Analysis seminar

In this talk, we will consider multiplier algebras of certain Hilbert function spaces on varieties in a complex ball. These are precisely the multiplier algebras of complete Nevanlinna-Pick spaces. The isomorphism problem for these algebras was studied by Davidson, Ramsey and Shalit. In particular, they showed that for two "nice'' varieties $V$ and $W$ with isomorphic corresponding multiplier algebras, the varieties $V$ and $W$ are biholomorphically equivalent.

I will speak about a possible converse of this result in the special case where the varieties are biholomorphic to the unit disc. Despite some positive results, there are multiple ways in which a naive converse fails. I will demonstrate some of the issues that arise, and talk about some surprises.

This is joint work with Ken Davidson and Orr Shalit.