Book
Papers and Preprints
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Local entropy theory and
applications (joint with Felipe
Garcia-Ramos)
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$C^*$-algebraic quantum Gromov-Hausdorff distance
[ps|pdf] Entropy, virtual Abelianness, and
Shannon orbit equivalence (joint with David
Kerr)
Ergodic
Theory Dynam. Systems to appear.
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Bernoullicity of lopsided
principal algebraic actions (joint with Kairan Liu)
Israel J.
Math. to appear.
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Expansive actions with
specification of sofic groups, strong topological Markov property,
and surjunctivity (joint with Tullio
Ceccherini-Silberstein and Michel Coornaert)
J.
Funct. Anal. 286 (2024), no. 9, 110376.
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Intrinsic ergodicity, generators
and symbolic representations of algebraic group actions (joint
with Klaus
Schmidt)
Funktsional. Anal. i Prilozhen.
58 (2024), no. 1, 50--83.
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Malcolmson semigroups (joint
with Tsz Fun
Hung)
J.
Algebra 623 (2023), 193--233.
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Strongly independent matrices and
rigidity of $\times A$-invariant measures on n-torus (joint
with Huichi Huang, Enhui
Shi, Hui Xu)
Front. Math. 18
(2023), no. 1, 153--166.
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Entropy, products, and bounded
orbit equivalence (joint with David
Kerr)
Ergodic
Theory Dynam. Systems 43 (2023), no. 3, 904--942.
[ps|pdf] Markovian properties of continuous
group actions: algebraic actions, entropy and the homoclinic group
(joint with Sebastián
Barbieri and Felipe
García-Ramos )
Adv.
Math. 397 (2022), 108196.
[ps|pdf] Entropy, Shannon orbit equivalence,
and sparse connectivity (joint with David
Kerr)
Math. Ann.
380 (2021), no. 3-4, 1497--1562.
[ps|pdf] Combinatorial independence and naive
entropy (joint with Zhen Rong)
Ergodic
Theory Dynam. Systems 41 (2021), no. 7, 2136--2147.
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Sylvester rank functions for
amenable normal extensions (joint with Baojie Jiang)
J.
Funct. Anal. 280 (2021), no. 6, 108913.
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Bivariant and extended Sylvester
rank functions
J. Lond. Math. Soc.
(2) 103 (2021), no. 1, 222--249.
[ps|pdf] Null actions and RIM non-open
extensions of strongly proximal actions (joint with Zhen
Rong)
Israel J. Math.
235 (2020), no. 1, 139--168.
[ps|pdf] Garden of Eden and specification
Ergodic
Theory Dynam. Systems 39 (2019), no. 11, 3075--3088.
[ps|pdf] Sofic mean length (joint with
Bingbing
Liang)
Adv.
Math. 353 (2019), 802--858.
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Homoclinically expansive actions
and a Garden of Eden theorem for harmonic models (joint
with Tullio
Ceccherini-Silberstein and Michel Coornaert)
Comm.
Math. Phys. 368 (2019), no. 3, 1175--1200.
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Mean dimension, mean rank, and von
Neumann-Lück rank (joint with Bingbing
Liang)
J. Reine Angew. Math.
739 (2018), 207--240.
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Ergodicity of principal algebraic
group actions (joint with Jesse Peterson
and Klaus
Schmidt)
Contemp. Math. 631
(2015), 201--210.
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Homoclinic group, IE group, and
expansive algebraic actions (joint with Nhan-Phu Chung)
Invent.
Math. 199 (2015), no. 3, 805--858.
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Entropy, determinants, and $L^2$-torsion (joint with Andreas
Thom)
J.
Amer. Math. Soc. 27 (2014), no. 1, 239--292.
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Sofic mean dimension
Adv.
Math. 244 (2013), 570--604.
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Combinatorial independence and
sofic entropy (joint with David
Kerr)
Comm.
Math. Stat. 1 (2013), no. 2, 213--257.
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Soficity, amenability, and
dynamical entropy (joint with David
Kerr)
Amer. J. Math. 135
(2013), no. 3, 721--761.
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A new short proof for the
uniqueness of the universal minimal space (joint with Yonatan Gutman)
Proc. Amer. Math. Soc. 141
(2013), no. 1, 265--267.
