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We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step °ag variety. We also give symplectic and orthogonal...
This is the written version of my ˉve lectures at the Banach Center mini-school on `Schubert Varieties', in Warsaw, Poland, May 18{22, 2003.
It is the Deligne-Mumford compacti cation of the moduli space Mg;n of smooth n-pointed genus g curves. It has n natural line bundles Li (roughly, the cotangent space to the ith marked point) and a n...
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
Abstract: Motivated by the celebrated Gromov-Lawson-Schoen-Yau surgery the- ory on metrics of positive scalar curvature, the present paper constructs a double manifold associated with a minimal isopar...
Abstract: In this expository article, we explain how to use localization to compute Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten invariants of smooth toric Deligne-Mum...
Abstract: In this paper we start with the applications of polyfold theory to symplectic field theory.
In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse B...
In this paper, the first of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs is an expander and the girth of the graphs tends to infin...
A short and almost elementary proof of the Boros–F¨uredi–B´ar´any–Pach–Gromov theorem on the multiplicity of covering by simplices in Rd is given.
Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary $\partial V$ for a standard conformally stationary spacetime V = ...
We study the enumerative significance of the s-pointed genus zero Gromov-Witten invariant on a homogeneous space X. For that, we give an interpretation in terms of rational curves on X.
Recently, the old notion of causal boundary for a spacetime V has been rede ned in a consistent way. The computation of this boundary @V on any standard conformally stationary spacetime V = R  M, sug...
For each k > 0 we find an explicit function fk such that the topology of S inside the ball BS(p, r) is ‘bounded’ by fk(r) for every complete Riemannian surface (compact or noncompact) S with K  W...

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