# Seminar at SMU Delhi

June 10, 2015 (Wednesday) , 3:30 PM at Webinar
Speaker: Neha Hooda, Indian Statistical Institute, Delhi
Title: Mod-2 invariants and subgroup embeddings of algebraic groups
Abstract of Talk
Let $G$ be a simple linear algebraic group defined over a field $k.$ It is an important problem to know what are all the simple $k$-subgroups of $G$ as well as the number of such subgroups required to generate $G$ over $k.$ In the talk we try to answer this for algebraic groups of type $A_2,$ $G_2,$ $D_4$ and $F_4.$ More precisely, in the talk we will address two problems. The first is to understand conditions that control $k$-embedding of algebraic groups of type $A_1$ and $A_2$ in simple groups of type $G_2$ and $F_4$ and the second is to understand $k$-embedding of rank-2 tori in simple groups of type $A_2,$ $G_2$ and $F_4.$ This study is done via the mod-2 invariants attached to these groups. The second problem is to find the number of $k$-subgroups of a fixed Cartan-Killing type as well as number of rank-2 k-tori required to generate the groups of type $A_2,$ $G_2$ and $F_4$ over $k.$