Aaron Tikuisis



Almost finiteness, comparison, and tracial Z-stability - Co-authored by Hung-Chang Liao.

Preprints (in press)

Nuclear dimension of simple C*-algebras - Co-authored by Jorge Castillejos, Sam Evington, Stuart White, and Wilhelm Winter. To appear in Invent. Math.
Uniform property Γ - Co-authored by Jorge Castillejos, Sam Evington, and Stuart White. To appear in IMRN.
Classifying maps into uniform tracial sequence algebras - Co-authored by Jorge Castillejos, Sam Evington, and Stuart White. To appear in Münster J. Math.
Decomposition rank of approximately subhomogeneous C*-algebras - Co-authored by George Elliott, Zhuang Niu, Luis Santiago. To appear in Forum Math. doi:10.1515/forum-2020-0018
The model theory of nuclear C*-algebras - Co-authored by Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Alessandro Vignati, and Wilhelm Winter. To appear in Mem. Amer. Math. Soc.

Published articles

Covering dimension of C*-algebras and 2-coloured classification - Co-authored by Joan Bosa, Nathanial Brown, Yasuhiko Sato, Stuart White, and Wilhelm Winter. Mem. Amer. Math. Soc., 2019.
Relative commutant pictures of Roe algebras - Co-authored by Ján Špakula. Comm. Math. Phys., 2019, doi:10.1007/s00220-019-03313-x
Rokhlin dimension for C*-correspondences - Co-authored by Nathanial Brown and Aleksey Zelenberg. Houston J. Math., 2018.
Maximally unitarily mixed states on a C*-algebra - Co-authored by Rob Archbold and Leonel Robert. J. Operator Theory, 2018, doi:10.7900/jot.2017sep24.2168.
Quasidiagonality of nuclear C*-algebras - Co-authored by Stuart White and Wilhelm Winter. Ann. of Math., 2017, doi:10.4007/annals.2017.185.1.4.
Relative commutants of strongly self-absorbing C*-algebras - Co-authored by Ilijas Farah, Bradd Hart, and Mikael Rørdam. Selecta Math., 2017, doi:10.1007/s00029-016-0237-y.
The Dixmier property and tracial states for C*-algebras - Co-authored by Rob Archbold and Leonel Robert. J. Funct. Anal., 2017, doi:10.1016/j.jfa.2017.06.026.
Nuclear dimension and Z-stability of non-simple C*-algebras - Co-authored by Leonel Robert. Trans. Amer. Math. Soc., 2017, doi:10.1090/tran/6842.
Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture. J. Aust. Math. Soc., 2016, doi:10.1017/S1446788716000033.
K-theoretic characterization of C*-algebras with approximately inner flip. IMRN, 2016, doi:10.1093/imrn/rnv334.
Corrigendum to "Regularity for stably projectionless, simple C*-algebras" [J. Funct. Anal. 263 (5) (2012) 1382–1407] - Co-authored with Henning Petzka. , J. Funct. Anal., 2016, doi:10.1016/j.jfa.2016.01.013.
High-dimensional Z-stable AH algebras - J. Funct. Anal., 2015, doi:10.1016/j.jfa.2015.05.013.
A simple C*-algebra with finite nuclear dimension which is not Z-stable - Co-authored by Ilijas Farah, Dan Hathaway, and Takeshi Katsura. Münster J. Math., 2014. doi:10.17879/58269761171.
On the structure of the Cuntz semigroup in (possibly) nonunital C*-algebras - Co-authored by Andrew Toms. Canad. Math. Bull., 2015, doi:10.4153/CMB-2014-040-5.
Decomposition rank of Z-stable C*-algebras - Co-authored by Wilhelm Winter. Anal. PDE., 2014 doi:10.2140/apde.2014.7.673.
Nuclear dimension, Z-stability, and algebraic simplicity for stably projectionless C*-algebras - Math. Ann., 2014, doi:10.1007/s00208-013-0951-0.
Regularity for stably projectionless, simple C*-algebras - J. Funct. Anal., 2012, doi:10.1016/j.jfa.2012.05.020.
A classification of finite rank dimension groups by their representations in ordered real vector spaces - Co-authored by Greg Maloney. J. Funct. Anal., 2011, doi:10.1016/j.jfa.2010.12.026.
An algebraic approach to the radius of comparison - Co-authored by Bruce Blackadar, Leonel Robert, Andrew Toms, and Wilhelm Winter. Trans. Amer. Math. Soc., 2012, doi:10.1090/S0002-9947-2012-05538-3.
The Cuntz semigroup of continuous functions into certain simple C*-algebras - Internat. J. Math., 2011, doi:10.1142/S0129167X11007136.
Hilbert C*-modules over a commutative C*-algebra - Co-authored by Leonel Robert. Proc. Lond. Math. Soc., 2011, doi:10.1112/plms/pdq017.

Ph.D. Thesis

The Cuntz semigroup of C(X,A).

Oberwolfach reports

Dimension reduction and Jiang-Su stability (joint work with Wilhelm Winter).
Central sequences, dimension, and Z-stability of C*-algebras (joint work with Leonel Robert).
Z-stability, property Gamma, partitions of unity and nuclear dimension (coauthored by Stuart White; joint work with Jorge Castillejos, Samuel Evington, and Wilhelm Winter).

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