BGU Non-commutative Analysis SeminarBGU Math<span class="mathjax">Tattwamasi Amrutam : Generalized Powers’ averaging for commutative crossed products</span>October 26, 11:00—12:00, 2021, seminar room -1012021-10-25T12:53:58+03:002021-10-21T10:47:01+03:00BGU MathTattwamasi Amrutam BGU<div class="mathjax"><p>In 1975, Powers proved that the free group on two generators is a <span class="kdmath">$C^{\star}$</span>-simple group. The key insight in Powers’s proof of the <span class="kdmath">$C^\star$</span>-simplicity is that the left regular representation of <span class="kdmath">$\mathbb{F}_2$</span> satisfies Dixmier type averaging property. Using the pioneering work of Kalantar-Kennedy, it was shown by Haagerup and Kennedy independently that the <span class="kdmath">$C^\star$</span>-simplicity of the group <span class="kdmath">$\Gamma$</span> 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 <span class="kdmath">$C(X)\rtimes_r\Gamma$</span> (for minimal <span class="kdmath">$\Gamma$</span>-spaces <span class="kdmath">$X$</span>) is equivalent to the crossed product having generalized Powers’ averaging. As an application, we will show that every intermediate <span class="kdmath">$C^\star$</span>-subalgebra <span class="kdmath">$\mathcal{A}$</span> of the form <span class="kdmath">$C(Y)\rtimes_r\Gamma\subseteq\mathcal{A}\subseteq C(X)\rtimes_r\Gamma$</span> is simple for an inclusion <span class="kdmath">$C(Y)\subset C(X)$</span> of minimal <span class="kdmath">$\Gamma$</span>-spaces whenever <span class="kdmath">$C(Y)\rtimes_r\Gamma$</span> is simple. This is a joint work with Dan Ursu.</p></div><span class="mathjax">Prahllad Deb: On Operators In The Cowen-Douglas Class And Homogeneity (part 1)</span>November 15, 14:30—16:00, 2021, -1012021-11-15T08:52:10+02:002021-11-15T08:50:09+02:00BGU MathPrahllad DebBGU<span class="mathjax">Prahllad Deb: On Operators In The Cowen-Douglas Class And Homogeneity (part 2)</span>November 23, 11:00—12:00, 2021, -1012021-11-15T08:53:12+02:002021-11-15T08:51:46+02:00BGU MathPrahllad DebBGU<span class="mathjax">Adam Dor-On: Graded isomorphism problems for graph algebras</span>November 30, 11:00—12:00, 2021, 72/1232021-11-25T13:39:43+02:002021-11-15T14:22:35+02:00BGU MathAdam Dor-OnMunster<div class="mathjax"><p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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</p></div><span class="mathjax">Robert Martin: Non-commutative measures and Non-commutative Function Theory in the unit row-ball</span>December 6, 15:00—16:00, 2021, seminar room -1012021-11-30T22:05:46+02:002021-11-16T00:02:52+02:00BGU MathRobert MartinManitoba<span class="mathjax">Sibaprasad Barik: Isometric dilations, von Neumann inequality and refined von Neumann inequality(part 1)</span>December 13, 14:30—15:30, 2021, seminar room -1012021-12-09T11:16:50+02:002021-11-15T09:57:06+02:00BGU MathSibaprasad BarikBGU<span class="mathjax">Sibaprasad Barik: Isometric dilations, von Neumann inequality and refined von Neumann inequality (part 2)</span>December 21, 11:00—12:00, 2021, seminar room -1012021-12-09T11:17:44+02:002021-11-23T21:56:56+02:00BGU MathSibaprasad BarikBGU<span class="mathjax">Paul Herstedt: Bratteli diagrams, dynamics, and classification beyond the minimal case</span>December 27, 14:30—15:30, 2021, seminar room -1012021-12-26T14:29:12+02:002021-12-06T13:22:18+02:00BGU MathPaul HerstedtBGU<div class="mathjax"><p>Earlier this year, we discovered a new class of zero-dimensional dynamical systems, which we call “fiberwise essentially minimal”, that are of importance to operator algebras because of the nice properties, in particular K-theoretic classification, of the crossed product. Today, we discuss the Bratteli diagrams associated to these systems, and extend the K-theoretic classification to include a dynamical condition called “strong orbit equivalence”, extending the existing result in the minimal case due to Giordano-Putnam-Skau.</p></div><span class="mathjax">Paul Herstedt: Bratteli diagrams, dynamics, and classification beyond the minimal case (part 2)</span>January 4, 11:00—12:00, 2022, seminar room -1012022-01-02T10:13:47+02:002021-11-24T14:14:35+02:00BGU MathPaul HerstedtBGU<div class="mathjax"><p>Earlier this year, we discovered a new class of zero-dimensional dynamical systems, which we call “fiberwise essentially minimal”, that are of importance to operator algebras because of the nice properties, in particular K-theoretic classification, of the crossed product. Today, we discuss the Bratteli diagrams associated to these systems, and extend the K-theoretic classification to include a dynamical condition called “strong orbit equivalence”, extending the existing result in the minimal case due to Giordano-Putnam-Skau.</p></div><span class="mathjax">Ilan Hirshberg: TBA</span>January 11, 11:00—12:00, 2022, seminar room -1012022-01-02T10:13:22+02:002022-01-02T10:13:22+02:00BGU MathIlan HirshbergBGU<div class="mathjax"><p>TBA</p></div>