Professor Charles Conley invites you to attend the PhD dissertation defense of Connor O'Dell

"Non-resonant uniserial representations of Vec(R)"

Abstract:

The non-resonant bounded uniserial representations of Vec(ℝ) form a certain class of extensions composed of tensor density modules, all of whose subquotients are indecomposable. In this talk, we describe our results on the classification of all non-resonant bounded uniserial extensions of Vec(ℝ) up to length 6. The problem of classifying the extensions with a given composition series is reduced via cohomological methods to computing the solution of a certain system of polynomial equations in several variables derived from the cup equations for the extension. Beyond this length, all such extensions appear to arise as subquotients of extensions of arbitrary length, many of which are explained by the psuedodifferential operator modules. Others are explained by a wedge construction and by the pseudodifferential operator cocycle discovered by Khesin and Kravchenko.