019w: Computing in topological structures: foundations and implementations

Nikolay Bazhenov, Sobolev Institute of Mathematics of SB RAS

Takayuki Kihara, Nagoya University

Victor Selivanov, Ershov Institute of Informatics Systems of SB RAS

In the last decades, a theory of computation on topological structures, similar to the well-known theory of computation on discrete structures, has been fast developing. This development is motivated by the existing gap between the computational practice of working with topological structures (numerical mathematics, computer algebra, and symbolic computation) and a lack of solid mathematical foundations. Although a huge number of practically important numerical algorithms for computing on the reals or in functional spaces are known, the standard floating-point realization of such algorithms does not always yield a solution with arbitrary guaranteed precision. The study of computability and complexity in the analysis is important not only as a foundation for numerical methods but also for modelling, specification, and verification of continuous-time and hybrid systems. The aim here is to investigate the structural complexity (in a broad sense) of infinite computations.

The central purpose of the workshop is to bring together researchers from relevant communities across mathematics and computer science, to refresh existing interactions between them, to encourage new interactions, and to foster long-lasting collaborations.

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