# Seminar in Real & Complex Geometry

## Polynomial automorphisms and Jacobian conjecture

Abstract

 Let $F:C^n\to C^n$ be a polynomial mapping. When is it invertible? The famous Jacobian conjecture says that the local invertibility implies the global invertibility. It is equivalent to Dixmier conjecture saying that $Aut(W_n)=End(W_n)$. Proof of the equivalence uses reduction to prime characteristics and quantization. We discourse relations betveen polynomial automorphism and quantization problems, structure of infinite-dimensional algebraic groups.