For genus $2$ and $3$ modular forms are intimately connected with the moduli of curves of genus $2$ and $3$. We describe an explicit way to construct such modular forms for genus $2$ and $3$ using invariant theory and give some applications. This is based on joint work with Fabien Clery and Carel Faber.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/7438