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### Frozen variables for open Richardson varieties

**Student-Run Research Seminar**

Speaker: | Soyeon Kim, UC Davis |

Related Webpage: | https://sites.google.com/ucdavis.edu/soyeon-kim/home |

Location: | 2112 MSB |

Start time: | Wed, Oct 2 2024, 12:10PM |

The open Richardson varieties $R_{v,w}^{\circ}$ are first introduced by Kazhdan and Lusztig in 1979. It is an intersection of Schubert cell $X_{w}^{\circ}$ and an opposite Schubert cell $(X^{v})^{\circ}$. By the work of Casals-Gorsky-Gorsky-Le-Shen-Simental and Galashin-Lam-Sherman-Bennett-Speyer, there is a cluster structure on open Richardson varieties. A cluster structure allows one to define mutable and frozen cluster variables which are certain functions on $R_{v,w}^{\circ}$. In this talk, I will discuss two problems related to the frozen variables for open Richardson varieties. In particular, we will see the combinatorial description for the number of frozens $f_{v,w}$ in a quiver of $R_{v,w}^{\circ}$ and that how a torus of dimension equal to $f_{v,w}$ acts on $R_{v,w}^{\circ}$.

Free pizzas as always:)