**2022 December QSMS Monthly Seminar**

**Date:**2022-12-02 (Fri) 14:00 ~ 17:00**Place:**27-101 (SNU)**Contents:**

**Speaker : **박의용 (14:00 ~ 15:00)

**Title : **Extended crystal structures of Hernandez-Leclerc categories

**Abstract** :

In this talk, we talk about the categorical crystal structure on the Hernandez-Leclerc category. We define extended crystals for quantum groups and show that there is a braid group action on extended crystals. We then explain how the set of the isomorphism classes of simple modules in the Hernandez-Leclerc category has an extended crystal structure, and discuss the braid group action from the viewpoint of the Hernandez-Leclerc category. This talk is based on a joint work with M. Kashiwara (arXiv: 2111.07255 and 2207.11644).

**Speaker : **김유식 (16:00 ~ 17:00)

**Title : **SYZ mirror symmetry of quadrics

**Abstract** :

In this talk, I recall various LG mirrors of quadric hypersurfaces including Pech--Rietsch--Williams (PRW) mirror, and explain its cluster structure. In particular, the PRW mirror contains Przyjalkowski's mirror or Lusztig's mirror as cluster charts. I will explain how to produce various mirrors via Lagrangian Floer theory.