REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Theo Johnson-Freyd

ABSTRACT: Wick's theorem, proven by Isserlis in 1918, provides simple algebraic relations describing the moments (i.e. correlation functions, expectation values) of a Gaussian probability measure in terms of the quadratic moments.  One can ask for similar explicit relations for probability measures of the form exp(cubic)dx or even higher-degree homogeneous polynomials in the exponent.  In this talk I will present a homological-algebraic approach to finding such relations, based ultimately on a derived-geometry interpretation of Batalin--Vilkovisky integration. This is joint work with Owen Gwilliam and joint work in progress with Shamil Shakirov.