Infinite Grassmannians and moduli spaces of G-bundles.
Intersection-theoretical computations on
In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].
Invariance of tautological equations I: conjectures and applications
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite-dimensional linear algebra. Other applications include the proofs of Witten’s conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to...
Invariant theory for and the rationality of
Invarianten der degenerierten Fasern in lokalen Familien von Kurven.
Invariants of plane algebraic curves via representations of the braid group.
Invertible cohomological field theories and Weil-Petersson volumes
We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....
Irreducibility and monodromy of some families of linear series
Irreducibility of some families of linear series with Brill-Noether number. I
Irreducible Components of the Chow Scheme of Space Curves.