Aperiodic Structures

Course guarantor:

Lecturer:

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:

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.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: