**Speaker:** Turgay Bayraktar, Sabancı University

**Title: **Expected depth of random real algebraic plane curves

**Date/Time:** November 06, 2019 / 13.40-14.30

**Place:** FENS G035

**Abstract: **A basic question in real algebraic geometry is to study the possible number and relative positions of connected components of a smooth algebraic curve in RP^{2}. This is known as the first part of Hilbert’s sixteenth problem. In this talk, we shall focus on a probabilistic version of it. More precisely, I’ll present a formula that gives the expected number of two-sided components (i.e. ovals) of a random real algebraic plane curve winding around a fixed point. This is joint work with O. Kişisel.

Abstracts and forthcoming talks can be found on our webpage //people.sabanciuniv.edu/~mlavrauw/algebra_seminar/sas.html .

**Contact:** Michel Lavrauw