אנליזה לא-קומוטטיבית

הסמינר מתכנס בימי שלישי, בשעות 11:00-12:00, בseminar room -101

השבוע


מקום: 72/123

Adam Dor-On (Munster)

Graded isomorphism problems for graph algebras

In a seminal 1973 paper, Williams recast conjugacy and eventual conjugacy for subshifts of finite type purely in terms of equivalence relations between adjacency matrices of the directed graphs. Williams expected these two notions to be the same, but after around 20 years the last hope for a positive answer, even under the most restrictive conditions, was extinguished by Kim and Roush.

In this talk, we will discuss operator algebras associated with adjacency matrices / directed graphs, which are naturally $\mathbb{Z}$-graded algebras. These operator algebras were first introduced by Cuntz and Krieger in tandem with early attacks on Williams’ problem, and manifest several natural properties of subshifts through their classification up to various kinds of isomorphisms.

The works on Cuntz-Krieger algebras later inspired a systematic study of purely algebraic versions called Leavitt path algebras, promoting new interactions between pure algebra and analysis. A well-known conjecture of Hazrat claims that two Leavitt path algebras are graded isomorphic if and only if their unital graded Grothendieck K0 groups are isomorphic. The topological version of this problem asks for a characterization of graded (stable) isomorphisms between Cuntz-Krieger algebras in terms of equivariant K-theory.

A solution to these problems has been sought after by many, and although substantial progress has been made, a proof is still missing in general. In joint work with Carlsen and Eilers we were able to discover subtle obstructions to certain algebraic methods of proof for the latter conjecture, by building on the counterexamples of Kim and Roush


מפגשים בסמסטר 22–2021–א

המפגשים הבאים

תאריך
כותרת
מרצה
תקציר
30 בנוב, In 72/123 Graded isomorphism problems for graph algebras Adam Dor-On (Munster)

In a seminal 1973 paper, Williams recast conjugacy and eventual conjugacy for subshifts of finite type purely in terms of equivalence relations between adjacency matrices of the directed graphs. Williams expected these two notions to be the same, but after around 20 years the last hope for a positive answer, even under the most restrictive conditions, was extinguished by Kim and Roush.

In this talk, we will discuss operator algebras associated with adjacency matrices / directed graphs, which are naturally $\mathbb{Z}$-graded algebras. These operator algebras were first introduced by Cuntz and Krieger in tandem with early attacks on Williams’ problem, and manifest several natural properties of subshifts through their classification up to various kinds of isomorphisms.

The works on Cuntz-Krieger algebras later inspired a systematic study of purely algebraic versions called Leavitt path algebras, promoting new interactions between pure algebra and analysis. A well-known conjecture of Hazrat claims that two Leavitt path algebras are graded isomorphic if and only if their unital graded Grothendieck K0 groups are isomorphic. The topological version of this problem asks for a characterization of graded (stable) isomorphisms between Cuntz-Krieger algebras in terms of equivariant K-theory.

A solution to these problems has been sought after by many, and although substantial progress has been made, a proof is still missing in general. In joint work with Carlsen and Eilers we were able to discover subtle obstructions to certain algebraic methods of proof for the latter conjecture, by building on the counterexamples of Kim and Roush

יום ב, 6 בדצמ, 15:00–16:00 TBA Robert Martin (Manitoba)

TBA

יום ב, 13 בדצמ, 14:30–15:30 TBA (part 1) Sibaprasad Barik (BGU)

TBA

21 בדצמ TBA (part 2) Sibaprasad Barik (BGU)

TBA

4 בינו TBA Ilan Hirshberg (BGU)

TBA

המפגשים הקודמים

תאריך
כותרת
מרצה
תקציר
26 באוק Generalized Powers‘ averaging for commutative crossed products Tattwamasi Amrutam (BGU)

In 1975, Powers proved that the free group on two generators is a $C^{\star}$-simple group. The key insight in Powers‘s proof of the $C^\star$-simplicity is that the left regular representation of $\mathbb{F}_2$ satisfies Dixmier type averaging property. Using the pioneering work of Kalantar-Kennedy, it was shown by Haagerup and Kennedy independently that the $C^\star$-simplicity of the group $\Gamma$ is equivalent to the group having Powers‘ averaging property. In this talk, we introduce a generalized version of Powers’ averaging property for commutative crossed products. Using the notion of generalized Furstenberg boundary introduced by Kawabe and Naghavi (independently), we show that the simplicity of the commutative crossed products $C(X)\rtimes_r\Gamma$ (for minimal $\Gamma$-spaces $X$) is equivalent to the crossed product having generalized Powers’ averaging. As an application, we will show that every intermediate $C^\star$-subalgebra $\mathcal{A}$ of the form $C(Y)\rtimes_r\Gamma\subseteq\mathcal{A}\subseteq C(X)\rtimes_r\Gamma$ is simple for an inclusion $C(Y)\subset C(X)$ of minimal $\Gamma$-spaces whenever $C(Y)\rtimes_r\Gamma$ is simple. This is a joint work with Dan Ursu.

יום ב, 15 בנוב, 14:30–16:00, In -101 On Operators In The Cowen-Douglas Class And Homogeneity (part 1) Prahllad Deb (BGU)
23 בנוב, In -101 On Operators In The Cowen-Douglas Class And Homogeneity (part 2) Prahllad Deb (BGU)