Invited Seminars Thematic month The five weeks |
## Multi-dimensional Subshifts And Tilings
## 1. DatesFrom February 15 to February 19, 2010. ## 2. Description of the weekA subshift in dimension 1 is a set of infinite words closed by the shift operator. Subshifts are widely used to study the behaviour of a dynamical system. They have been studied for long, and their dynamics and computational behaviors are now well understood. Techniques used in dimension 1 however do not translate easily to higher dimensions, where subshifts (especially subshifts of finite type) correspond to the well known concept of tilings from theoretical computer science. This week will focus on combining both dynamical and computational approaches to study these higher-dimensional objects. ## 3. Confirmed morning lectures (3h each)- Mike Boyle: Multidimensional Shifts of Finite Type and Sofic Shifts
- Jean-Marc Gambaudo
- Chaim Goodman-Strauss: From local combinatorial constraints to global structure
## 4. Schedule
## 5. Proposed workshops (add your suggestions here)- Jean-Rene Chazottes.
- Maria Isabel Cortez and Samuel Petite propose an afternoon session on Toeplitz systems and odometers for general group actions.
- François Gautero.
- Edmund Harriss: "How to create substitution rules on the plane and some ideas towards how to characterize them."
- Uijin Jung proposes a short afternoon session on relations among certain properties of finite-to-one maps between multidimensional transitive subshifts.
- Michael Schraudner proposes an afternoon session on (Non-)Uniqueness of measures of maximal entropy for multidimensional shifts of finite type.
- Marc Monticelli :
**xDim**, Interactive Numerical Experimentation software - Ricardo Gómez : I would like to discuss the possibility and relevance of considering quotients of multidimensional zeta functions as analogues of first return loop systems.
- Christoph Bandt : Topology of multidimensional self-affine tiles.
- Lorenzo Sadun : Understanding tilings without finite local complexity.
## 6. General Schedule**Monday 15th****11h-12h30**M. Boyle -*Multidimensional Shifts of Finite Type and Sofic Shifts***14h30-15h30**A. Ballier -*An order on subshifts***15h45-16h45**M.Schraudner -*(Non-)Existence of full shift factors for Z^d shifts of ﬁnite type***17h00-18h**Uijin Jung -*Fiber-mixing codes between Z-subshifts and relations of codes between Z*^{d}subshifts**18h-19h15**Apéritif, IML.
**Tuesday 16th****09h-10h30**J. Kari -*Cellular automata*.**11h-12h30**J.M. Gambaudo**15h30-16h15**R. Gomez -*Quotients of multidimensional zeta functions as analogues of first return loop systems.***16h30-17h30**L. Sadun -*Understanding tilings without finite local complexity.***18h00-19h00**N. Pytheas Fogg -*Open problems session : bring your favorite and personal open problem.*
**Wednesday 17th****09h-10h30**C. Goodman Strauss -*From local combinatorial constraints to global structure*.**11h-12h30**M. Boyle -*Multidimensional Shifts of Finite Type and Sofic Shifts*.**15h30-16h**S. Akiyama-*Pisot conjecture session: Introductory talk.***16h15-17h15: Introductory talks**- M. Schraudner -
*Uniqueness and non-uniqueness of measures of maximal entropy for Z*^{d}subshift of finite type - R. Pavlov -
*Approximating topological entropy of Z*^{2}shift of finite type: Introductory talk.
- M. Schraudner -
**17h30-19h: Two parallel sessions**- R. Pavlov, M. Schraudner and others -
*Approximating topological entropy of Z*.^{2}shift of finite type**and**Uniqueness and non-uniqueness of measures of maximal entropy for Z^{d}subshift of finite type: Informal discussions - M. Barge and A. Siegel-
*Pisot conjecture session: Informal discussions.*
- R. Pavlov, M. Schraudner and others -
**20h30-...**J.M. Gambaudo et M. Monticelli-*xdim: simulations numériques pour quasi-cristaux*
**Thursday 18th****09h-10h30**J.M. Gambaudo**11h-12h30**J. Kari. -*Cellular automata*.**15h30-16h15**Proposed by A. Julien and J. Savinien -*Tilings equivalence relation(s) Bratteli diagrams and orbit equivalence: Introductory talk.***16h30-17h15: Parallel sessions**- Proposed by J. Cassaigne-
*Universal counter example for complexity function*. - M.I. Cortez and S. Petite-
*Toeplitz systems and odometers for general group actions*
- Proposed by J. Cassaigne-
**17h45-19h: Parallel sessions**- Proposed by A. Julien and J. Savinien and others -
*Tilings equivalence relation(s) Bratteli diagrams and orbit equivalence: Informal discussion.* - Proposed by A. Shen-
*Every one dimensional effectively closed subshift is a projection of two dimensional finite type subshift*. - Proposed by A. Hilion-
*Topological substitutions*
- Proposed by A. Julien and J. Savinien and others -
**Friday 19th****09h-10h30**A. Dennunzio-*Workshop on cellular automata*.**11h-12h30**C. Goodman Strauss. -*From local combinatorial constraints to global structure*.**14h-14h30**C. Bandt-*Topology of multidimensional self-affine tiles***14h45-17h***Substitution tiling and matching rules*- C. Goodman Strauss
- Th. Fernique and N. Ollinger ''A Robinson-like construction of matching rules for combinatorial substitutions"
- E. Harriss -
*How to create substitution rules on the plane and some ideas towards how to characterize them*
## 7. Currently uploaded slides- AlexisBallier-OrderingTilings.pdf ... 508,454 bytes ... 25 February 2010 à 11h58
- ChaimGoodmanStrauss-I-AperiodicSetOfTiles.pdf ... 2,785,220 bytes ... 22 February 2010 à 10h44
- ChaimGoodmanStrauss-II-CurvatureAndSubstitutions.pdf ... 8,362,208 bytes ... 22 February 2010 à 10h44
- ChaimGoodmanStrauss-III-MargensternProof.pdf ... 1,246,492 bytes ... 22 February 2010 à 10h45
- JarkkoKari-CellularAutDomataAndTilings-I.pdf ... 373,308 bytes ... 17 February 2010 à 11h26
- JarkkoKari-CellularAutDomataAndTilings-II.pdf ... 1,057,876 bytes ... 18 February 2010 à 16h39
- MichaelSchraudner-NonExistenceOfFullShiftFactorsForZdShiftsOfFiniteType.pdf ... 134,670 bytes ... 15 February 2010 à 20h46
- MikeBoyle-MultidimensionalShiftsOfFiniteTypeAndSoficShifts-I.pdf ... 121,314 bytes ... 15 February 2010 à 11h02
- MikeBoyle-MultidimensionalShiftsOfFiniteTypeAndSoficShifts-II.pdf ... 91,232 bytes ... 18 February 2010 à 16h45
- RonniePavlov_ApproximatingEntropyOfZ2SFTsWithStrips.pdf ... 1,055,887 bytes ... 24 February 2010 à 16h59
- ShigekiAkiyama-PisotConjecture.pdf ... 641,817 bytes ... 17 February 2010 à 17h24
- UijinJung-FiberMixingCodesBetweenZ-SubshiftsAndRelationsOfCodesBetweenZd-Subshifts.pdf ... 676,497 bytes ... 15 February 2010 à 20h47
## 8. ParticipantsSee the page Multi-dimensional Subshifts And Tilings Participants |

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