 CARMA COLLOQUIUM
 Speaker: Stephan Harrap, Department of Mathematical Sciences, Durham University
 Title: Topological games, Cantor sets and Diophantine approximation: An introduction
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 5^{th} Mar 2015
 Abstract:
When attacking various difficult problems in the field of Diophantine approximation the application of certain topological games has proven extremely fruitful in recent times due to the amenable properties of the associated 'winning' sets. Other problems in Diophantine approximation have recently been solved via the method of constructing certain treelike structures inside the Diophantine set of interest. In this talk I will discuss how one broad method of treelike construction, namely the class of 'generalised Cantor sets', can be formalized for use in a wide variety of problems. By introducing a further class of socalled 'Cantorwinning' sets we may then provide a criterion for arbitrary sets in a metric space to satisfy the desirable properties usually attributed to winning sets, and so in some sense unify the two above approaches. Applications of this new framework include new answers to questions relating to the mixed Littlewood conjecture and the $\times2, \times3$ problem. The talk will be aimed at a broad audience.
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