Aperiodic structures
Code | Completion | Credits | Range |
---|---|---|---|
D01APST | ZK | 2 | 2 |
- Course guarantor:
- Edita Pelantová
- Lecturer:
- Edita Pelantová
- Tutor:
- Supervisor:
- Department of Mathematics
- Synopsis:
-
The seminar is devoted to combinatorics oninfinite words, non-standard numeration systems and aperiodic tilings of the space.
The seminar often hosts foreign researcher. Students participate actively in solution of open problems in the field.
- Requirements:
-
Knowledge of mathematics in the extent of the
FNSPE bachelor's specialization Mathematical modeling.
- Syllabus of lectures:
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1. Combinatorics on words over a finite alphabet, infinite aperiodic words with low complexity. Morphisms and substitutions, their incidence matrix. 2. Aperiodic tilings of the space, self-similarity, aperiodic Delone sets, cut-and-project sets, mathematical models of quasicrystals. 3. Number representation
in systems with irrational base, arithmetics in such systems.
- Syllabus of tutorials:
- Study Objective:
-
The seminar is an iniciation to research.
Acquired knowledge: sources of relevant mathematical literature
Acquired skills: independent research
- Study materials:
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P. Fogg, Substitutions in Dynamics, Arithmetics, and Combinatorics (Lecture Notes in Mathematics, Vol. 1794).
M. Lothaire, Algebraic Combinatorics on Words Cambridge University Press, 2002.
- Note:
- Time-table for winter semester 2024/2025:
- Time-table is not available yet
- Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans: