An upper bound on the expected areas of amoebas of plane algebraic curves

Abstract: The amoeba of a complex plane algebraic curve has an area bounded above by $\pi^2 d^2/2$. This is a deterministic upper bound due to Passare and Rullgard. In this talk I will argue that if the plane curve is chosen randomly with respect to the Kostlan distribution, then the expected area cannot be more than $\mathcal{O}(d)$. The results in the talk will be based on our joint work in progress with Turgay Bayraktar.

algebraic geometry

Audience: researchers in the discipline

ODTU-Bilkent Algebraic Geometry Seminars