Mathematics Colloquia and Seminars

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Despite its tremendous theoretical and experimental successes, there are good reasons to think that our current understanding of quantum field theory is incomplete in important ways. One of these reasons is the apparent existence of quantum field theories that cannot be given a conventional definition in terms quantum fields and Lagrangians. In this talk, I will introduce such a puzzling class of interacting quantum field theories in six dimensions that have resisted direct analysis since their discovery in the 90s. I will then describe an algebraic approach to these theories based on the superconformal bootstrap. This approach has led to the first exact calculations of correlation functions in these theories and appears to provide a useful framework for their systematic analysis.