Numeration and Substitution

Numeration refers to the arithmetic and symbolic representation of mathematical objects, such as the decimal expansion of a real number.  Although we always had ten fingers, decimal expansions are by no means the only, or the oldest, or the most efficient way of representation, as it comes to data storage or particular operations we want to carry out.  For example, continued fractions, dating back to Greek mathematics, are the foremost method for achieving rational approximations of real numbers. Their importance has not dwindled, due to applications in mechanics (resonance), mathematical analysis (normal forms, small divisor problems, KAM theory) and in complex dynamics. Variations of continued fraction continue to be developed and refined. Also in higher dimensions, the study of continued fractions algorithms (such as Brun, Jacobi-Perron, Selmer and many others) with special emphasis on their dynamical, Diophantine and combinatorial behaviour are important objects of current investigations.

On the other hand, digit systems have to be generalized in various ways and objects such as β-expansions, Cantor expansions, canonical number systems, and shift radix systems show a great variety of interesting dynamical, geometric, and combinatorial properties and have even links to complex dynamics recently.

It remains a fascinating fact how many similarities exist between algorithmic approaches to fractal geometry, tiling spaces, complexity theory of symbolic dynamics, piecewise isometries such as interval exchange transformations, but also many problems in combinatorics. In this sense, the theory of numeration systems remains a unifying link between many areas of mathematics and computer science.

Schedule (pdf)

Coming soon.


Name Affiliation
Henk Bruin University of Vienna
Clemens Heuberger Alpen-Adria-Universität Klagenfurt
Daniel Krenn Alpen-Adria-Universität Klagenfurt
Jörg Thuswaldner Montanuniversität Leoben


Name Affiliation
Jean-Paul Allouche CNRS
Myriam Amri University of Leoben
Drew Ash Albion College
Valérie Berthé CNRS
Celia Cisternino University of Liege
Maria Isabel Cortez Universidad de Chile
Ligia-Loretta Cristea University of Graz
Karma Dajani Utrecht University
Hanka Dlouhá Czech Technical University Prague
Paulius Drungilas Vilnius University
Fabien Durand University of Picardie Jules Verne
Sebastien Ferenczi Institut de Mathematiques de Marseille
Robbert Fokkink Technical University Delft
Charles Fougeron CNRS
Christiane Frougny University Paris-Diderot
Peter Grabner Technical University of Graz
Kevin Hare University of Waterloo
Pascal Hubert Institut de Mathematiques de Marseille
Jonas Jankauskas Montanuniversität Leoben
Sangtae Jeong Inha University
Charlene Kalle Leiden University
Attila Kovàcz Eötvös Loránd University Budapest
Jakub Krasensky Czech Technical University Prague
Dominik Kwietniak Jagiellonian University
Sebastien Labbé University of Bordeaux
Niels Langeveld Leiden University
Jeong-Yup Lee Catholic Kwandong University
Marie Lejeune University of Liege
Lingmin Liao University Paris-Est, Creteil
Benoit Loridant Montanuniversität Leoben
Alejandro Maass University of Chile
Manfred Madritsch University of Lorraine
Marta Maggioni Leiden University
Radhakrishnan Nair University of Liverpool
Hitoshi Nakada Keio University
Roman Nikiforov Dragomanov National University
Marco Pedicini University Roma Tre
Edita Pelantovà Czech Technical University Prague
Attila Pethö University of Debrecen
Anthony Quas University of Victoria
Michel Rigo University of Liege
Jeffrey Shallit University of Waterloo
Alexandra Skripchenko Higher School of Economics Moscow
Lukas Spiegelhofer Technical University of Vienna
Wolfgang Steiner CNRS
Paul Surer Universität für Bodenkultur Wien
Robert Tichy Technical University of Graz
Magdalena Tinkova Charles University Prague
Sascha Troscheit University of Vienna
Tomas Vavra Charles University Prague
Wanlou Wu University Paris-Est, Creteil
Benthen Zeegers Leiden University
Shugin Zhang Montanuniversität Leoben
Huilin Zhu Xiamen University
At a glance
July 8, 2019 — July 12, 2019
ESI Boltzmann Lecture Hall
Henk Bruin (U of Vienna)
Clemens Heuberger (AAU, Klagenfurt)
Daniel Krenn (AAU, Klagenfurt)
Jörg Thuswaldner (Montanuniversität Leoben)