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  • 1. Adiprasito, Karim
    et al.
    Björner, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Goodarzi, Afshin
    Freie Universität, Germany.
    Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals2017Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 19, nr 12, s. 3851-3865Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A numerical characterization is given of the h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree <= d and shifted pure. (d - 1)-dimensional simplicial complexes.

  • 2.
    Andréasson, Håkan
    et al.
    Chalmers.
    Ringström, Hans
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Proof of the cosmic no-hair conjecture in the T3-Gowdy symmetric Einstein-Vlasov setting2016Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 18, nr 7, s. 1565-1650Artikel i tidskrift (Refereegranskat)
  • 3. Canto-Martín, Francisco
    et al.
    Hedenmalm, Håkan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Montes-Rodríguez, Alfonso
    Perron-Frobenius operators and the Klein-Gordon equation2014Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 16, nr 1, s. 31-66Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For a smooth curve Gamma and a set Lambda in the plane R-2, let AC(Gamma; Lambda) be the space of finite Borel measures in the plane supported on Gamma, absolutely continuous with respect to arc length and whose Fourier transform vanishes on Lambda. Following [12], we say that (Gamma, Lambda) is a Heisenberg uniqueness pair if AC(Gamma; Lambda) = {0}. In the context of a hyperbola Gamma, the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Gamma of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the issue of finding the dimension of AC(Gamma; Lambda) when it is nonzero. We will fix the curve Gamma to be the hyperbola x(1)x(2) = 1, and the set Lambda = Lambda(alpha,beta) to be the lattice-cross Lambda(alpha,beta) = (alpha Zeta x {0}) boolean OR ({0} x beta Z), where alpha, beta are positive reals. We will also consider Gamma(+), the branch of x(1)x(2) = 1 where x(1) > 0. In [12], it is shown that AC(Gamma; Lambda(alpha,beta)) = {0} if and only if alpha beta <= 1. Here, we show that for alpha beta > 1, we get a rather drastic "phase transition": AC(Gamma; Lambda(alpha,beta)) is infinite-dimensional whenever alpha beta > 1. It is shown in [13] that AC(Gamma(+); Lambda(alpha,beta)) = {0} if and only if alpha beta < 4. Moreover, at the edge alpha beta = 4, the behavior is more exotic: the space AC(Gamma(+); Lambda(alpha,beta)) is one-dimensional. Here, we show that the dimension of AC(Gamma(+); Lambda(alpha,beta)) is infinite whenever alpha beta > 4. Dynamical systems, and more specifically Perron-Frobenius operators, play a prominent role in the presentation.

  • 4. Dolbeault, Jean
    et al.
    Laptev, Ari
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Loss, Michael
    Lieb-Thirring inequalities with improved constants2008Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 10, nr 4, s. 1121-1126Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrodinger operators.

  • 5.
    Ekholm, Tomas
    et al.
    Department of Mathematics, Lund University.
    Frank, Rupert
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lieb-Thirring inequalities on the half-line with critical exponent2008Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 10, nr 3, s. 739-755Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the operator -d(2)/dr(2) - V in L-2(R+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound for any alpha is an element of [0, 1) and gamma >= (1 - alpha)/2. This includes a Lieb-Thirring inequality in the critical endpoint case.

  • 6.
    Faber, Carel
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Pandharipande, R.
    Relative maps and tautological classes2005Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 7, nr 1, s. 13-49Artikel i tidskrift (Refereegranskat)
  • 7.
    Jochemko, Katharina
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Sanyal, R.
    Combinatorial positivity of translation-invariant valuations and a discrete Hadwiger theorem2018Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 20, nr 9, s. 2181-2208Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce the notion of combinatorial positivity of translation-invariant valuations on convex polytopes that extends the nonnegativity of Ehrhart h∗-vectors. We give a surprisingly simple characterization of combinatorially positive valuations that implies Stanley’s nonnegativity and monotonicity of h∗-vectors and generalizes work of Beck et al. (2010) from solid-angle polynomials to all translation-invariant simple valuations. For general polytopes, this yields a new characterization of the volume as the unique combinatorially positive valuation up to scaling. For lattice polytopes our results extend work of Betke–Kneser (1985) and give a discrete Hadwiger theorem: There is essentially a unique combinatorially-positive basis for the space of lattice-invariant valuations. As byproducts, we prove a multivariate Ehrhart–Macdonald reciprocity and we show universality of weight valuations studied in Beck et al. (2010).

  • 8.
    Kurlberg, Pär
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Ueberschär, H.
    Superscars in the Šeba billiard2017Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 19, nr 10, s. 2947-2964Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the Laplacian with a delta potential (a "point scatterer") on an irrational torus, where the square of the side ratio is diophantine. The eigenfunctions fall into two classes: "old" eigenfunctions (75%) of the Laplacian which vanish at the support of the delta potential, and therefore are not affected, and "new" eigenfunctions (25%) which are affected, and as a result feature a logarithmic singularity at the location of the delta potential. Within a full density subsequence of the new eigenfunctions we determine all semiclassical measures in the weak coupling regime and show that they are localized along four wave vectors in momentum space-we therefore prove the existence of so-called "superscars" as predicted by Bogomolny and Schmit [5]. This result contrasts with the phase space equidistribution which is observed for a full density subset of the new eigenfunctions of a point scatterer on a rational torus [14]. Further, in the strong coupling limit we show that a weaker form of localization holds for an essentially full density subsequence of the new eigenvalues; in particular quantum ergodicity does not hold. We also explain how our results can be modified for rectangles with Dirichlet boundary conditions with a point scatterer in the interior. In this case our results extend previous work of Keating, Marklof andWinn who proved the existence of localized semiclassical measures under a clustering condition on the spectrum of the Laplacian.

  • 9.
    Kurlberg, Pär
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Ueberschär, Henrik
    Superscars in the Seba billiard2017Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, To appear in J. Eur. Math. Soc. (JEMS)Artikel i tidskrift (Refereegranskat)
  • 10.
    Xu, Disheng
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Density of positive Lyapunov exponents for symplectic cocycles2019Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 21, nr 10, s. 3143-3190Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that Sp(2d, R)-cocycles, HSp(2d)-cocycles and pseudo-unitary cocycles with at least one non-zero Lyapunov exponent are dense in all usual regularity classes for non-periodic dynamical systems. For Schrodinger operators on the strip, we prove a similar result about the density of positive Lyapunov exponents. This generalizes a result of A. Avila [2] to higher dimensions.

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