Title: Modular curves, invariant theory and $E_8$,
Abstract: The $E_8$ root lattice can be constructed from the modular curve $X(13)$ by
the invariant theory for the simple group $\text{PSL}(2, 13)$. This gives a
different construction of the $E_8$ root lattice. It also gives an explicit
construction of the modular curve $X(13)$.