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"Renormalons and their resurgent hyperasymptotics"
Perturbation expansions in quantum field theory fail to converge for at least two reasons. The number of diagrams may increase too fast with the loop number. The process of renormalization may make the contribution of each diagram too large. I shall give an example of the latter case, from phi^3 theory in 6 dimensions, where a renormalon is responsible for the problem. It can be tamed in the physical case. If we allow an imaginary coupling constant, the problem is radically different and becomes of considerable interest to mathematicians. I shall give a gentle introduction, for a general audience, followed by recent results on the mathematical structure, obtained in https://arxiv.org/pdf/2202.01513.pdf with Michael Borinsky.