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MT Postdoc Seminar: Counting rational points on definable sets May 02, 2014 (11:00 AM PDT - 12:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Margaret Thomas (Purdue University)
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The results outlined in this talk are part of a wider, flourishing interaction between diophantine geometry and model theory, in particular o-minimality. We are concerned with bounds on the density of rational and algebraic points lying on certain subsets of the reals - more specifically those which are first-order definable in various o-minimal expansions of the real field. Following influential work by Pila and Wilkie in this area, Wilkie conjectured an improvement to their main result for sets definable in the (o-minimal) real exponential field. This conjecture we established in the case of curves and certain surfaces (joint with Jones). We will briefly review the context and then outline these results; time permitting we will also consider some related results and applications.

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