Dipl.-Ing. Dr.mont. Benoît Loridant
Inhaltsverzeichnis
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.)
20) Intersecting the Twin Dragon with rational lines,
Journal of Fractal Geometry (EMS) 11 (2024) no. 3, 205-217, together with S. Akiyama, P. Grosskopf, and W. Steiner.
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.
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 |
Slides of the talks:
| Samuel PETITE, lecture 1 | lecture 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.
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 |
Slides of the talks:
| Vincent DELECROIX, | lecture 1 | lecture 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 15:30-16:00 | Hanspeter FISCHER | A characterization of cotorsion-free groups in terms of homomorphisms from fundamental groups of Peano continua | abstract | slides |
| TU 12.09.2017 16:00-16:30 | Ziga VIRK | A comparison of topologies on the fundamental group | abstract | slides |
| TU 12.09.2017 16:30-17:00 | Petar PAVESIC | Geometry of compact lifting spaces | abstract | slides |
| TU 12.09.2017 17:00-17:30 | Wolfram HOJKA | Suspensions in wild topology | abstract | |
| TU 12.09.2017 17:30-18:00 | Andreas ZASTROW | A progress-report about investigating Milno-Thurston homology theory on wild topological spaces | abstract | |
| TU 12.09.2017 18:00-18:30 | Ligia Lorietta CRISTEA | Families of labyrinth fractals and their magic | abstract | slides |
| WE 13.09.2017 10:15-10:45 | Paul SURER | Real sets induced by endomorphisms of the free monoid | abstract | slides |
| WE 13.09.2017 10:45-11:15 | Mario WEITZER | An introduction to p-adic systems: A new kind of number system | abstract | slides |
| WE 13.09.2017 11:15-11:45 | Wolfgang HERFORT | Freely indecomposable groups in wild topology | abstract | slides |
| WE 13.09.2017 11:45-12:15 | Oleg BOGOPOLSKI | The 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
- Since November 2016: Senior lecturer at Montanuniversität Leoben.
- 2016: Habilitation for Mathematics at Vienna University of Technology.
- 2015-2016: Post-Doc at Montanuniversität Leoben.
Project Fractals and Numeration financed by the Austrian Science Fund (FWF) and the Agence Nationale de la Recherche (ANR). - 2011-2016: University assistant at Montanuniversität Leoben.
- 2010-2015: Post-Doc at Montanuniversität Leoben and Vienna University of Technology.
Stand alone Project Topology of fractal tiles financed by the FWF. - 2008-2010: Post-Doc at Niigata University (Japan).
Project Self-similar tiles and tilings related to numeration systems with Shigeki Akiyama,
financed by the Japanese Society for Promotion of Science (JSPS). - 2007-2008: Post-Doc at Montanuniversität Leoben.
Research assistant in the Network Analytic combinatorics and probabilistic number theory financed by the FWF. - 2005-2007: PhD studies of Mathematics at Montanuniversität Leoben,
PhD thesis on Topological properties of tiles, supervisor Jörg Thuswaldner.
Research assistant in the Network Analytic combinatorics and probabilistic number theory financed by the FWF. - 2003-2005: Master at the Vienna University of Technology (exchange program TIME).
Master thesis on Kinetic transport equations in transistors, supervisor Christian Schmeiser. - 2001-2003: Graduate studies at Ecole Centrale Paris (ECP).
Licence and Maîtrise of Mathematics at University Paris Sud 11. - 1998-2001: Undergraduate studies at Lycée Faidherbe, Lille (France).
Lehrveranstaltungen
Wintersemester 2023-24
MINT, VU Mathematik 1 (Übungsteile)
VO Statistische Versuchsplanung und -auswertung
SEM aus Höhere Mathematik
Konversatorium aus Mathematik I