My research goal is to contribute to a deeper understanding of quantum field theory, which is the underlying framework of Nature. All matter, and their interactions, are excitations of quantum fields. Much is known about quantum fields, e.g. quantum electrodynamics is the most accurately verified theory in all of human knowledge in terms of certain predictions. But strongly coupled quantum fields, for example the confining phase of quantum chromodyamics are much harder to analyze directly. Many aspects of quantum fields remain surprising and mysterious. I explore the varied phenomena and phases of quantum fields by developing symmetry-based method to find new exact results, interconnections, and dualities among theories. Some of the theories include connections to string theory
and use supersymmetry and conformal symmetry as illuminating lampposts. Quantum field theory has also been an idea generating machine for mathematics, and there has been increasingly fruitful synergy in both directions. We are currently exploring the symmetry-based interconnections between QFT and mathematics in our Simons Collaboration on Global Categorical Symmetries.
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