Aperiodic Structures
Code  Completion  Credits  Range  Language 

01APST  Z  2  2+0  Czech 
 Course guarantor:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The seminar is devoted to combinatorics oninfinite words, nonstandard 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:

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, selfsimilarity, aperiodic Delone sets, cutandproject 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.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: