My Research Interests
My research interests are mainly on polynomial automorphisms and the Jacobian conjecture. My earlier research also involves vertex operator algebra and Conformal Field Theory; Infinitely Dimensional Lie Algebras; Noncommutative Symmetric Functions; and Combinatorics on root trees, etc.
Currently I am mainly working on a new notion of Mathieu subspaces, which I introduced in 2009. The new notion not only generalize the fundamental notion of ideals, but also provides a uniform setting for several hard conjectures such as the Jacobian conjecture; the Dixmier conjecture; the Mathieu conjecture; the Image conjecture; the Vanishing conjecture; and the Gaussian Moment conjecture, etc. It is highly expected that the study of this new concept will also have profound impacts to many other mathematics areas besides the conjectures above.