# Tomoyuki Arakawa (Research Institute for Mathematical Sciences, Kyoto University)

## Friday 19th April, 12:05-12:55pm, Carslaw 373

### Affine W-algebras and Vinberg's problem for centralizers

Let $$\mathfrak{g}=\mathfrak{gl}(n,\mathbb{C})$$ and $$e$$ be a nilpotent element of $$\mathfrak{g}$$, $$\mathfrak{g}_e$$ the centralizer of $$e$$ in $$\mathfrak{g}$$. In my talk I will show the existence of a quantization of the Mishchenko-Fomenko algebra in $$S(\mathfrak{g}_e)$$ associated with any regular element in the dual of $$\mathfrak{g}_e$$. The proof uses affine $$W$$-algebras.