Aperiodic Structures 1
- Garant předmětu:
- Department of Mathematics
The seminar is devoted to combinatorics on infinite 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.
Knowledge of mathematics in the extent of the
FNSPE bachelor's specialization Mathematical Informatics or Mathematical modeling.
- Syllabus of lectures:
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:
P. Fogg, Substitutions in Dynamics, Arithmetics, and Combinatorics (Lecture Notes in Mathematics, Vol. 1794).
M. Lothaire, Algebraic Combinatorics on Words Cambridge University Press, 2002.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
- Matematické inženýrství (elective course)
- Matematická informatika (elective course)