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### Lyapunov Exponents of Free Operators

**Colloquium**

Speaker: | Vladislav Kargin, Courant Institute of Mathematical Sciences |

Location: | 1147 MSB |

Start time: | Wed, Jan 30 2008, 4:10PM |

Lyapunov exponents are an interesting mathematical object that can be used to gauge the stability and complexity of a dynamical system. Their study in the context of products of random matrices was initiated by Furstenberg, Kesten, Oseledec, and Newman. My research is focused on a generalization of these results to the case of infinite-dimensional free operators. In this talk, I will provide background information on both Lyapunov exponents and free operators, and then explain results of my research. In particular, I will discuss possible variants of the definition of Lyapunov exponents for free operators, and the tools that are available for their calculation.

Job Talk, Refreshments provided