Patricio Gallardo

postdoctoral researcher
University of Georgia
Athens, Georgia, USA

As a mathematician, I want the beauty and structure of math to resonate into the mind of others. I hope for them to see, through art, the geometric shapes that I find in my work, so everyone knows about this mathematical land so full of wonders.

A colony of cubic surfaces
A colony of cubic surfaces
60 x 45 cm
Mixed Media Painting

A central problem in Geometry is to construct complete databases, or colonies, of geometric objects. These databases are known as moduli spaces. In this painting, we explore the moduli space of cubic surfaces obtained with Geometric Invariant Theory and first described by Hilbert in 1893. The cubic surfaces are represented here
by white balls. Red dots represent their singular points. A closer look reveals some of the 27 lines that every smooth cubic surface contains and the variation among them represents the four dimensions of the moduli space. Finally, we include, at the center, the unique point associated with more than one type of cubic surfaces.