### Speaker

### Description

Let $X$ be a smooth complex variety. In previous joint work with V. Dolgushev and T. Willwacher, we exhibited an explicit action of $\mathrm{GRT_1}$ on the Gerstenhaber algebra $H^\ast(X,\mathcal{T}_{\mathrm{poly}})$. This action produces a large supply of nontrivial $\mathrm{GRT}_1$ representations. After reviewing this construction, I will discuss extending it to an action of $\mathrm{KRV}_2$ on the set of those isomorphisms $H^\ast(X,\mathcal{T}_{\mathrm{poly}}) \cong HH^*(X)$ which correct the HKR map between the harmonic and Hochschild structures of $X$. A key ingredient is the recent characterization of $\mathrm{KRV}_2$ by Z. Dancso, I. Halacheva, and M. Robertson as automorphisms of a wheeled PROP. This is joint work in progress with M. Robertson.