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  • 1. Aka, Menny
    et al.
    Breuillard, Emmanuel
    Rosenzweig, Lior
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    de Saxce, Nicolas
    On metric Diophantine approximation in matrices and Lie groups2015In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 353, no 3, p. 185-189Article in journal (Refereed)
    Abstract [en]

    We study the Diophantine exponent of analytic submanifolds of m x n real matrices, answering questions of Beresnevich, Kleinbock, and Margulis. We identify a family of algebraic obstructions to the extremality of such a submanifold, and give a formula for the exponent when the submanifold is algebraic and defined over Q. We then apply these results to the determination of the Diophantine exponent of rational nilpotent Lie groups.

  • 2.
    Benelkourchi, Slimane
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A Note on the approximation of plurisubharmonic functions2006In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 342, no 9, p. 647-650Article in journal (Refereed)
    Abstract [en]

    Let Omega subset of C-n be a strongly hyperconvex domain and Omega(j) be a decreasing sequence of hyperconvex domains such that Omega = (boolean AND Omega(j))degrees. We show that every plurisubharmonic function rho is an element of F-s (Omega) is a limit of an increasing sequence of functions rho(j) is an element of F-a (Omega(j)).

  • 3. Borcea, J.
    et al.
    Brändén, Petter
    Department of Mathematics, Stockholm University.
    Hyperbolicity preservers and majorization2010In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, ISSN 1631-073X, Vol. 348, no 15-16, p. 843-846Article in journal (Refereed)
    Abstract [en]

    The majorization order on R(n) induces a natural partial ordering on the space of univariate hyperbolic polynomials of degree n. We characterize all linear operators on polynomials that preserve majorization, and show that it is sufficient (modulo obvious degree constraints) to preserve hyperbolicity.

  • 4.
    Bucher-Karlsson, Michelle
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Gelander, Tsachik
    Milnor-Wood inequalities for manifolds locally isometric to a product of hyperbolic planes2008In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 346, no 11-12, p. 661-666Article in journal (Refereed)
    Abstract [en]

    This Note describes sharp Milnor-Wood inequalities for the Euler number of flat oriented vector bundles over closed Riemannian manifolds locally isometric to products of hyperbolic planes. One consequence is that such manifolds do not admit an affine structure, confirming Chern-Sullivan's conjecture in this case. The manifolds under consideration are of particular interest, since in contrary to some other locally symmetric spaces they do admit interesting flat vector bundles in the corresponding dimension. When the manifold is irreducible and of higher rank, it is shown that flat oriented vector bundles are determined completely by the sign of the Euler number.

  • 5.
    Ernvall-Hytönen, Anne-Maria
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On certain exponential sums related to GL(3) cusp forms2010In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 348, no 1-2, p. 5-8Article in journal (Refereed)
  • 6.
    Faber, Carel
    et al.
    KTH, Superseded Departments, Mathematics.
    van der Geer, G.
    On the cohomology of local systems on the moduli spaces of curves of genus 2 and of Abelian surfaces, II2004In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 338, no 6, p. 467-470Article in journal (Refereed)
    Abstract [fr]

    On the cohomology of local systems on the moduli spaces of curves of genus 2 and of Abelian surfaces, II. We consider the cohomology of local systems on the moduli space of curves of genus 2 and the moduli space of Abelian surfaces. We dive an explicit formula for the Eisenstein cohomology and a conjectural formula for the endoscopic contribution. We show how, counting curves over finite fields provides Lis with detailed information about Siegel modular forms.

  • 7. Gosse, L.
    et al.
    Runborg, Olof
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Resolution of the finite Markov moment problem2005In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 341, no 12, p. 775-780Article in journal (Refereed)
    Abstract [en]

    We expose in full detail a constructive procedure to invert the so-called 'finite Markov moment problem'. The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations.

  • 8.
    Gustafsson, Björn
    et al.
    KTH, Superseded Departments, Mathematics.
    Mossino, J.
    Explicit limits for nonperiodic homogenization and reduction of dimension2002In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 334, no 11, p. 977-982Article in journal (Refereed)
    Abstract [en]

    The aim of this Note is to give explicit limit expressions. for diffusion equations involving a small parameter E, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials.

  • 9.
    Gustafsson, Björn
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Putinar, Mihai
    Saff, Edward B.
    Stylianopoulos, Nikos
    Bergman orthogonal polynomials on an archipelago2008In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 346, no 9-10, p. 499-502Article in journal (Refereed)
    Abstract [fr]

    Growth estimates for orthogonal polynomials with respect to area measure (Bergman polynomials) over the union of finitely many Jordan regions with piecewise smooth boundary are obtained by a careful investigation of the Green function of the complement, and of Schwarz reflection in analytic arcs of the boundary. As applications we obtain a detailed picture of the limiting zero distribution of Bergman's orthogonal polynomials, and also we propose a robust reconstruction algorithm of the original open set, starting from incomplete data (such as obtained by geometric tomography).

  • 10.
    Karlsson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ledrappier, Francois
    Liouville property and the linear drift of Brownian motion2007In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 344, no 11, p. 685-690Article in journal (Refereed)
    Abstract [fr]

    Liouville property and the linear drift of Brownian motion. Let M be a complete connected Riemannian manifold with bounded sectional curvature. Under the assumption that M is a regular covering of a manifold with finite volume, we establish that M is Liouville if, and only if, the linear rate of escape of Brownian motion on M vanishes.

  • 11.
    Klurman, Oleksiy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Kurlberg, Pär
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A note on multiplicative automatic sequences2019In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 357, no 10, p. 752-755Article in journal (Refereed)
    Abstract [en]

    We prove that any q-automatic completely multiplicative function f: N -> C essentially coincides with a Dirichlet character. This answers a question of J.-P. Allouche and L. Gold-makher and confirms a conjecture of J. Bell, N. Bruin and M. Coons for completely multiplicative functions. Further, assuming GRH, the methods allow us to replace completely multiplicative functions with multiplicative functions.

  • 12.
    Kurlberg, Pär
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Wigman, Igor
    Non-universality of the Nazarov-Sodin constant2015In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 353, no 2, p. 101-104Article in journal (Refereed)
    Abstract [en]

    We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for "arithmetic random waves", i.e. random toral Laplace eigenfunctions.

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