A5033382752- Advanced Operator Algebra Research
- Advanced Topics in Algebra
- Mathematical Analysis and Transform Methods
- Advanced Banach Space Theory
- Homotopy and Cohomology in Algebraic Topology
- Geometric and Algebraic Topology
- graph theory and CDMA systems
- Algebraic structures and combinatorial models
- Coastal and Marine Management
- Coding theory and cryptography
- Advanced Numerical Analysis Techniques
- Optical Coherence Tomography Applications
- Holomorphic and Operator Theory
- Advanced Topology and Set Theory
- Rings, Modules, and Algebras
- Finite Group Theory Research
- Advanced Mathematical Modeling in Engineering
- Digital Filter Design and Implementation
- Mathematics and Applications
- Nonlinear Partial Differential Equations
- Species Distribution and Climate Change
- Limits and Structures in Graph Theory
- PAPR reduction in OFDM
- Geographies of human-animal interactions
- Advanced Algebra and Logic
University College Cork
2024
Vanderbilt University
2009-2024
University of California, Los Angeles
2008-2024
Swedish University of Agricultural Sciences
2022-2023
KU Leuven
2023
University of California, San Diego
2023
KTH Royal Institute of Technology
2016-2019
U.S. Air Force Institute of Technology
2010-2017
Office of Naval Research
2016-2017
University of Missouri
2011-2012
abstract: We prove an operator algebraic superrigidity statement for homomorphisms of irreducible lattices, and also their commensurators, from certain higher-rank groups into unitary finite factors. This extends the authors' previous work regarding non-free measure-preserving actions, answers a question Connes such groups.
We consider amalgamated free product II1 factors M = M1*BM2*B… and use "deformation/rigidity" "intertwining" techniques to prove that any relatively rigid von Neumann subalgebra Q ⊂ can be unitarily conjugated into one of the Mi's. apply this case where Mi's are w-rigid factors, with B equal either C, a Cartan A in Mi, or regular hyperfinite subfactor R obtain following type unique decomposition results, àla Bass–Serre: If (N1 * CN2*C…)t, for some t > 0 other similar inclusions algebras C Ni...
Abstract We present a general setting to investigate 𝒰 fin -cocycle superrigidity for Gaussian actions in terms of closable derivations on von Neumann algebras. In this we give new proofs some results S. Popa and produce examples phenomenon. also use result K. R. Parthasarathy Schmidt necessary cohomological condition group representation order the resulting action be superrigid.
Abstract In this paper we study characters on special linear groups <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>SL</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo></m:mo> <m:mo>(</m:mo> <m:mi>R</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> ${\mathrm{SL}_{n}(R)}$ , where R is either an infinite field or the localization of order in a number field. We give several applications to theory measure-preserving actions, operator-algebraic superrigidity, and almost homomorphisms.
Using an approach emerging from the theory of closable derivations on von Neumann algebras, we exhibit a class groups CR satisfying following property: given any Γ1,Γ2∈CR, then free, ergodic, measure-preserving action probability space Γ1×Γ2↷X gives rise to algebra with unique group-measure Cartan subalgebra. Pairing this result Popa's orbit equivalence superrigidity theorem obtain new examples W∗-superrigid actions.
We prove that any ergodic measure-preserving action of an irreducible lattice in a semisimple group, with finite center and each simple factor having rank at least two, either has orbits or stabilizers. The same dichotomy holds for many commensurators such lattices. above are derived from more general results on groups the Howe-Moore property <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper T...
We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact non-elementary convergence and lattices in non-compact semi-simple Lie but excludes inner amenable groups. show that crossed product II$_1$ factors arising from free ergodic probability measure preserving actions groups this have at most one weakly compact Cartan subalgebra, up to unitary conjugacy. As an application, we obtain the first $W^*$-strong rigidity results for...
We introduce the notion of proper proximality for finite von Neumann algebras, which naturally extends groups. Apart from group algebras properly proximal groups, we provide a number additional examples, including examples in settings free products, crossed and compact quantum Using this notion, answer question Popa by showing that algebra nonamenable inner amenable cannot embed into factor. also probability measure-preserving actions, gives an invariant orbit equivalence relation. This new...
We obtain a characterization of property (T) for von Neumann algebras in terms 1-cohomology, similar to the Delorme-Guichardet theorem groups.
Abstract Biological recording is a prominent and widely practised form of citizen science, but few studies explore long-term demographic trends in participation knowledge production. We studied age gender participants reporting to large online science multi-taxon biodiversity platform ( www.artportalen.se ). Adoption by user communities continually developing Information Communications Technologies (ICTs) greatly increased the number data, profound imbalances contribution across species...
We introduce Poisson boundaries of II $_1$ factors with respect to density operators that give the traces. The boundary is a von Neumann algebra contains factor and particular example unital completely positive map as introduced by Izumi. Studying inclusion into its boundary, we develop number notions, such double ergodicity entropy, can be seen natural analogues results regarding Furstenberg. use techniques developed answer problem Popa showing all finite satisfy his MV property. also...
We consider amalgamated free product II$_1$ factors $M = M_1 *_B M_2 ...$ and use ``deformation/rigidity'' ``intertwining'' techniques to prove that any relatively rigid von Neumann subalgebra $Q\subset M$ can be intertwined into one of the $M_i$'s. apply this case $M_i$ are w-rigid factors, with $B$ equal either $\Bbb C$, a Cartan $A$ in $M_i$, or regular hyperfinite subfactor $R$ obtain following type unique decomposition results, à la Bass-Serre: If (N_1 *_C N_2 ...)^t$, for some $t>0$...