Submission date: 29 March 2016.

Abstract:

This survey paper explains how one can attach geometric invariants to semialgebraic sets defined over non-archimedean fields, using the theory of motivic integration of Hrushovski and Kazhdan. It also discusses tropical methods to compute these invariants in concrete cases, as well as an application to refined curve counting, developed in collaboration with Sam Payne and Franziska Schroeter.

Mathematics Subject Classification:

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Full text arXiv 1603.08732: pdf, ps.