# HOẠT ĐỘNG TRONG TUẦN

On the topology of geometric and rational orbits for algebraic group actions over valued fields
 Speaker: Đào Phương Bắc Time: 9:30 - 11:30, April 14, 2021 Venue: Room 612, A6, Institute of Mathematics, VAST Abstract: In this talk, we study the relationship between Zariski and relative closedness for actions of (smooth) algebraic groups defined over valued (mainly local) fields of any characteristic. In particular, we use some recent basic results regarding the completely reducible subgroups and cocharacter-closedness due to Bate-Herpel-Roehrle-Tange and Uchiyama to construct some actions of simple algebraic groups $G$ of the types $D_{4}, E_{6}, E_{7}, E_{8}, G_{2}$ on an affine variety defined over a local function field $k$, and $v in V(k)$ such that the geometric orbit $G.v$ is Zariski closed although the corresponding relative orbit $G(k).v$ is not closed in the topology induced from $k$. Besides, we show that this phenomenon does not appear when we consider the action of nilpotent groups defined over an admissible valued (e.g., local) field. In fact, we show that the class of nilpotent groups is optimal in some sense. This is joint work with Vu Tuan Hien.

### Tin tức nổi bật

 01/12/22, Hội nghị, hội thảo:International Conference on Discrete Mathematics and Computer Science (ICDMCS) 05/12/22, Hội nghị, hội thảo:Winter School on Mathematical Models and Dynamical Systems 19/12/22, Hội nghị, hội thảo:Một số vấn đề trong hình học và tô pô 08/08/23, Hội nghị, hội thảo:Đại hội Toán học Việt Nam lần thứ X