# Anne Moreau (Université de Poitiers)

## Mishchenko-Fomenko algebras and nilpotent bicone

Let $$\mathfrak{g}$$ be a complex semisimple algebra. We consider the Mishchenko-Fomenko subalgebra at a regular element $$x$$. It is a maximal Poisson-commutative subalgebra of $$S(\mathfrak{g})$$, constructed by the so-called argument shift method. Moreover, it is a polynomial algebra. We show that the free generators of this algebra form a regular sequence. This generalizes a result of Ovsiensko (for $$\mathfrak{sl}_n$$ and x semisimple regular). Our proof is related to geometrical properties of the nilpotent bicone. In this talk, I will explain this and discuss some open questions.