**abstract:**
Broadly speaking Hilbert’s sixteenth problem suggests studying possible number
and arrangement of connected components of a smooth real algebraic plane curve.
One can also approach this problem from a probabilistic point-view and try to
obtain statistical results such as computing the expected number of components,
depth of nested ovals etc. In this talk, I’ll review some recent probabilistic results
on this problem. In particular, I will give a Kac-Rice type formula computing the
expected number of nested ovals winding around a fixed point.

Wed 22 Jun, 10:20 - 11:20, Aula Dini

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