Traditionally, analysis was the branch of mathematics which had the closest ties to quantum physics. Today, quantum mathematics intersects with all the major branches of pure mathematics such as geometry, topology, algebra and analysis, but also with such areas as logic, combinatorics and number theory.
Focus on pure mathematics and internationally leading research
Some of the most advanced parts of algebra, geometry and topology have seen a great impact from quantum physics over the last four decades with many applications of quantum field theory and string theory predicting new results in these areas. As the latest push, this is further progressing into number theory. Thus, a great deal of pure mathematics will be pursued at the centre, with the aim of building a strong pure mathematics component of the centre. This will constitute our efforts to build a world leading team of excellent mathematicians impassioned to develop the mathematical foundations for quantum theory. The centre will further combine its pure mathematical initiatives with an ambitious build-up in the theoretical foundations of quantum field theory and string theory and further in the theoretical foundations of quantum engineering.
Development of theoretical physics
This all goes very well hand in hand with the latest advances in the study of both quantum field theory and string theory, which heavily relies on deep algebraic, geometric, topological and number theoretical insights. Hence, we are seeing the first signs of this flow from theoretical physics to mathematics reversing. Via its involvement in the ERC-Synergy project Recursive and Exact New Quantum Theory (ReNewQuantum), the centre will be at the forefront of this development. Researchers from the centre will pioneer the application of a combination of techniques from resurgent analysis with techniques from the advanced geometric and topological machinery to understand the relationship between the Poincaré asymptotics and exact solutions of certain quantum field theories. This has further strong ties to the theory of modular forms and thus deep relations to number theory.
Quantum engineering prospects
Moreover, there are a number of quantum engineering prospects of these new methods in studying quantum theories, which will be developed at the centre. In particular, applications to certain topological phases of matter are already under investigation, as far as their quantum engineering and quantum computation capabilities are concerned. On top of this, quantum phenomena in a bio-molecular context will be explored. Researchers now part of the centre have previously successfully applied techniques from quantum field theory to advance our understanding of RNA and protein folding. Investigations are now ongoing to uncover the extent to which there also are quantum phenomena of biological significance in macro-molecular biology.