Fachbereich Mathematik und Informatik FB 10

Private Homepage	https://www.uni-muenster.de/IVV5WS/WebHop/user/kerrd/index.html
Research Interests	Operator algebras Ergodic theory
Selected Publications	• Kerr D, Li H Ergodic Theory: Independence and Dichotomies. , 2016 online • Kerr D Dimension, comparison, and almost finiteness. J. Eur. Math. Soc. Vol. 22, 2020 online • Kerr D, Li H Entropy and the variational principle for actions of sofic groups. Invent. Math. Vol. 186, 2011 online • Kerr D, Li H Entropy, Shannon orbit equivalence, and sparse connectivity. Mathematische Annalen Vol. 380, 2021 online • Conley C, Jackson S, Kerr D, Marks A, Seward B, Tucker-Drob R Følner tilings for actions of amenable groups. Math. Ann. Vol. 371, 2018 online • Kerr D, Li H Soficity, amenability, and dynamical entropy.. Amer. J. Math. Vol. 135, 2013 online • Brannan M, Kerr D Quantum groups, property (T), and weak mixing. Comm. Math. Phys. Vol. 360, 2018 online
Topics in Mathematics Münster	T3: Models and universes T4: Groups and actions T8: Random discrete structures and their limits
Current Publications	• Bell, Jamie; Geffen, Shirly; Kerr, David Stable rank one in nonnuclear crossed products. , 2025 online • Kerr D, Li H Entropy, products, and bounded orbit equivalence. Ergodic Theory Dynam. Systems Vol. TBA, 2022 online • Kerr D, Tucker-Drob R Dynamical alternating groups, stability, property Gamma, and inner amenability. Ann. Sci. Éc. Norm. Supér. (4) Vol. TBA, 2022 online • Kerr D, Li H Entropy, Shannon orbit equivalence, and sparse connectivity. Mathematische Annalen Vol. 380, 2021 online • Kerr D Dimension, comparison, and almost finiteness. J. Eur. Math. Soc. Vol. 22, 2020 online • Kerr D, Szabó G Almost finiteness and the small boundary property. Comm. Math. Phys. Vol. 374, 2020 online • Conley C, Jackson S, Kerr D, Marks A, Seward B, Tucker-Drob R Følner tilings for actions of amenable groups. Math. Ann. Vol. 371, 2018 online • Brannan M, Kerr D Quantum groups, property (T), and weak mixing. Comm. Math. Phys. Vol. 360, 2018 online
Current Projects	• 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 • EXC 2044 - T08: Random discrete structures and their limits Discrete structures are omnipresent in mathematics, computer science, statistical physics, optimisation and models of natural phenomena. For instance, complex random graphs serve as a model for social networks or the world wide web. Such structures can be descriptions of objects that are intrinsically discrete or they occur as an approximation of continuous objects. An intriguing feature of random discrete structures is that the models exhibit complex macroscopic behaviour, phase transitions in a wide sense, making the field a rich source of challenging mathematical questions. In this topic we will concentrate on three strands of random discrete structures that combine various research interests and expertise present in Münster. online • CRC 1442 - D04: Entropy, orbit equivalence, and dynamical tilings This project aims to advance the theory of rigidity and classification for Bernoulli actions of general groups with respect to orbit equivalence and its quantitative strengthenings. One overarching problem is to determine the extent to which the boundary between rigid and flexible behaviour is reflected in geometric or analytic properties of the group, and specifically, whether such properties intervene in questions of entropy invariance under Shannon orbit equivalence. online • *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. online • 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
E-Mail	kerrd@uni-muenster.de
Phone	+49 251 83-32672
Room	507
Secretary	Elke Enning Frau Elke Enning Telefon +49 251 83-33088 Zimmer 402
Address	Prof. Dr. David Kerr Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland
	Diese Seite editieren