The Subspace Theorem is a powerful tool in number theory. Its applications include diophantine approximation, results about integral points on algebraic curves and the construction of transcendental numbers. But its usefulness extends beyond the realms of number theory. Other applications of the Subspace Theorem include linear recurrence sequences and finite automata. The Subspace Theorem also has a number of remarkable combinatorial applications. The purpose of this talk is to give a survey of some of these applications including sum-product estimates and bounds on unit distances.
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