What is... Random Algebraic Geometry?

TL;DR

This paper surveys Random Algebraic Geometry, a field applying probabilistic methods to classical real algebraic geometry problems, providing new insights and modern approaches to longstanding questions like Hilbert's Sixteenth Problem.

Contribution

It introduces the probabilistic perspective to classical algebraic geometry, highlighting recent developments and potential future directions in the field.

Findings

Provides an overview of probabilistic methods in algebraic geometry

Connects classical problems with modern probabilistic approaches

Suggests new research avenues in the field

Abstract

We survey some ideas from the subject of Random Algebraic Geometry, a field that introduces a probabilistic perspective on classical topics in real algebraic geometry. This offers a modern approach to classical problems, such as Hilbert's Sixteenth Problem.