Dynamical systems and systems of equations

Expected topology of random real algebraic plane curves

speaker: Turgay Bayraktar (Sabancı University)

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.

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