| Date: | November 15, 2019 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Chris Gartland, University of Illinois at Urbana-Champaign |
| Title: | Markov Convexity of Model Filiform Groups |
| Abstract: | The Ribe program is the research program concerned with generalizing local properties of Banach spaces to biLipschitz invariant properties of metric spaces. Among such generalizations that have been found is the notion of Markov p-convexity, proven by Mendel-Naor to generalize uniform p-convexity. One of the first important spaces for which this invariant has been calculated is the Heisenberg group, proven by Li to be Markov p-convex for every p ≥ 4 and not Markov p-convex for any p<4. In this talk, we'll start with background on Carnot groups and model filiform groups - a class of Carnot groups containing the Heisenberg group - and then explain how to use random walks on graphs to compute their Markov convexities. |
|
| Date: | December 6, 2019 |
| Time: | 4:00pm |
| Location: | BLOC 628 |
| Speaker: | Chris Phillips, University of Oregon |
| Title: | The Cuntz semigroup of the crossed product by a finite group action with the weak tracial Rokhlin property |
| Abstract: | Let A be a simple unital C*-algebra. Suppose that a finite group
G acts on A, and that the action has the weak tracial Rokhlin
property, a generalization of the Rokhlin property which uses
positive elements instead of projections, and is fairly common. We
prove that, after discarding the classes of the nonzero projections,
the Cuntz semigroup of the fixed point algebra is just the fixed
points in the Cuntz semigroup of A. For context, for algebras
without strict comparison, the Cuntz semigroup is often very hard
to compute.
As a corollary, we prove that the radius of comparison of the
crossed product satisfies
rc (C^* (G, A)) \leq [1 / card (G)] rc (A).
We also give an example of a simple separable unital AH algebra A
and an action of the two element group G on A which has the Rokhlin
property, and such that rc (A) and rc (C^* (G, A)) are both strictly
positive.
The way the weak tracial Rokhlin property is used in the proof is
different from the usual methods in C*-algebras.
Joint work with M. Ali Asadi-Vasfi and Nasser Golestani. |
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