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I discuss some recent work linking certain aspects of the second part ofHilbert's 16th problem to the theory of \hbox{o-minimality}.  These notes are adapted from a lecture I gave in the Jour fixe seminar seriesat the Zukunfts\-kolleg of Universit\"at Konstanz in June 2017.

Limit cycles of planar vector fields: Hilbert's 16th problem and o-minimality