Operator Algebras Seminar
Organizers: Marius Dadarlat, Andrew Toms, and Thomas Sinclair
Tuesday, 2:30-3:30pm, REC 315
Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015
- Date: 2/13
- Jianchao Wu (Penn State)
- Title: Demystifying Rokhlin dimension
The theory of Rokhlin dimension was introduced by Hirshberg, Winter and Zacharias as a tool to study the regularity properties of C*-algebras in relation with group actions. It was inspired by the classical Rokhlin lemma in ergodic theory. Since then, it has been greatly developed as well as simplified, and connections to other areas have been discovered. In this talk, I will present some newer perspectives to help us understand this concept. In particular, I will explain its relation to the Schwarz genus for principal bundles in the context of generalized Borsuk-Ulam theorems. I will also indicate how one can extend the theory beyond residually finite groups. This includes recent and ongoing joint projects with Gardella, Hajac, Hirshberg, Hamblin, Tobolski and Zacharias.
- Date: 2/24
- Date: 3/6
- Ali Kavruk (VCU)
- Title: Relative Weak Injectivity for Operator Systems (Slides)
- Extending C. Lance's weak expectation property, E. Kirchberg introduces the notion of relative weak injectivity for pairs of C*-algebras. Subsequent studies exhibit that this concept has a key role in Riesz interpolations, Riesz-Arveson extension theory, Ando's theory on numerical radius etc. In this talk we focus on two natural extensions of this notion to operator systems and overview their properties. As applications, we first characterize Kirchberg and Wasserman's C*-systems in terms of nuclearity and see that these objects coincide with (c,max)-nuclear objects. We then carry out the nuclearity criteria given by Namioka and Phelp's test systems to C*-systems. We finally focus on the notion of quasi-nuclearity in operator system setting, and outline that it is equivalent to classical nuclearity. In this introductory presentation we also have the opportunity talk about many open questions in this context.
- Date: 3/12-3/17
- Date: 3/20 *CANCELLED*
- Benben Liao (Texas A&M)
- Date: 4/21
- Date: 4/24
- Kyle Austin (Ben Gurion)
- Title: A Functorial Approach to Groupoid Modeling of C*-algebras
- Abstract: In joint works with Magdalena Georgescu and Atish Mitra, we have devised a way to do categorical modeling of c*-algebras using groupoids. Specifically, we have found morphisms of groupoids with Haar systems of measures that induce morphisms of maximal groupoid c*-algebras; moreover, our association of groupoid to maximal groupoid c*-algebra and our morphisms of groupoids to their induced morphisms is functorial and generalizes the Gelfand duality functor for spaces. We use this to construct explicit examples of lots of c*-algebras including the Jiang-Su and Razak Jacelon algebras. If there is time, I will also talk about our current project on finding an inverse functor from certain pairs of c*-algebras to groupoids.
- Date: 5/9, 11:00, MATH 431
- Alessandro Vignati (Jussieu)
- Title: Who embeds where?