Seminar at SMU Delhi

In the first part of this talk, we will summarize the structure theory of connected algebraic groups over an algebraically closed field. The theory over non-algebraically closed fields needs different techniques. We will introduce Galois cohomology in the second part of the talk and apply it to obtain new groups from known groups by a technique called "twisting". This technique gives all forms of an algebraic group defined over a field. The classification of algebraic groups over non-algebraically closed fields is largely open and is a very active area of research.