Rational cohomology via field theories

This talk will report on joint work with Nathaniel Stapleton in which we provide a (super symmetric) quantum field theoretic model of R-cohomology for any rational algebra R. Over a simplicial set, this gives a new interpretation of Sullivan's polynomial differential forms. This is the
first step in a more ambitious project whose goal is to provide a quantum field theoretic explanation for the Hopkins-Kuhn-Ravenel higher character theory in chromatic homotopy theory.