Patrick Speissegger, McMaster University
"Limit cycles of planar vector fields, Hilbert’s 16th problem and o-minimality"
Recent work links certain aspects of the second part of Hilbert’s 16th problem (H16) to the theory of o-minimality. One of these aspects is the generation and destruction of limit cycles in families of planar vector fields, commonly referred to as ”bifurcations”. I will outline the significance of bifurcations for H16 and explain how logic–in particular, o-minimality–can be used to understand them well enough to be able to count limit cycles.