Analysis Seminar: 11/4

Abstract: A consequence of implicit function theorem is that any algebraic set is a complex manifold except at some singular points which form a strictly lower dimension algebraic subset. Accordingly, the non commutative implicit function theorem of Agler-McCarthy might suggest that an nc algebraic set is genetically an nc manifold. However, in this talk, we provide a type of nc polynomials whose zero locus cannot be nc manifolds.