Jonathan Brown (University of Dayton) Canonical Cartan Subalgebras of Étale Groupoid -Algebras and the Construction of Twists Sponsored by the Meyer Fund
Dec. 12, 2017 12:10pm (MATH …
Kenneth McLaughlin (CSU) Random matrices, d-bar problems, and approximation theory
Let be an étale groupoid. In joint work with Nagy, Reznikoff, Sims and Williams, we study a subgroupoid of consisting of isotropy, in an effort to determine when a representation of is injective. We show that a representation is injective on if and only if its restriction to is, and that when is closed, then is a Cartan subalgebra of . Now, Renault in 2008 showed that given a Cartan subalgebra of a -algebra , one can construct a twist so that is isomorphic to . In this talk, I will first describe my joint results with Nagy et al. and then show how the work of Muhly, Renault and Williams can be used to explicitly construct a twist associated to the inclusion of into when is all of the isotropy. I will then point out how this fails more generally.
Some surprising questions in analysis arise in the interconnections of the topics in the title. We will encounter zeros of the Taylor approximants of exp(z), and other analytic functions. We will consider questions of support of equilibrium charge distributions in the plane. Semi-classical analysis of d-bar problems will provide merriment along the way.