Joint Theory Seminar: Jake Bourjaily

What is the mathematical form of the (perturbative) predictions made by quantum field theory?—what kinds of numbers arise? what special functions? What symmetries do these enjoy? I will survey what is known today in answer these questions, and raise another: Why is quantum field theory so hard?—and what can be done to make it easier?

Despite incredible advances in our understanding of quantum field theory and the exponential growth in our access to computational resources, our technology for doing Feynman integrals remains woefully inadequate for many modern applications of quantum field theory and is largely responsible for the paucity of predictions ever made beyond the lowest-orders of perturbative approximation. I will review the state of affairs regarding this technology, and describe the new ideas being used to fashion more powerful computational (and conceptual) tools.