# From the Jacobian Conjecture to Mathieu Subspaces

Date:
22.05.17
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Wenhua Zhao
University:
Illinois State University

## Abstract

We will mainly discuss the approaches or equivalent formulations of the Jacobian conjecture in terms of the inviscid Burgers' equations; the Hamilton-Jacobi equations; and the Laplace operators; etc. From these approaches we will see how the Jacobian conjecture leads to the notion of Mathieu subspaces, a new notion that generalizes the notion of ideals of associative algebras.

If the time permits, we will also discuss some recent study on the relations of Mathieu subspaces with locally nilpotent or locally finite derivations and $\mathcal E$-derivations, where by an $\mathcal E$-derivation of an algebra $\mathcal A$ we mean a linear map of the form $\mathrm{Id}_{\mathcal A}-\phi$ for some algebra endomorphism $\phi$ of $\mathcal A$.