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Smooth approximation of Lipschitz projection
Canad. Math. Bull. 55 (2012),
no. 4, 762--766.
[ps|pdf] Harmonic models and spanning forests
of residually finite groups (joint with Lewis Bowen)
J.
Funct. Anal. 263 (2012), no. 7, 1769--1808.
[ps|pdf] Family-independence
for topological and measurable dynamics (joint with Wen
Huang and Xiangdong Ye)
Trans.
Amer. Math. Soc. 364 (2012), no. 10, 5209--5245.
[ps|pdf] Compact
group automorphisms, addition formulas and Fuglede-Kadison
determinants
Ann. of Math. (2)
176 (2012), no. 1, 303--347.
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Entropy and the variational principle for actions of sofic groups
(joint with David
Kerr)
Invent.
Math. 186 (2011), no. 3, 501--558.
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Bernoulli actions and infinite
entropy (joint with David
Kerr)
Groups
Geom. Dyn. 5 (2011), no. 3, 663--672.
[ps|pdf] Appendix
to V. Mathai and J. Rosenberg's paper "A noncommutative
sigma-model"
J.
Noncommut. Geom.
5 (2011), no. 2, 295--298.
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Strict p-negative type of a metric space (joint with Anthony Weston)
Positivity
14 (2010), no. 3, 529--545.
[ps|pdf] A
Hilbert $C^*$-module admitting no frames
Bull. Lond. Math. Soc.
42 (2010), no. 3, 388--394.
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Turbulence, representations, and trace-preserving actions
(joint with David
Kerr and Mikaël
Pichot)
Proc. Lond. Math. Soc. (3)
100 (2010), no. 2, 459--484.
[ps|pdf] Metric
aspects of noncommutative homogeneous spaces
J.
Funct. Anal. 257 (2009), no. 7, 2325--2350.
[ps|pdf] On
Gromov-Hausdorff
convergence for operator metric spaces (joint with David
Kerr)
J. Operator Theory 62
(2009), no. 1, 83--109.
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Compact quantum metric spaces and ergodic actions of
compact quantum groups
J.
Funct. Anal. 256 (2009), no. 10, 3368--3408.
[ps|pdf] Combinatorial
independence in measurable dynamics (joint with David
Kerr)
J.
Funct. Anal. 256 (2009), no. 5, 1341--1386.
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Strong Morita equivalence of higher-dimensional
noncommutative tori. II (joint with George A. Elliott)
Math.
Ann. 341 (2008), no. 4, 825--844.
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Morita equivalence of smooth noncommutative tori
(joint with George A. Elliott)
Acta
Math. 199 (2007), 1--27.
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Independence in topological and $C^*$-dynamics (joint
with David
Kerr)
Math.
Ann. 338 (2007), no. 4, 869--926.
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Positive Voiculescu-Brown entropy in noncommutative toral
automorphisms (joint with David
Kerr)
Ergodic
Theory Dynam. Systems 26 (2006), no. 6, 1855--1866.
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Order-unit quantum Gromov-Hausdorff distance
J.
Funct. Anal. 231 (2006), no. 2, 312--360.
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Dynamical entropy in Banach spaces (joint with David
Kerr)
Invent.
Math. 162 (2005), no. 3, 649--686.
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Zeta functions of totally ramified p-covers of the
projective line (joint with Hui June Zhu)
Rend. Sem. Mat. Univ.
Padova 113 (2005), 203--225.
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Strict quantizations of almost Poisson manifolds
Comm. Math. Phys.
257 (2005), no. 2, 257--272.
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Theta-deformations as compact quantum metric spaces
Comm. Math. Phys.
256 (2005), no. 1, 213--238.
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Flabby strict deformation quantizations and K-groups
K-Theory
32 (2004), no. 4, 323--329.
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Strong Morita equivalence of higher-dimensional
noncommutative tori
J. Reine Angew.
Math. 576 (2004), 167--180.
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Construction of some families of 2-dimensional crystalline
representations (joint with Laurent
Berger and Hui June Zhu)
Math.
Ann. 329 (2004), no. 2, 365--377.
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On embeddings of full amalgamated free product C*-algebras
(joint with Scott Armstrong,
Ken Dykema,
and Ruy Exel)
Proc. Amer. Math. Soc. 132
(2004), no. 7, 2019--2030.
Notes
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