Various algebraic structures in geometry and group theory have appeared to be governed by certain universal rings. Examples include: the cohomology rings of Hilbert schemes of points on projective surfaces and quasiprojective surfaces; the Chen-Ruan orbifold cohomology rings of the symmetric products; the class algebras of wreath products, as well as their associated graded algebras with respec...

The BRST cohomology analysis of Lian and Zuckerman leads to physical states at all ghost number for c < 1 matter coupled to Liouville gravity. We show how these states are related to states at ghost numbers zero(pure vertex operator states – DK states) and ghost number one(ring elements) by means of descent equations. These descent equations follow from the double cohomology of the String BRST ...

We find presentations by generators and relations for the equivariant quantum cohomology of the Grassmannian. For these presentations, we also find determinantal formulae for the equivariant quantum Schubert classes. To prove this, we use the theory of factorial Schur functions and a characterization of the equivariant quantum cohomology ring.