Ajay Kumar Karri, Texas A&M University
Results on general Toepltiz random matrices
We prove the convergence of $*$-moments of Toeplitz matrices in two cases: (1) matrix entries are independent Gaussian random variables and (2) matrix entries are free semicircular entries. We also study joint $*$- moments of Toeplitz matrices in both cases with $ L^\infty[0,1]$ functions.
Pradyut Karmakar, Sam Houston State University
Fejer property of groupoids and galois correspondence
Let $G$ be a topological étale groupoid. We introduce a notion of the Fejér property for topological étale groupoids. As a consequence, we show that when $G$ is a principal étale second countable groupoid satisfying the Fejér property, every closed $C_0(\GG)$-bimodule $M\subset C_r^*(G)$ is of the form $\overline{C_c(U)}^r$ for some open set $U$. As a result, for such groupoids, we show that every intermediate algebra $\B$ with $C_0(\GG)\subseteq \B\subseteq C_r^*(G)$ is of the form $C_r^*(H)$ for some open subgroupoid $H \leq G$.
This is joint ongoing work with Tattwamasi Amrutam and Anshu
Gregory Faurot, The Ohio State University
Homotopy 3-Type of Abelian C*-Algebras
C*-categories have a rich history in the study of C*-algebras, going back to work of Rieffel in the 1970s. Recent work of Ferrer provides a framework for C*-3-categories, a higher category theoretic analogue of a C*-category. Given an object $C$ of a higher category, one may compute the homotopy groups of $C$ in this category. In the C*-3-category $\mathsf{AbC^*Alg}$, we decompose the first higher homotopy group of $C(T)$ as an extension of the homeomorphism group of $T$ by a subgroup of its third cohomology group. This work is joint with Giovanni Ferrer.
Mikkel Munkholm, University of Nebraska–Lincoln
Stability now with action(s)
Stability is a potent property of C*-algebras. Stabilized C*-algebra frequent throughout the field and feature prominently in K-theory, KK-theory, the completed Cuntz-semigroups and when examining the corona factorization property. However, verifying whether a C*-algebra is stable poses a non-trivial question. The best tool available for establishing stability is the Hjelmborg-Rørdam criterion: an approximation property equivalent to stability. Much alike nuclearity and exactness, local characterizations are salient to have at one's disposal and this begs the question whether a dynamical version exists. In this talk, I will present a dynamical Hjelmborg-Rørdam criterion and discuss a dynamical companion to Hjelmborg and Rørdam's theorem on stability.
Alex Myers, University of Nebraska–Lincoln
More AF C*-Algebras from Non-AF Groupoids
Ian Mitscher and Jack Spielberg demonstrated a novel construction of the Effros-Shen Algebras through groupoid C*-Algebras. This construction can be generalized to produce additional families of AF Algebras.
Benjamin Jones, Arizona State University
C*-Correspondences for Ordinal Graphs
We present criteria for when the C*-algebra of an ordinal graph is naturally isomorphic to a Cuntz-Pimsner algebra. This condition also characterizes when certain homomorphisms from algebras of distinguished subcategories into the ordinal graph algebra are all simultaneously injective. We describe how an application of these results leads to a slight generalization of a previous Cuntz-Krieger uniqueness theorem.