DMS Linear Algebra/Algebra Seminar

Speaker: Matthew Speck

Title: Mathieu-Zhao Subspaces and the Jacobian Conjecture

Abstract: Posed in 1939 by Ott-Heinrich Keller, the Jacobian Conjecture, famous for its large number of attempted proofs, claims to provide a sufficient criterion for the invertibility of certain polynomials over a field of characteristic 0.  In 2010, Wenhua Zhao introduced the notion of a type of generalized ideal, now called a Mathieu-Zhao subspace, of a ring-algebra which provides a concise generalization of the Jacobian Conjecture.  In this talk, we provide an overview of the Mathieu-Zhao subspace structure and introduce a generalization of that structure to a differential algebra.