Research Interests

Research Interests

$\bullet$ Operator algebras and noncommutative geometry.
$\bullet$ Structure and classification of nuclear C$^{*}$-algebras.
$\bullet$ Topological dynamics.
$\bullet$ Noncommutative dynamical systems.
$\bullet$ Operator algebras and model theory.

Selected Publications

Selected Publications of Prof. Dr. Wilhelm Winter

$\bullet$ A. Tikuisis, S. White, and W. Winter. Quasidiagonality of nuclear $\mathrm C^*$-algebras. Ann. of Math. (2), 185:229–284, 2017.

$\bullet$ W. Winter. {QDQ vs. UCT}. In T. M. Carlsen, N. S. Larsen, S. Neshveyev, and C. Skau (eds), Operator Algebras and Applications. Abel Symposia, 12:327–348. Springer, Cham, 2016.

$\bullet$ W. Winter. {Classifying crossed product $\mathrm C^*$-algebras}. Amer. J. Math., 138:793–820, 2016.

$\bullet$ Y. Sato, S. White, and W. Winter. {Nuclear dimension and $\mathcal Z$-stability}. Invent. Math., 202:893–921, 2015.

$\bullet$ I. Hirshberg, W. Winter, and J. Zacharias. {Rokhlin dimension and $\mathrm C^*$-dynamics}. Comm. Math. Phys., 335:637–670, 2015.

$\bullet$ W. Winter. {Nuclear dimension and $\mathcal Z$-stability of pure $\mathrm C^*$-algebras}. Invent. Math., 187:259–342, 2012.

$\bullet$ E. Christensen, A. Sinclair, R. Smith, S. White, and W. Winter. Perturbations of nuclear $\mathrm C^*$-algebras. Acta Math., 208:93–150, 2012.

$\bullet$ W. Winter and J. Zacharias. {The nuclear dimension of $\mathrm C^ *$-algebras}. Adv. Math., 224:461–498, 2010.

$\bullet$ W. Winter. {Decomposition rank and $\mathcal Z$-stability}. Invent. Math., 179(2):229–301, 2010.

$\bullet$ A. S. Toms and W. Winter. {Minimal dynamics and the classification of $\mathrm C^*$-algebras}. Proc. Natl. Acad. Sci. USA, 106(40):16942–16943, 2009.

Current Cluster Publications

Current Cluster Publications of Prof. Dr. Wilhelm Winter

$\bullet $ Kristin Courtney and Wilhelm Winter. Nuclearity and CPC$^*$-systems. arXiv e-prints, April 2023. arXiv:2304.01332.

$\bullet $ Kang Li, Hung-Chang Liao, and Wilhelm Winter. The diagonal dimension of sub-$\mathrm C^*$-algebras. arXiv e-prints, March 2023. arXiv:2303.16762.

$\bullet $ Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Aaron Tikuisis, Alessandro Vignati, and Wilhelm Winter. Model theory of $\rm C^*$-algebras. Memoirs of the American Mathematical Society, 271(1324):viii+127, May 2021. doi:10.1090/memo/1324.

$\bullet $ Jorge Castillejos, Samuel Evington, Aaron Tikuisis, Stuart White, and Wilhelm Winter. Nuclear dimension of simple C$^*$-algebras. Inventiones mathematicae, 224(1):245–290, April 2021. doi:10.1007/s00222-020-01013-1.

$\bullet $ Laura Brake and Wilhelm Winter. The Toeplitz algebra has nuclear dimension one. Bull. Lond. Math. Soc., 51(3):554–562, April 2019. doi:10.1112/blms.12250.

$\bullet $ Joan Bosa, Nathanial P. Brown, Yasuhiko Sato, Aaron Tikuisis, Stuart White, and Wilhelm Winter. Covering dimension of $\rm C^*$-algebras and 2-coloured classification. Mem. Amer. Math. Soc., 257(1233):vii+97, January 2019. doi:10.1090/memo/1233.