Geometry working seminar

Talk 1. Matthew Beckett - 9:30am

Pure Mathematics Department, University of Waterloo

“Monopoles and S1-invariant instantons”

Abstract

By extending the Hopf map radially, we obtain a map from R4 to R3 whose fibres away from the origin are copies of S1. Pullbacks under the Hopf map give a correspondence between pairs of connections and endomorphisms over R3 and connections over R4 which are invariant under an S1 action. Under this correspondence, monopoles on R3 \{0} are associated precisely to instantons on R4 \ {0}. In this talk, I will investigate this correspondence.

Talk 2. Justin Shaw - 11:00am

Pure Mathematics Department, University of Waterloo

“Invariant Vector Calculus 3:”

Abstract

We complete our study of undergraduate vector calculus from the differential geometry standpoint by finishing our survey of undergraduate continuum mechanics. Using physical assumptions and the framework we have constructed in Vector Calculus 1 and 2 we derive the governing equations for a fluid flow which is physically meaningful. These are the Navier-Stokes equations. This talk is a direct continuation of Vector Calculus 2.