Abstract

Algebraic geometers care a lot about (algebraic) curves and their moduli spaces. These are spaces that parametrize elliptic curves and their higher-genus variants. For example, an elliptic curve can be expressed as the zero locus of a polynomial with two free parameters. While these moduli spaces are natural, they exhibit behavior that is sometimes surprising and mysterious. This  difficulty in "navigating" these spaces motivates the need for well-place landmarks as a guide. This is what Weierstrass points provide for us. I will explain the definition of Weierstrass points, and mention some ways to understand them using tropical geometry which is a way to approach geometry at "extreme magnitudes".

 

Organizers: Kuan-Wei Chen (NCTS), Wille Liu (AS)