Seminar talk, 5 May 2010

Speaker: Pavel Bibikov

Title: On $\mathrm{SL}_2$-orbits of binary forms

Joint work with Valentin Lychagin

Abstract:
The talk will discuss a new approach to the classical problem of description of orbits of the natural action of the group $\mathrm{SL}_2(\mathbb{C})$ on the space of binary forms. The main idea of this approach is to realize the space of binary forms of degree $n$ as the space of solutions of the Euler differential equation $xu_x+yu_y=nu$; this make it possible to attack our algebraic problem using differential-geometric methods. In particular, it is possible to find the algebra of differential invariants of action of $\mathrm{SL}_2$ and to describe the orbits of the action in terms of this algebra.