New Directions in Fractal Geometry

 In Workshop reports

Australian National University & its Coastal Campus at Kioloa, 23–28 November 2014

Fractal geometry is a fast growing and dynamic area of mathematics. This meeting succeeded in stimulating research and collaboration between theory and application with a focus on key areas within fractal geometry including, antenna design, materials design, image analysis and fractal scanners.

Presentations from leading international figures Valerie Berthe, Doug Hardin, Jun Kigami and Konstantin Igudesmann explained research on links between fractals and Kronecker dynamics, discrete minimum energy problems, self-similar sets as quotients of shifts and applications to fractal antennas.

Jörg Thuswaldner spoke on the topology of self-affine tiles, Jeff Geronimo on a separation condition for fractal attractors, Irmina Herburt on fractal star bodies and Mike Whittaker on fractal substitution tilings.

The program provided a platform for discussions between early career researchers and established experts, as well as people from different specialisations and those working in theory and application.

Key talks were given by Michel Lapidus on links between fractals and non-commutative geometry, Károly Simon on multi-fractal analysis of traffic on the internet, Christoph Bandt on fractal morphisms, Jon Borwein on short walks, Markus Hegland on connections between numerics and fractals, Christian Gentil on applications of fractals in computer aided design and Andrei Tetenov on self-similar Jordan arcs.

There was a strong groundswell that this conference should be the starting point of a series.

MathSciNet Classification
60G18, 37N35, 28A80

Program structure
The symposium began with a full day of research talks. This was followed by four half days with afternoons to free to encourage attendees to interact amongst themselves.

Public Lecture
In the evening Professor Michel Lapidus (UCal) gave a public lecture titled An Invitation to Fractal Geometry and its Applications to an appreciative audience.

Web Links
http://maths.anu.edu.au/people/louisa-barnsle
http://maths.anu.edu.au/events/new-directionsfractal-geometry/

Other Sponsors
AustMS, CARMA, Australian National University, Fractal Antenna Inc. and ACEMS

Contact
Professor Michael Barnsley, Australian National University
Michael.barnsley@anu.edu.au

Organisers

Professor Michael Barnsley, Australian National University
Professor Chistoph Bandt, University of Greifswald
Laureate Professor Jon Borwein, The University of Newcastle
Professor Markus Hegland, Australian National University
Professor Ka-Sing Lau, Chinese University of Hong Kong

Special presenters

Professor Valerie Berthe, CNRS-University Paris Diderot
Research interests: symbolic dynamics, ergodic theory, Diophantine analysis, combinatorics on words and discrete geometry
Professor Michel Lapidus, University of California
Research interests: spectral and fractal geometry, a higher-dimensional theory of complex fractal dimensions, fractal geometry, dynamical systems, and their applications
Professor Jun Kigami, Kyoto University
Research interests: mathematical foundation of fractals, in particular, analysis of fractals
Professor Jörg Thuswaldner, University of Leoben
Research interests: elementary and analytic number theory, fractal geometry and topology

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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