An invariant theoretic approach to algebraic curves

Date

Nov 13, 2025

Time

3:00 PM - 3:45 PM

Speaker

Thomas Bouchet

Affiliation

MPI-CBG

Language

en

Main Topic

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Description

In this talk, I will present key tools from invariant theory and show how they can be used for explicit computations with algebraic curves. I will begin by introducing invariants that classify curves of a given genus up to geometric isomorphism. Beyond providing explicit equations for moduli spaces of curves, these invariants play a major role in constructing explicit examples of curves. Then, I will introduce the notion of covariants, and explain how one can reconstruct a curve/hypersurface from its invariants. I will illustrate this process through examples of curves with “interesting properties” obtained in this way. Finally, I will show how covariants can provide an efficient way to compute linear changes of variables between homogeneous polynomials, largely outperforming existing implementations.

Last modified: Nov 13, 2025, 7:35:29 AM