• Publications
  • Influence
Towards the geometry of double Hurwitz numbers
Abstract Double Hurwitz numbers count branched covers of CP 1 with fixed branch points, with simple branching required over all but two points 0 and ∞ , and the branching over 0 and ∞ specified byExpand
Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable pointed curvesExpand
Counting curves on rational surfaces
Abstract:In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points).Expand
Murphy’s law in algebraic geometry: Badly-behaved deformation spaces
We consider the question: “How bad can the deformation space of an object be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad asExpand
Discriminants in the Grothendieck Ring
We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus onExpand
A geometric Littlewood-Richardson rule
We describe a geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties into the union of Schubert varieties. There are no restrictions on the baseExpand
A desingularization of the main component of the moduli space of genus-one stable maps into ℙn
We construct a natural smooth compactification of the space of smooth genus-one curves with k distinct points in a projective space. It can be viewed as an analogue of a well-known smoothExpand
On Conway's recursive sequence
TLDR
We take a step towards unravelling this mystery by showing that a ( n ) can (and should) be viewed as a simple ‘compression’ operation on finite sets. Expand
Schubert induction
We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson ruleExpand
Twelve points on the projective line, branched covers, and rational elliptic fibrations
Abstract. The following divisors in the space ${\rm Sym}^{12}{\mathbb P}^1$ of twelve points on ${\mathbb P}^1$ are actually the same: $({\mathcal A})$ the possible locus of the twelve nodalExpand
...
1
2
3
4
5
...