Actions of C^* and C_+ on affine algebraic varieties
-- Shulim Kaliman

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In the last years there has been serious progress
in the study of algebraic actions of one-parametric groups on
contractible affine algebraic threefolds starting with a solution
of the Linearization Conjecture by Koras and Russell.  We give a
survey of results and discuss also classification of
C^*-actions on smooth affine surfaces.