The heart of circle dynamics, operator algebra, and their relationship

PhD defence, Thursday 27 April 2017. Benjamin Randeris Johannesen

2017.04.27 | Steffi Hjerrild Iversen

Benjamin Randeris Johannesen

A dynamical system is a system that evolves over time (either discrete or continuous). They are ubiquitous, e.g. in the rythm of a beating heart or the breathing of a living being. They are important in their own right but also have a particular relation to operator algebra. The special relationship between dynamical systems and operator algebra is long-lived and has been developed in many different directions. 

In his thesis Benjamin Randeris Johannesen explored the (one-dimensional) discrete dynamical system arising from iterating a piecewise monotone map from the unit circle into itself, as well as the C*-algebra of an equivalence relation associated with the dynamical system. This investigation places the C*-algebras in Elliott's classification programme for C*-algebras and includes a thorough exploration of transitive critically finite circle maps and a complete classifiation of these up to topological conjugacy. The (surjective) piecewise monotone circle maps in the thesis differ from (local) homeomorphisms by rarely being (locally) injective, and the results thus build on the relationship between dynamical systems and operator algebra.

The PhD degree was completed at the Department of Mathematics, Science and Technology, Aarhus University.

This résumé was prepared by the PhD student.

 Thursday 27 April 2017 at 10.15
Place: Building 1531, room 113, Lecture Theatre D1, Department of Mathematics, Aarhus University
Title of dissertation: The core of C*-algebras associated with circle maps
Contact information: Benjamin Randeris Johannesen, e-mail:, tel.: +45 51843381
Members of the assessment committee:
Professor Jean Renault, Department of Mathematics, University of Orléans, France
Professor Nadia Larsen, Department of Mathematics, University of Oslo, Norway
Professor Bent Ørsted (chair), Department of Mathematics, Aarhus University
Main supervisor:

Associate professor Klaus Thomsen, Department of Mathematics, Aarhus University
 The PhD dissertation will be defended in English

The defence is public.
The dissertation is available for reading at the Graduate School of Science and Technology/GSST, Ny Munkegade 120, building 1520, rooms 128-134, 8000 Aarhus C.

PhD defence
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Revised 23.02.2018