Objectives:
The project is devoted to the study of topological and geometric properties of Banach spaces and their duals, aiming at a better understanding of their structure. Properties of the weak topology often imply important geometric properties of the Banach space in question. On the other hand, geometric properties of the Banach space often give information about its weak topology. Similar statements are true for duals of Banach spaces with the weak-star topology. We are going to explore this interplay in detail. The main project goals are:
1. Developing new tools for constructing and studying Banach spaces, using techniques from set theory and category theory.
2. Exploring different types of networks and related concepts in weak topologies, determining connections with renorming theory.
Results of Goal 1 will lead to new examples, settling some of the problems concerning interplay between geometric and topological properties of non-separable Banach spaces. Goal 2 will lead to a better understanding of the weak topology and its relations to the geometric structure of a Banach space.
Objectives:
Project of basic research in mathematical logic and theoretical computer science. We focus on bounded arithmetic and proof complexity, set theory, computational complexity theory, and the theory of algorithms. The topics range from foundational areas of mathematics to algorithmic problems motivated by applied research. The results of the project will be published in high quality international scientific journals and in the proceedings of selective conferences.
grants
