Now showing items 1-20 of 250

    • The 1-2 model 

      Grimmett, Geoffrey Richard; Li, Zhongyang (American Mathematical Society, 2016)
      The current paper is a short review of rigorous results for the 1-2 model. The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. It was ...
    • A 2-adic automorphy lifting theorem for unitary groups over CM fields 

      Thorne, Jack Arfon (Springer, 2016)
      We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitary type, over imaginary CM fields. We use this to improve an automorphy lifting theorem of Kisin for GL_2.
    • A 3-manifold group which is not four dimensional linear 

      Button, Jack (Elsevier, 2014-01-28)
      We give examples of closed orientable graph 3-manifolds having a fundamental group which is not a subgroup of GL(4, F) for any field F. This answers a question in the Kirby problem list from 1977 which is credited to the ...
    • 3-manifolds everywhere 

      Calegari, Danny; Wilton, Henry John
      A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This ...
    • Abelian quotients of mapping class groups of highly connected manifolds 

      Galatius, Søren; Randal-Williams, Oscar (Springer, 2015-10-12)
      We compute the abelianisations of the mapping class groups of the manifolds W²ⁿ_g = g(Sⁿ × Sⁿ) for n ≥ 3 and g ≥ 5. The answer is a direct sum of two parts. The first part arises from the action of the mapping class group ...
    • About Kac's Program in Kinetic Theory 

      Mischler, Stéphane; Mouhot, Clement Gabriel
      In this Note we present the main results from the recent work arxiv:1107.3251, which answers several conjectures raised fifty years ago by Kac. There Kac introduced a many-particle stochastic process (now denoted as Kac's ...
    • About L-P estimates for the spatially homogeneous Boltzmann equation 

      Desvillettes, L; Mouhot, Clement Gabriel (2005)
    • Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for $\kappa > 8$ 

      Gwynne, Ewain; Kassel, Adrien; Miller, Jason Peter; Wilson, David
      We consider the Peano curve separating a spanning tree from its dual spanning tree on an embedded planar graph, where the tree and dual tree are weighted by $y$ to the number of active edges, and "active" is in the sense ...
    • Acylindrical Hyperbolicity, non-simplicity and SQ-universality of groups splitting over $\mathbb{Z}$ 

      Button, Jack (De Gruyter, 2016-09-15)
      We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\mathbb{Z}$ cannot be simple. We also obtain SQ-universality in most cases, for instance a balanced group (one where if two powers ...
    • Adaptation in log-concave density estimation 

      Kim, AKH; Guntuboyina, A; Samworth, Richard John
      The log-concave maximum likelihood estimator of a density on the real line based on a sample of size n is known to attain the minimax optimal rate of convergence of O(n −4/5 ) with respect to, e.g., squared Hellinger ...
    • The algebra of bounded linear operators on ℓp ⊕ ℓq has infinitely many closed ideals 

      Schlumprecht, T; Zsák, A
      We prove that in the reflexive range 1 < p < q < ∞, the algebra ℒ(ℓp⊕ℓq) of all bounded linear operators on ℓp⊕ℓq has infinitely many closed ideals. This solves a problem raised by A. Pietsch [Operator ideals, Math. Monogr. ...
    • Algebraic boundaries of Hilbert's SOS cones 

      Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd (Cambridge University Press, 2012-10-15)
      We study the geometry underlying the difference between nonnegative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be ...
    • Almost sure multifractal spectrum of SLE 

      Gwynne, E; Miller, Jason Peter; Sun, X
      Suppose that $\eta$ is a Schramm-Loewner evolution (SLE$_\kappa$) in a smoothly bounded simply connected domain $D \subset {\mathbb C}$ and that $\phi$ is a conformal map from ${\mathbb D}$ to a connected component of $D ...
    • Alperin–McKay natural correspondences in solvable and symmetric groups for the prime p=2 

      Giannelli, Eugenio; Murray, J; Tent, J (Nicola Zanichelli, 2017-10-29)
      Let G be a finite solvable or symmetric group and let B be a 2-block of G. We construct a canonical correspondence between the irreducible characters of height zero in B and those in its Brauer first main correspondent. ...
    • Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds 

      Dervan, Ruadhai (Université Paul Sabatier, 2016)
      We give a criterion for the coercivity of the Mabuchi functional for general Kàhler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the ...
    • Alpha Invariants and K-Stability for General Polarizations of Fano Varieties 

      Dervan, Ruadhai (Oxford University Press, 2014-09-26)
      We provide a sufficient condition for polarisations of Fano varieties to be K-stable in terms of Tian’s alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system ...
    • Ample subvarieties and q-ample divisors 

      Ottem, John Christian (Elsevier, 2012-03-20)
      We introduce a notion of ampleness for subschemes of any codimension using the theory of q-ample line bundles. We also investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz ...
    • Analysis of spectral methods for the homogeneous Boltzmann equation 

      Filbet, Francis; Mouhot, Clement Gabriel
    • Arithmetic invariant theory and 2-descent for plane quartic curves 

      Thorne, Jack Arfon (Mathematical Sciences Publishers, 2016-09-27)
      Given a smooth plane quartic curve C over a field $\textit{k}$ of characteristic 0, with Jacobian variety $\textit{J}$, and a marked rational point P $\in$ C($\textit{k}$), we construct a reductive group $\textit{G}$ and ...
    • Asymptotics of Partial Density Functions for Divisors 

      Ross, Julius; Singer, Michael (Springer, 2016-09-19)
      We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$ . Assuming the data in question is ...