In the first part of the talk, we discuss the ubiquitous problem of ill-defined path integrals in quantum field theory. We then discuss the speaker's work making rigorous sense of perturbatively defined path integrals that clarifies this murky subject. This involves having a proper understanding of the Wick expansion, a formal series expansion attached to integrals.

In the second part of this talk, we discuss one of the most central of quantum field theories, namely quantum Yang-Mills theory. We focus on the special case of two dimensions, for which a rigorous construction is well-known. We then discuss the fundamental (and overlooked) question of relating perturbative results to exact results in this particular setting. We present a variety of results of the author pertaining to the various gauge-fixing procedures one can invoke in calculating Wilson loop expectations.

No prior knowledge of quantum field theory is required for this talk. Speaker(s): Timothy Nguyen (Michigan State)