Aperiodic Structures 2
Code  Completion  Credits  Range  Language 

01APST2  Z  2  2+0  English 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The seminar is a continuation of 01APST1. It is devoted to advanced issues of combinatorics on infinite 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 Informatics or Mathematical modeling.
 Syllabus of lectures:

1. Properties of infinite words constructed as fixed points of morphisms, palindromic and pseudopalindromic closures, codings of interval exchanges.
2. Aperiodic tilings of the space, selfsimilarity, aperiodic Delone sets, cutandproject sets, mathematical models of quasicrystals.
3. Number systems with complex alphabets or complex digits. Algorithms in nonstandard numeration 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:

 Matematické inženýrství (elective course)