Investigations in Quantum Field Theory

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Quantum Field Theory is perhaps the most successful tool physicists use to describe the physical world. For example, the Standard Model, which describes in precise detail the behaviour of all known particles, is a quantum field theory. Other quantum field theories are used to describe systems of very practical interest, including superconductors and other exotic materials which lie at the core of modern and future electronic devices, such as quantum computers. The ubiquity of Quantum Field Theory in theoretical physics means that every novel idea in Quantum Field Theory reverberates through many different subjects and scientific communities, irrespectively of which community originally developed it. The study of Quantum Field Theory often involves ideas of great mathematical sophistication, which have lead to whole new perspectives on important mathematical subjects and novel connections between previously disconnected areas. This strong interdisciplinary activity at the intersection of physics and mathematics greatly benefits both subjects.   Despite being such a well-established tool, many aspects of Quantum Field Theory are still mysterious or poorly understood. Depending on the specific situation, a quantum field theory may be "weakly coupled" or "strongly coupled". Weakly coupled field theories allow us precise calculations which match in detail experimental results. They are usually considered to be well understood, though many important subtleties are still being discovered today. Strongly coupled field theories are poorly understood, and very hard to use for precise calculations. Many such theories may be still unknown and we do not have a systematic way to search for them.  These limitations in our understanding of Quantum Field Theory obstruct our progress in a variety of subjects, ranging from deep questions about the nature of the Universe to very concrete problems in material science, such as the development of superconductors able to function at room temperature.  The main objective of this proposal is to develop new computational tools and mathematical ideas to study Quantum Field Theory and to apply these tools to the solution of long standing theoretical problems in High Energy Physics, Condensed Matter Physics and Mathematics. The research activities in this program will also offer unique training opportunities to several students and young researchers, which will disseminate these tools and idea through the scientific community and beyond.  In the long term, this progress in our theoretical understanding of quantum field theories will impact our ability to tailor exotic quantum systems to practical applications, advance out understanding of the fundamental laws of the universe, and lead to deep mathematical advances. Beyond its concrete applications, reaching a full understanding of Quantum Field Theory will be one of humanity great intellectual achievements and it is worth pursuing for its own sake.