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### Weakly positive and directed Anosov representations

**Geometry/Topology**

Speaker: | Sungwoon Kim, Jeju National University (Korea), visiting UC Davis |

Location: | Zoom Zoom |

Start time: | Tue, Jan 18 2022, 1:10PM |

Given a finitely generated group Γ with finite generating set R, we introduce the notion of an R-directed Anosov representation. This is a weakening of the notion of Anosov representations. Our main theorem gives a procedure to construct R-directed Anosov representations using Fock-Goncharov positivity. As an application of our main theorem, we construct large families of primitive stable representations from a rank 2 free group to PGL(n,R), including non-discrete and non-faithful examples. This is a joint work with Ser Peow Tan and Tengren Zhang.