# Mathematics Colloquia and Seminars

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### Equilibrium Theorems of the Perron-Frobenius type

**Algebra & Discrete Mathematics**

Speaker: | Martha Yoko Takane Imay, Universidad Nacional Autonoma de Mexico |

Location: | 1147 MSB |

Start time: | Mon, Nov 18 2013, 11:00AM |

The Perron-Frobenius theorem is one of the most important and deepest theorems in Linear Algebra, which is applied in many areas of Mathematics, Economics, Physics, Chemistry, etc. (even Google uses it). There are quite a few generalizations of this theorem, one of the nicest is the Birkhoff-Vandergraft theorem using the so-called Theory of Cones.

In this talk we give the definition of a cone, some of its main properties; we recall the mentioned theorems and give a generalization of the Fan Theorem which generalizes Perron's one.