Combinatorics on Words
March 14-18, 2016
Combinatorics on words is an area of research which has matured into a separate discipline in the last few decades. It is concerned with properties of sequences of symbols, either finite or infinite, taken from a finite alphabet. The focus on words can be algebraic, combinatorial, or algorithmic. Typical to the field is its manifold connections, not only to topics in mathematics, but also to other scientific disciplines. Such areas inside mathematics include, for example, certain parts of algebra (e.g. combinatorial group theory and semigroups), probability theory, number theory, and discrete symbolic dynamics. Areas in other sciences include, for example, crystallography, and computational biology. Combinatorics on words has been particularly connected to and motivated by theoretical computer science, e.g. automata theory and pattern matching algorithms.
Recent breakthroughs, however, like the resolution of the decades-old Ehrenfeucht-Silberger conjecture, have led to new interest and momentum in this area.
This workshop aims to bring together world experts in the various flavours of combinatorics on words to identify, attack, and even solve some of the outstanding problems of this field.
The main goal of the workshop is to invite the leading experts on different directions of combinatorics on words together with brilliant young researchers to analyze the current state of the art of combinatorics on words and identify the major problems and perspectives of research in the field. The organizers would like to keep the program open until the actual meeting. However, lectures emphasising current open problems about avoidability, word equations, and transcendental and normal numbers, as well as lectures treating the connections to the areas of number theory, symbolic dynamics, and geometric group theory are suggested.
Srecko Brlek (Université du Québec à Montréal)
Conjugacy languages and growth series in group
Sur la continuation d’un programme de Schützenberger
k-bonacci substitutions and thermodynamic formalism
Ergodic measures for shifts with eventually constant complexity growth
Equidistributed sequences generated by binary morphisms
Invariant measures for stationary train-track towers
Separating words with tropical automata
Square root map on Sturmian words
Binary periodic trajectories and generalized Collatz functions
k-abelian complexity and fluctuation
k-abelian singletons in connection with Gray codes for Necklaces