Operads and topological conformal field theories (MAGIC005)
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We explain the basics of the Feynman path integral formulation of quantum field theory and how it leads to asymptotic expansions of oscillating integrals and Feynman graphs. We then make a connection to pure mathematics via operads, modular operads and related notions. We will see how operads are applied in various problems in geometry and physics, particularly to the study of moduli spaces of Riemann surfaces. Time permitting, we consider such topics as deformation quantization, the Witten conjecture and/or Chern-Simons theory.
Spring 2008 (Monday, January 21 to Friday, March 14; Monday, April 28 to Friday, May 16)
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