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Abstract: Complexity of infinite words is a widely studied field in combinatorics on words. A classical notion of a complexity of an infinite word is defined as a function counting, for each n, the number of its distinct factors (or blocks of consecutive letters) of length n. In their 1938 seminal paper on symbolic dynamics, Morse and Hedlund gave a relation between factor complexity and periodicity in infinite words; namely, they proved that each aperiodic infinite word w has factor complexity at least n+1 for each length n. They further showed that an infinite word w has factor complexity n+1 for each length n if and only if w is binary, aperiodic and balanced, i.e., w is a Sturmian word. In the talk, we will consider various modifications of the notion of a complexity of infinite words and generalizations of Morse and Hedlund theorem.
Bio: Svetlana Puzynina is an associate professor at Saint Petersburg State University, Russia. She obtained her PhD from the Sobolev Institute of Mathematics in 2008 and spent several years at University of Turku, Finland, Ecole Normale Supérieure de Lyon, Université Paris Diderot, France. Svetlana's main field of expertise is combinatorics on words and its interactions with other fields of mathematics including symbolic dynamics, Ramsey theory and automata.
