Time: Tuesday, September 5, from 2pm to 4pm (Hanoi time)

Venue: Room 301, Building A5, Institute of Mathematics

Abstract: Let $k$ be an arbitrary field, $G$ a reductive group acting $k$-morphically on an affine variety $V$. We say that the orbit $G(k).v$ is cocharacter closed over $k$ if it contains the limit points $v'={rm lim}_{alphato 0}lambda(alpha).v$ for all $k$-cocharacters $lambda: mathbb{G}_{m} to G$. When $k$ is algebraically closed, the orbit $G(k).v$ is cocharacter closed if and only if it is Zariski closed by using the celebrated Hilbert-Mumford Theorem. In this talk, we discuss some important results due to G. Rohrle et al regarding the relationship between the cocharacter closedness and the notion of completely reducible subgroups, and some applications.