Abstract: There are a lot of questions related to affine algebraic geometry which have very simple formulations but which, sometimes, are very difficult to answer. For example, are the surfaces given by $x^ny=z^2-1$ isomorphic for different $n$? or is a hypersurface given by $x+x^2y+z^2+t^3=0$ isomorphic to three-dimensional affine space?
In my talk I'll answer these and some other questions with the help of automorphism groups of these objects.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/249