideal ele- ments that are the result of a computation (approximation) process. Since we want to reason on such processes in a formal (automated) way the structures also have to contain the partial (and finite) objects appearing during a computation. Only these finite objects can be observed in finite time. At least three types of computationally convenient structures for topology have been studied, and all of them may be developed in the direction of geometry. The first is domains, the second locales (and formal topology), and the third cell complexes. Domains, originally introduced by Dana Scott for the formal definition of pro- gramming language semantics, have recently found a broader field of applications. Domain theory provides interesting possibilities for exact infinitary computation. There are the “maximal point models”. The interval domain in which the real numbers are embedded as maximal elements is an example of this. Escard´o has used it for his development of a programming language that allows computing with intervals. But there are also domain models for convexity and intended applications in computer-aided design (Edalat et al.). Closely related to domain theory is the theory of locales (Coquand, Resende, Vickers, ... ) and its logical counterpart: formal topology (Martin-L¨ of, Sambin, 1