| Abstract | Whether a (quasi-)affine variety X is determined by its automorphism group Aut(X)? The answer is no in general. On the other hand, it has positive answer in many cases, especially when Aut(X) is large. In these lectures, we discuss this problem mainly when X is the affine space. We discuss two different approaches to attack this problem. One is to study commutative algebraic subsets of Aut(X), the other one it to study certain finitely generated subgroup of Aut(X) using p-adic method. The first approach works in any characteristic, but we ask the base field to be uncountable. The second approach works over any field of characteristic zero. My lectures are based on some joint work with S.Cantat and A.Regeta. |
