Measurable Group Theory

By Yehuda Shalom. 2005

67 citations recorded by the source corpus.

Subfields: Mathematical Physics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0ec817e2695a0638c68084e2b844741f9f8067d4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Adrian Ioana
2. S. Vaes
3. Sorin Popa
4. A. Furman
5. Damien Gaboriau
6. Thomas Sinclair
7. J. Peterson
8. Y. Kida

In Numerical Analysis

1. J. Peterson
2. Sorin Popa
3. Thomas Sinclair
4. A. Furman
5. Damien Gaboriau
6. Y. Kida
7. S. Vaes
8. Xin Li

In Statistical and Nonlinear Physics

1. Adrian Ioana
2. J. Peterson
3. Xin Li
4. A. Furman
5. S. Vaes
6. Sorin Popa
7. Thomas Sinclair
8. Damien Gaboriau

Citations in the corpus

• On cocycle superrigidity for Gaussian actions (2009, background): “We direct the reader to the survey articles [39, 49] for a summary of these recent developments.”
• Amalgamated free products of weakly rigid factors and calculation of their symmetry groups (2005, methodology): “∀i≥ 1. Like in ([P6II]), the terminology “vNE rigidity” is used here in a broad sense, in the same spirit the terminology “OE rigidity” is being used in orbit equivalence ergodic theory ([Fu1], [MS], [S]). It can designate results which from an isomorphism of group measure space factors derives orbi”
• Cartan subalgebras in C*-algebras. Existence and uniqueness (2017, result): “The situation we are describing here is completely analogous to the measurable framework, where a fruitful interplay between Cartan subalgebras in von Neumann algebras (vN-algebras), orbit equivalence for measure-preserving dynamical systems and geometric group theory has been established [56, 20, 1”
• Cocycle Superrigidity for Profinite Actions of Property (T) Groups (2008, background): “ion. During the past decade, the orbit equivalence theory of measure preserving actions of groups has been an extremely active area, with many new rigidity results having been proven (see the surveys [Sh1],[P4]). In particular, certain classes of group–actions Γ y Xhave been shown to be orbit equiva”
• Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa) (2006, background): “In this talk, we discuss Popa’s recent breakthrough rigidity results for Bernoulli actions2 of Kazhdan groups.”
• The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, background): “The references [29], [95] are quite detailed surveys in which various recent progress about measure equivalence are treated.”
• Orbit Equivalence and Measured Group Theory (2010, background): “See [Fur99a] for the basis in ME and the surveys [Gab05a, Sha05, Fur09] for more recent developments.”
• Measure conjugacy invariants for actions of countable sofic groups (2008, unknown): “e implications are false in general (cf. [Dy59], [CJ82]). In recent years, many striking new orbit equivalence rigidity and von Neumann equivalence rigidity results have been proven. For surveys, see [Sh05] and [Po07]. These results posit that under certain hypotheses, an orbit equivalence or a von ”
• Orbit inequivalent actions for groups containing a copy of $\mathbb{F}_{2}$ (2006, background): “A basic question in measurable group theory is to find groups which admit many non-orbit equivalent actions (see the survey [35]).”
• On Popa's Cocycle Superrigidity Theorem (2006, background): “Zimmer’s Cocycle Superrigidity Theorem [36] paved the way to many very strong OE rigidity results in ergodic theory for higher rank lattices and other similar groups (see Zimmer’s monograph [37] and references therein, Furman [7], [8], [9], Monod–Shalom [19], Hjorth–Kechris [15]), also (Gaboriau [11”
• Measure equivalence rigidity of the mapping class group (2006, background): “The reader should be referred to [15], [37], [38] for more details of recent development of measure equivalence and orbit equivalence.”
• On the superrigidity of malleable actions with spectral gap (2006, background): “ory ([Z1,2]). This changed dramatically over the last 7-8 years, with the advent of a variety of striking rigidity results ([Fu1], [G1,2], [MoSh], [P1-8], [H], [HK], [Ki]; see [P9] for a survey; also [Sh] for a survey on OE rigidity). Our aim in this paper is to investigate the most “extreme” such p”