Sprechstunde: Montag, Mittwoch 11:00-12:00. Dienstort: Raum 01HG HP 43
My research is devoted to numeration systems and their
connections to fractal tilings.
It requires methods from discrete dynamical systems, number theory, automata theory, point set topology, fractal geometry, tiling theory.
(Copyright of all papers either by the author or by the publisher.)
20) Topology of planar self-affine tiles with collinear digit set,
together with S. Akiyama and J. Thuswaldner, submitted.
19) A core decomposition of compact sets in the plane,
together with J. Luo and Y. Yang, submitted.
18) Modified fibers and local connectedness of planar continua,
together with J. Luo, submitted.
17) Geometrical models for a class of reducible Pisot substitutions,
together with M. Minervino, to appear in Discrete and Computational Geometry.
16) Topology of a class of p2-crystallographic replication tiles,
Indagationes Mathematicae 28 (2017) no. 4, 805 - 823, together with S. Zhang.
15) Boundary parametrization and the topology of tiles,
Nagoya Mathematical Journal 226 (2017), 127 - 164, together with S. Akiyama.
14) On cut sets of attractors of iterated function systems,
Proceedings of the American Mathematical Society 144 (2016) no. 10, 4341 - 4356, together with J. Luo, T. Sellami and J. Thuswaldner.
13) A numerical scale for non locally connected planar continua,
Topology and its Applications 202 (2016), 21 - 39, together with T. Jolivet and J. Luo,
12) Topological properties of a class of cubic Rauzy fractals,
Osaka Journal of Mathematics 53 (2016), 161 - 221.
11) Rauzy fractals with countable fundamental groups,
Journal of Fractal Geometry (EMS) 1 (2014) no. 4, 427 - 447, together with T. Jolivet and J. Luo.
10) Tilings induced by a class of cubic Rauzy fractals,
Theoretical Computer Science 477 (2013), 6 - 31, together with A. Messaoudi, P. Surer and J. Thuswaldner.
9) Crystallographic number systems,
Monatshefte für Mathematik 167 (2012) no. 3-4, 511 - 529.
8) Boundary parametrization of self-affine tiles,
Journal of Mathematical Society of Japan 63 (2011) no. 2, 525 - 579, together with S. Akiyama.
7) Boundary parametrization of planar self-affine tiles with collinear digit set,
Science in China 53 (2010) no. 9, 2173 - 2194, together with S. Akiyama.
6) Interior components of a tile associated to a quadratic canonical number system-Part II,
Fractals 18 (2010), 385 - 397, together with J. Bernat and J. Thuswaldner.
5) On a theorem of Bandt and Wang and its extension to p2-tiles,
Discrete and Computational Geometry 41 (2009) no. 2, 616 - 642, together with J. Luo.
4) Interior components of a tile associated to a quadratic canonical number system,
Topology and its Applications 155 (2008) no. 7, 667 - 695, together with J. Thuswaldner.
3) Fundamental group of tiles associated to quadratic canonical number systems,
Mathematica Slovaca 58 (2008) no. 2, 241 - 251.
2) A new criterion for disk-like crystallographic reptiles,
Topology Proceedings 31 (2007) no. 2, 593 - 610, together with J. Luo and J. Thuswaldner.
1) Topology of crystallographic tiles,
Geometriae Dedicata 128 (2007), 113 - 144, together with J. Luo and J. Thuswaldner.
• JSPS (Japan Society for the Promotion of Science) / FWF Joint Project I3346
Topology of planar and higher dimensional self-replicating tiles, 2017-2019.
• FWF (Austrian Science Fund) Stand-alone Project P22855 Topology of fractal tiles, 2010-2015.
• PhD Thesis
Topological properties of tiles,
under the supervision of J. Thuswaldner, defended in November 2007 at MU Leoben.
• Master Thesis Analysis of kintetic transport equations and application to MOSFETs,
under the supervision of C. Schmeiser, defended in June 2005 at TU Vienna.