Talk Abstract: Markov chains, mathematical models that describe sequences of dependent events, were created to make a point in a philosophical discussion and to explain the beauty of the poetry. Even though we may debate the practicality of explanations of aesthetics, it is generally accepted that Andrey Markov (1856-1922) contributed to this philosophical dispute and, in the process, originated one of the most powerful tools of applied mathematics, physics and data science.

In this talk, I first give an accessible introduction to Markov chains and in particular to singularly perturbed Markov chains. These are stochastic dynamical models with several time scales and, as such, are well suited to represent many natural and technological phenomena. In particular, I discuss the application of Markov chains and singularly perturbed Markov chains in linguistics, linked data analysis and reinforcement learning.

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