Words and noncommutative algebraic combinatorics

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Words and noncommutative algebraic combinatorics: Words appear in linguistics, in computer science and in communications. They are also a mathematical concept for itself. They are crucial for the notion of noncommutativity, which plays an important role in the contemporary mathematical sciences. Indeed, noncommutativity is the property that the effect of two operations depends on the order where these operations are done. This is a typical property of the letters of a word: the order of letter matters. Thus, computations in noncommutative algebraic structures rest on combinatorial properties of words. They are also used to encode images in the plane. Their mathematical study is at the center of the present program, which is in the area of pure and applied mathematics.