Workshop on Algebraic, Number Theoretic and Graph Theoretic Aspects of Dynamical Systems

 In Workshop reports

University of New South Wales, 2–6 February 2015

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. Despite this recent profusion of scientific activity in ADS, many algebraic, number theoretic and graph theoretic problems remain wide open. Interest in this also comes from connections 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 gain a better understanding of the structure of functional graphs of arithmetical dynamical systems.

The DS_NT_GT Workshop brought together distinguished researchers of different backgrounds (dynamical systems, graph theory and number theory) interested in expanding the scope of problems they investigate and in developing the exciting and versatile research directions in ADS.

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 to hot areas of number theory, such as additive combinatorics.

Professor Tony Guttmann changed the topic of his previously-planned talk to reflect robust discussions and new developments during the workshop.

The workshop was structured to provide plenty of time for informal interaction and networking, which greatly stimulated discussion and resulting in the establishment of collaborative links.

Dr Peter van der Kamp’s recent arXiv contribution, Somos-4 and Somos-5 are arithmetic divisibility sequences, relates to 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.

MathSciNet Classification
11T06, 37P05, 05C20

Program structure

Web Links
http://web.maths.unsw.edu.au/~jagr/ADS_NT_GT.html

Other Sponsors
AustMS, School of Mathematics and Statistics, University of New South Wales, MASCOS

Contact
Professor John A. G. Roberts, University of New South Wales
jag.roberts@unsw.edu.au

Organisers

Professor Brendan McKay, Australian National University
Dr Alina Ostafe, University of New South Wales
Professor John Roberts, University of New South Wales
Professor Igor Shparlinski, University of New South Wales

Special presenters

Professor Alex Gamburd, City University of New York
Research interests: number theory and expander graphs
Professor Tony Guttmann, The University of Melbourne
Research interests: random matrices, lattices, random walks
Professor Cheryl Praeger, The University of Western Australia
Research interests: graph theory and group theory
Professor Klaus Schmidt, University of Vienna
Research interests: ergodic theory and algebraic dynamics
Professor Joe Silverman, Brown University
Research interests: arithmetic dynamics and number theory
Professor Franco Vivaldi, Queen Mary University of London
Research interests: algebraic dynamics and number theory
Professor Thomas Ward, Durham University
Research interests: ergodic theory and algebraic dynamics
Professor Nick Wormald, Monash University
Research interests: graph theory and combinatorics

Participant Summary

Attendees

NUMBER OF ATTENDEES

XX

  • Academic

    64%

  • Postdocs

    0%

  • Post Graduates

    28%

  • Students

    8%

  • Industry

    0%

Gender

Gender Breakdown

State Breakdown
Victoria
50%
Australian Capital Territory
50%
New South Wales
50%
Queensland
0%
South Australia
0%
Western Australia
0%
Tasmania
0%
Northern Territory
0%
International
0%
Citizenship Status
Domestic - 60%
50%
International - 40%
50%
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