The subject of my thesis is focused on
numeration systems and fractal structures arising from them.
In particular I'm dealing with beta-numeration and with a very interesting
class of combinatorial objects, Pisot substitutions.
In this settings, many
different branches of mathematics join up together, such as
dynamical systems, algebraic
number theory, combinatorics, numeration systems, fractal
geometry and ergodic theory.
Some talks and posters:
- The geometry of non-unit Pisot
substitutions, with J.
Thuswaldner, to appear in Ann. Inst. Fourier 64 (2014).
- Tilings for Pisot
beta-numeration, with W. Steiner,
to appear in Indagationes Mathematicae (2014). DOI,
- Dynamics of reducible
Pisot substitutions, in preparation.
- Geometric representations for
reducible Pisot substitutions, FAN workshop,
Porquerolles (France), June 16, 2014.
- Tilings for Pisot beta numeration,
DK advanced topics seminar, MU Leoben (Austria), January 10,
- Rauzy fractals and tilings
(poster), at ICERM, Brown University, Providence (Usa),
November 20, 2013.
- Fractals arising from numeration and
substitutions, at ÖMG-DMV Congress, Innsbruck (Austria),
September 26, 2013.
- Escaping unimodularity and
irreducibility for Pisot numeration, at LIAFA, Paris 7
(France), May 3, 2013.
- Escaping unimodularity for Pisot
numeration, at Subtile 2013, CIRM Marseille (France),
January 14, 2013.
- Pisot substitutions, numeration and
tilings, at Macquarie University, Sydney (Australia),
February 28, 2012.