Dipl.-Ing. Dr.mont. Benoît Loridant

Research

Research interests

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.

Publications

(Copyright of all papers either by the author or by the publisher.)

21) Intersecting the Twin Dragon with rational lines,
together with S. Akiyama, P. Grosskopf, and W. Steiner, submitted.

20) Modified fibers and local connectedness of planar continua,
together with J. Luo, submitted.

19) Topology of planar self-affine tiles with collinear digit set,
Journal of Fractal Geometry (EMS) 8 (2021) no. 1, 53-93, together with S. Akiyama and J. Thuswaldner.

18) A core decomposition of compact sets in the plane,
Advances in Mathematics 343 (2019), 219-244, together with J. Luo and Y. Yang.

17) Geometrical models for a class of reducible Pisot substitutions,
Discrete and Computational Geometry 60 (2018) no. 4, 981 - 1028, together with M. Minervino.

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.

Projects

• ANR (Agence Nationale de la Recherche) / OeAD (Austrian Agency for International Cooperation in Education and Research) Project FR 07/2019 Topology, dynamics and number theory of fractal structures, 2019-2020, together with Wolfgang Steiner (IRIF, Paris 7).

• JSPS (Japan Society for the Promotion of Science) / FWF Joint Project I3346 Topology of planar and higher dimensional self-replicating tiles, 2017-2020.

• FWF (Austrian Science Fund) Stand-alone Project P22855 Topology of fractal tiles, 2010-2015.

FWF/JSPS Joint Project I3346
Topology of planar and higher dimensional self-replicating tiles 2017-2019

Project leaders: Shigeki AKIYAMA (Tsukuba University) and Benoît LORIDANT (University of Leoben)

PROJECT MEETING
held at St Virgil Salzburg (Austria)

Organizers: Benoît LORIDANT and Jörg THUSWALDNER (University of Leoben)

The meeting takes place from February 20 (9:30) to February 22 (12:30), 2019.

Access to St Virgil

 

List of participants (arrival-departure date):

 

Shigeki AKIYAMA (Tsukuba University)19-22.02
Myriam AMRI (University of Leoben)19-22.02
Pierre ARNOUX (Université de la Méditerranée, Marseille)19-22.02
Henk BRUIN (University of Vienna)19-20.02
Hiromi EI (Hirosaki University)19-22.02
Sébastien FERENCZI (Luminy, Université Aix-Marseille)19-22.02
Maki FURUKADO (Yokohama National University)18-22.02
Maik GRÖGER (University of Vienna)19-22.02
Charlene KALLE (Universiteit Leiden)19-22.02
Sébastien LABBÉ (LaBRI, Bordeaux)19-22.02
Benoît LORIDANT (University of Leoben)19-22.02
Yasushi NAGAI (University of Leoben)19-22.02
Hitoshi NAKADA (Keio University)19-22.02
Rie NATSUI (Japan Women's University)19-22.02
Samuel PETITE (Université de Picardie, Amiens)19-22.02
Lukas SPIEGELHOFER (Vienna University of Technology)19-22.02
Wolfgang STEINER (University Paris Diderot)20-22.02
Jörg THUSWALDNER (University of Leoben)18-22.02
Sascha TROSCHEIT (University of Vienna)19-22.02
Hisatoshi YUASA (Osaka Kyoiku University)19-22.02
Shuqin ZHANG (University of Leoben)19-22.02

Schedule of talks

Slides of the talks:

 

Samuel PETITE, lecture 1lecture 2 lecture 3
Sébastien FERENCZI
Hisatoshi YUASA

FWF/JSPS Joint Project I3346
Topology of planar and higher dimensional self-replicating tiles 2017-2019

Project leaders: Shigeki AKIYAMA (Tsukuba University) and Benoît LORIDANT (University of Leoben)

PROJECT MEETING
held at St Virgil Salzburg (Austria)

Organizers: Benoît LORIDANT and Jörg THUSWALDNER (University of Leoben)

The meeting takes place from February 20 (9:30) to February 23 (noon), 2018.

Access to St Virgil

 

List of participants (arrival-departure date):

 

Shigeki AKIYAMA (Tsukuba University)19-23.02
Valérie BERTHÉ (IRIF, Université Paris Diderot)19-23.02
Henk BRUIN (University of Vienna)19-23.02
Vincent DELECROIX (LaBRI, Université de Bordeaux)19-23.02
Hiromi EI (Hirosaki University)18-23.02
Sébastien FERENCZI (Luminy, Université Aix-Marseille)19-23.02
Maik GRÖGER (University of Vienna)19-23.02
Jonas JANKAUSKAS (University of Leoben)19-23.02
Henna KOIVUSALO (University of Vienna)19-23.02
Benoît LORIDANT (University of Leoben)18-23.02
Yasushi NAGAI (University of Leoben)19-23.02
Hitoshi NAKADA (Keio University)19-24.02
Rie NATSUI (Japan Women's University)19-24.02
Hui RAO (Central China Normal University, Wuhan)19-23.02
Wolfgang STEINER (IRIF, Université Paris Diderot)19-23.02
Jörg THUSWALDNER (University of Leoben)19-24.02
Hisatoshi YUASA (Osaka Kyoiku University)19-22.02
Shuqin ZHANG (University of Leoben)19-23.02

 

Programme

Slides of the talks:

 

Vincent DELECROIX,lecture 1lecture 2 lecture 3
Sébastien FERENCZI
Henk BRUIN

Minisymposium M2 Fractals and Wild Topology,
held at the ÖMG-DMV-Congress 2017 in Salzburg

Organizers: Gerhard DORFER (TU Wien) and Benoît LORIDANT (MU Leoben)

 

TU 12.09.2017 15:30-16:00Hanspeter FISCHERA characterization of cotorsion-free groups in terms of homomorphisms from fundamental groups of Peano continua abstract slides
TU 12.09.2017 16:00-16:30Ziga VIRKA comparison of topologies on the fundamental group abstract slides
TU 12.09.2017 16:30-17:00Petar PAVESICGeometry of compact lifting spaces abstract slides
TU 12.09.2017 17:00-17:30Wolfram HOJKASuspensions in wild topology abstract  
TU 12.09.2017 17:30-18:00Andreas ZASTROWA progress-report about investigating Milno-Thurston homology theory on wild topological spaces abstract  
TU 12.09.2017 18:00-18:30Ligia Lorietta CRISTEAFamilies of labyrinth fractals and their magicabstract slides
WE 13.09.2017 10:15-10:45Paul SURERReal sets induced by endomorphisms of the free monoid abstract slides
WE 13.09.2017 10:45-11:15Mario WEITZERAn introduction to p-adic systems: A new kind of number system abstract slides
WE 13.09.2017 11:15-11:45Wolfgang HERFORTFreely indecomposable groups in wild topology abstract slides
WE 13.09.2017 11:45-12:15Oleg BOGOPOLSKIThe automorphism group of the free group of infinite countable rank: a survey abstract  

 

Theses

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.

Short Curriculum Vitae

Lehrveranstaltungen

Wintersemester 2023-24

MINT und VU Mathematik 1 Übungsteil

VO Ausgewählte Kapitel der Analyse von Algorithmen, mit Peter Kirschenhofer

Seminar aus Höhere Mathematik

Konversatorium aus Mathematik I

VO Statistische Versuchsplanung und -auswertung, mit Lukas Spiegelhofer