Aperiodic Structures 2

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, 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 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, self-similarity, aperiodic Delone sets, cut-and-project sets, mathematical models of quasicrystals.

3. Number systems with complex alphabets or complex digits. Algorithms in non-standard 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 time-table has been prepared for this course

The course is a part of the following study plans: