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The Kolmogorov]Smirnov distance is an important tool for constructing confidence sets and tests in univariate problems. In multivariate settings, an analogous role is played by the halfspace di...
We prove that for any compact set B in R^d and for any epsilon >0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points such that the maximum absolute value of any linear function ell: R^d ...
We show that Hilbert’s Tenth Problem is undecidable for complementary subrings of number fields and that the p-adic and archimedean ring versions of Mazur’s conjectures do not hold in these rings .
In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced ρ′-mixing condition.
Suppose B = F[x, y, z]/h is the homogeneous coordinate ring of a characteristic p degree 3 irreducible plane curve C with a node. Let J be a homogeneous (x, y, z)-primary ideal and n → en be the Hilbe...
We compute the dimension of the Hilbert scheme of subvarieties of positive dimension in projective space which are defined as vanishing loci of maximal minors of a matrix with polynomial entries.
Let X be a separable real Hilbert space. We show that for every Lipschitz function f : X ! R, and for every " > 0, there exists a Lipschitz, real analytic function g : X ! R such that |f(x) − g(...
We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bun...
We propose a relative trace formula approach and state the corresponding fundamental lemma toward the global restriction problem involving Bessel or Fourier-Jacobi periods of unitary groups Un×Um, ex...
In this article we study the period map for a family of K3 surfaces which is given by the anticanon-ial divisor of a toric variety. We determine the period di erential equation and its monodromy group...
For a smooth projective variety P, we construct a Cartier divisor supported on the incidence locus in Ca(P) × Cdim(P)−a−1(P). There is a natural definition of the corresponding line bundle...
We want to understand the geometry of all irreducible components of the toric Hilbert scheme. Until now it is known that the coherent component is (up to normalisation)the toric variety associated to ...
The problem of estimating the tail index from truncated data is addressed in Chakrabarty and Samorodnitsky (2009). In that paper, a sample based (and hence random) choice of k is uggested,and it is sh...
Given a finite subgroup 􀀀  SL2(C) we define an additive 2-category H􀀀 whose Grothendieck group is isomorphic to an integral form h􀀀 of the Heisenberg algebra. We construct...
Let Q = P1 × P1 and let X  Q be a 0-dimensional scheme. This paper is a first step towards the characterization of Hilbert functions of 0-dimensional schemes in Q. In particular we show how, under so...

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