Topology, Algebraic Geometry, and Dynamics Seminar (TADS): Supermanifolds and derived differential geometry

Speaker:  David Carchedi, George Mason University

Title:  Supermanifolds and derived differential geometry

Abstract:  Supermanifolds are a generalization of smooth manifolds to allow extra coordinates that anti-commute. They arise in physics in the study of particles with half integer spin- (fermions), e.g. electrons, protons, neutrons etc. We will show how supermanifolds with extra structure can be used to model non-transverse intersections in differential geometry, and present a theory of derived manifolds.

Time permitting (though unlikely), we will explain how in turn derived differential geometry naturally arises as a tool to make sense of Feynman path integrals in quantum field theory.

Time:  Friday, April 1, 2022, 1:30pm – 2:30pm

Place:  Exploratory Hall, room 4208