Alexander Perepechko (Saint Petersburg State University)
The affine algebraic surfaces admit quite various automorphism groups, from finitely generated abelian groups to infinitely dimensional ones, i.e. ind-groups, including amalgamated products of algebraic groups, fundamental groups of graphs of groups, and even more complicated ones.
We will describe the arising automorphism groups with regard to the number of additive group actions. We use the following technique. Each automorphism of an affine surface induces a birational transformation of its compactification that is represented by a sequence of blowups and blowdowns with centers at the boundary divisor. Thus, we obtain combinatorial transformations of the dual graph of the divisor and describe through them the automorphism group up to a finite index.