Edward Witten talk "What One Can Hope To Prove About Three-Dimensional Gauge Theory," at the Simons Center Workshop "Mathematical Foundations of Quantum Field Theory" (scgp.stonybrook.edu/scientific/workshops/1498). Slides at media.scgp.stonybrook.edu/presentations/20120117_3_Witten.pdf . Original video at media.scgp.stonybrook.edu/video/video.php?f=20120117_3_qtp.mp4 . The workshop was organized by Mike Douglas, Kevin Costello and Arthur Jaffe. "Quantum field theory is a rich subject, with a long history in physics and in mathematics. In recent years it has inspired many profound developments in topology, in algebra and representation theory, and in analysis. Given the growing interest in the subject among mathematicians, it seems timely to hold a workshop to review the current state of the field, agree on what has been accomplished and what could be accomplished by a systematic application of the known ideas and techniques, try to identify where new ideas and techniques could have the most impact, and agree on a list of important problems and questions whose resolution would at the least serve as benchmarks to measure our progress, and at best significantly advance the field."

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