Dates: 2-6 February 2015
Location: The University of New South Wales
Arithmetical dynamical systems, that is, dynamical systems generated by iterations of rational functions over fields of number-theoretic interest, have seen a significant explosion of work in recent years but still many algebraic, number theoretic and graph theoretic problems remain wide open. The interest in such dynamical systems comes also from connections that have been forged with many different areas of pure and applied mathematics.
The purpose of this workshop was to further explore the complex algebraic and number theoretic behaviour, as well as to gain a better understanding of the structure of functional graphs of arithmetical dynamical systems.
The DS_NT_GT Workshop brought together researchers in dynamical systems, graph theory and number theory interested in learning the research activities of these fields and expand their own research.
The invited speakers had very broad research interests so as to reflect the goal of the workshop. Each invited talk covered several different topics. For example, Professor Cheryl Praeger talked about problems of graph theory, which are related to dynamical systems on graphs (e.g. mixing) and also to hot areas of number theory, such as additive combinatorics.
The workshop was very dynamic; Professor Tony Guttmann, influenced by some discussions at the workshop, changed the topic of his previously-planned talk to another one to reflect these discussions and new developments.
The structure of the workshop, which allocated plenty of time for informal interaction, greatly stimulated discussion and interaction. New contacts and collaborative links were established; it is expected that these links will mature to long-term collaborative projects with publications in high impact journals.
Dr Peter van der Kamp’s recent arXiv contribution, Somos-4 and Somos-5 are arithmetic divisibility sequences, relates work described in his contributed talk as well as making reference to discussions at the workshop in the acknowledgements as a source of additional knowledge.
More details and slides of presented lectures and contributed talks are available from the workshop website: http://web.maths.unsw.edu.au/~jagr/ADS_NT_GT.html