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Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Information theory aims to find mathematically precise answers to fundamental questions such as how information is stored, processed, or sent reliably through noisy communication links. Towards the end of the 20th century, researchers started asking how these information-processing tasks change when information is encoded in systems exhibiting quantum-mechanical behavior. Remarkably, features of quantum mechanics such as the superposition principle and entanglement give rise to phenomena in information theory that cannot be realized with classical information-processing systems. Their discovery has led to the creation of the now thriving field of quantum information theory. A cornerstone of quantum information theory is the principle of non-additivity of information measures. Roughly speaking, non-additivity occurs if a communication resource becomes more powerful when used repeatedly or in conjunction with another resource. On the one hand, non-additivity effects are desirable as they push the limits of faithfully communicating information. On the other hand, they complicate an exact characterization of these limits in both mathematical and computational terms. Our workshop gathers experts from all areas of quantum information theory, with the goal of shedding further light on, and identifying new methods to study, the nature of non-additivity phenomena in quantum information-processing systems.

Isaac Newton Institute for Mathematical Sciences, Cambridge

Many of the fundamental concepts and problems in complexity theory originated at least partially in mathematical logic. The power of various feasible computational models appears to be linked with the strength of weak formal theories, and understanding the strength of formal theories may be useful --- if not key --- to resolving some of the open conjectures about the power of feasible computation. The workshop will be devoted to research on logical facets of complexity theory, especially the interplay between formal logical theories and computational complexity.

Analysis,    Numerische Analysis