Transference principle in Diophantine approximation

The talk will be devoted to one of the fundamental principles in Diophantine approximation called transference principle. It reflects the relation of duality between certain problems. This principle is usually formulated in terms of Diophantine exponents - they generalise to the multidimensional case the measure of irrationality of a real number. We plan to give an account on the existing relations Diophantine exponents satisfy and try to reveal the geometric nature of those relations. After having described some basic geometric constructions, we shall look from this perspective at the famous linear independence criterion that belongs to Nesterenko. It appears that our approach provides an alternative proof of this criterion, which bases on rather simple geometric considerations.