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What is quantum field theory?

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Quantum field theory (QFT) has been very successful in describing nature, in some cases yielding the most precise agreement between experiment and theory ever achieved. It underlies our current understanding of high energy physics, cosmology and condensed matter physics. Despite this, the theory does not have a satisfactory first-principles definition. Even its most accurate predictions mentioned above, come from summing the first few terms of series which is ultimately divergent. I will review this problem and also review various ways in which QFT has influenced (and been influenced by) different areas of mathematics.

This talk is part of the The Archimedeans (CU Mathematical Society) series.

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