| Private Homepage | https://wilhelm-winter.de |
| Selected Publications | • Castillejos, Jorge; Evington, Samuel; Tikuisis, Araon; White, Stuart; Winter, Wilhelm Nuclear dimension of simple C*-algebras. Inventiones Mathematicae Vol. 224, 2020 online • Christensen, Erik; Sinclair, Allen M.; Smith Roger R.; White, Stuart A.; Winter, Wilhelm Perturbations of nuclear C*-algebras. Acta Mathematica Vol. 208 (1), 2012, pp 93-150 online • Farah, Ilijas; Hart, Bradd; Lupini, Martino, Robert L.; Tikuisis, Aaron; Vignati, Alessandro; Winter, Wilhelm Model theory of C*-algebras. Memoirs of the American Mathematical Society Vol. 271 (1324), 2021 online • Sato, Yasuhiko; White, Stuart; Winter, Wilhelm Nuclear dimension and Z-stability. Inventiones Mathematicae Vol. 202 (2), 2015, pp 893-921 online • Tikuisis, Aaron; White, Stuart; Winter, Wilhelm Quasidiagonality of nuclear C*-algebras. Annals of Mathematics Vol. 185 (1), 2017, pp 229-284 online • Winter, Wilhelm Decomposition rank and Z-stability. Inventiones Mathematicae Vol. 179 (2), 2010 online • Winter, Wilhelm Nuclear dimension and Z-stability of pure C*-algebras. Inventiones Mathematicae Vol. 187 (2), 2012, pp 259-342 online • Winter, Wilhelm Classifying crossed product C*-algebras. American Journal of Mathematics Vol. 138 (3), 2016, pp 793-820 online • Winter, Wilhelm; Zacharias, Joachim The nuclear dimension of C*-algebras. Advances in Mathematics Vol. 224 (2), 2010, pp 461-498 online |
| Topics in Mathematics Münster | T1: K-Groups and cohomology T3: Models and universes T4: Groups and actions |
| Current Publications | • Farah, Ilijas; Hart, Bradd; Lupini, Martino, Robert L.; Tikuisis, Aaron; Vignati, Alessandro; Winter, Wilhelm Model theory of C*-algebras. Memoirs of the American Mathematical Society Vol. 271 (1324), 2021 online • Castillejos, Jorge; Evington, Samuel; Tikuisis, Araon; White, Stuart; Winter, Wilhelm Nuclear dimension of simple C*-algebras. Inventiones Mathematicae Vol. 224, 2020 online • Brake, Laura; Winter, Wilhelm The Toeplitz algebra has nuclear dimension one. Bulletin of the London Mathematical Society Vol. 51, 2019 online |
| Current Projects | • EXC 2044 - T01: K-Groups and cohomology K-groups and cohomology groups are important invariants in different areas of mathematics, from arithmetic geometry to geometric topology to operator algebras. The idea is to associate algebraic invariants to geometric objects, for example to schemes or stacks, C∗-algebras, stable ∞-categories or topological spaces. Originating as tools to differentiate topological spaces, these groups have since been generalized to address complex questions in different areas. online • EXC 2044 - T03: Models and universes This topic focusses on model theory and its applications in group theory and algebraic geometry, as well as on inner model theory and forcing axioms. Central to our research on model theory are the classification of groups or fields under model-theoretic assumptions. The interplay of the axiom of determinacy with large cardinal hypotheses and strong hypotheses which settle prominent combinatorial statements is studied in our research on set theory. online • EXC 2044 - T04: Groups and actions The study of symmetry and space through the medium of groups and their actions has long been a central theme in modern mathematics, indeed one that cuts across a wide spectrum of research within the Cluster. There are two main constellations of activity in the Cluster that coalesce around groups and dynamics as basic objects of study. Much of this research focuses on aspects of groups and dynamics grounded in measure and topology in their most abstract sense, treating infinite discrete groups as geometric or combinatorial objects and employing tools from functional analysis, probability, and combinatorics. Other research examines, in contrast to abstract or discrete groups, groups with additional structure that naturally arise in algebraic and differential geometry. online • CRC 1442 - D01: Amenable dynamics via C*-algebras We study Cartan pairs of nuclear C*-algebras through their completely positive approximations. We are particularly interested in Cartan pairs for which the ambient C*-algebra is classifiable by K-theory data, and we explore first steps to classify such pairs themselves, at least under suitable additional conditions. • CRC 1442 - D05: C*-algebras, groups, and dynamics: beyond amenability Our project will explore the regularity properties of non-nuclear C*-algebras, with a particular emphasis on stable rank one and strict comparison. We focus on two main classes of examples: C*-algebras associated with non-amenable groups and crossed product C*-algebras arising from non-amenable actions on compact Hausdorff spaces. We intend to leverage dynamical tools, including dynamical comparison and the structure of topological full groups. • EXC 2044 - B3: Operator algebras & mathematical physics The development of operator algebras was largely motivated by physics since they provide the right mathematical framework for quantum mechanics. Since then, operator algebras have turned into a subject of their own. We will pursue the many fascinating connections to (functional) analysis, algebra, topology, group theory and logic, and eventually connect back to mathematical physics via random matrices and non-commutative geometry. online | wwinter@uni-muenster.de |
| Phone | +49 251 83-33756 |
| Room | 403 |
| Secretary | Elke Enning Frau Elke Enning Telefon +49 251 83-33088 Zimmer 402 |
| Address | Prof. Dr. Wilhelm Winter Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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