Math page of Thierry Monteil

Papers

Illumination in translation surfaces

• A counter-example to the theorem of Hiemer and Snurnikov (J. Statist. Phys., 114 (2004), no. 5-6, 1619--1623).
• On the finite blocking property (Ann. Inst. Fourier, Tome 55 fasc. 4 (2005) 1195--1217).
• Finite blocking property versus pure periodicity (Ergodic Theory Dynam. Systems, (2009), 29 : 983--996).
• A homological condition for a dynamical and illuminatory classification of torus branched coverings (preprint).
• Introduction to the theorem of Kerkhoff, Masur and Smillie (Oberwolfach Report, No. 17 (2010), 989--994).
• Finite blocking property on translation surfaces (summary of the first 4 papers toward open questions, Oberwolfach Report, No. 25 (2011), 1394--1396).
• Everything is illuminated with Samuel Lelièvre et Barak Weiss (Geometry & Topology, No. 20 (2016), 1737--1762).

Symbolic dynamics

• Estimating the number of ergodic measures of a minimal subshift knowing the geometry of its Rauzy graphs (preprint).
• Quasiperiodic infinite words : multi-scale case and dynamical properties with Solomon Marcus (preprint).
• Topological Martin's Delirium (draft answering a question of Martin Lustig).
• Infinite words with uniform frequencies, and invariant measures with Sébastien Ferenczi (preliminary version of Chapter 7 of the book Combinatorics, Automata and Number Theory, V. Berthé, M. Rigo (Eds), Encyclopedia of Mathematics and its Applications 135, Cambridge University Press (2010)).
• Symbolic coding of linear complexity for generic translations on the torus, using continued fractions with N. Pytheas Fogg and Camille Noûs, (Journal of Modern Dynamics, 2024, 20: 527-596).

Discrete geometry

• Another definition for digital tangents (note presented at DGCI 2011, Lecture Notes in Computer Science, 6607 (2011), 95--103).
• The complexity of tangent words (note presented at WORDS 2011, Electronic Proceedings of Theoretical Computer Science, 63 (2011), 152--157).
• Persistent patterns in integer discrete circles with André Hoarau (note presented at DGCI 2013, Lecture Notes in Computer Science, 7749 (2013), 35--46).
• Freeman Digitization and Tangent Word Based Estimators (note présented at DGCI 2014, Lecture Notes in Computer Science, 8668 (2014), 176--189).

Combinatorics

• Minimizing submodular functions with Stéphan Thomassé (mini-survey for the JCALM 2007).
• From the complexity of infinite permutations to the profile of bichains with Maurice Pouzet (proceedings of Rogics'08).
• Asymptotics for connected graphs and irreducible tournaments with Khaydar Nurligareev (note présented at Eurocomb 2021, Extended Abstracts EuroComb 2021. Trends in Mathematics, vol 14.)

Linear algebra

• Symmetric Determinantal Representations in Characteristic 2 with Bruno Grenet and Stéphan Thomassé (Linear Alg. Appl., 439(5), 1364--1381, 2013).

Computability

• A Universal Oracle for Signal Machines, (note présented at CiE 2017, Lecture Notes in Computer Science, 10307 (2017), 315-326).

Software spreading

• Spreading huge free software without internet connection via self-replicating USB keys (ExtremeCom 2013).

Study reports

• Aspects quantitatifs du théorème de récurrence de Poincaré (mémoire de DEA 2000-2001).
• Six facettes de la sphère d'homologie de Poincaré (mémoire de maîtrise 1999-2000).
• Classification non-linéaire des espaces de Banach (mémoire de licence 1998-99).
• Homéomorphismes du tore : nombre de rotation (TIPE spé 1997-98).
• Théorème de Sharkovsky (TIPE spé 1996-97).
• La Métrique de Hausdorff (TIPE sup 1995-96).