Journal: Journal of the London Mathematical Society

Abbreviation

J. London Math. Soc.

Publisher

Wiley

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ISSN

0024-6107
1469-7750

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Publications 1 - 10 of 19
  • Concentration phenomena for the fractional Q-curvature equation in dimension 3 and fractional Poisson formulas
    Item type: Journal Article
    DelaTorre, Azahara; Del Mar Gonzalez, Maria; Hyder, Ali; et al. (2021)
    Journal of the London Mathematical Society
    We study the compactness properties of metrics of prescribed fractional Q-curvature of order 3 in R3. We will use an approach inspired from conformal geometry, seeing a metric on a subset of R3 as the restriction of a metric on R+4 with vanishing fourth-order Q-curvature. We will show that a sequence of such metrics with uniformly bounded fractional Q-curvature can blow up on a large set (roughly, the zero set of the trace of a non-positive bi-harmonic function phi in R+4), in analogy with a four-dimensional result of Adimurthi-Robert-Struwe, and construct examples of such behaviour. In doing so, we produce general Poisson-type representation formulas (also for higher dimension), which are of independent interest.
  • The regularity method for graphs with few 4-cycles
    Item type: Journal Article
    Conlon, David; Fox, Jacob; Sudakov, Benny; et al. (2021)
    Journal of the London Mathematical Society
    We develop a sparse graph regularity method that applies to graphs with few 4-cycles, including new counting and removal lemmas for 5-cycles in such graphs. Some applications include: Every n-vertex graph with no 5-cycle can be made triangle-free by deleting o(n3/2) edges. For r > 3, every n-vertex r-graph with girth greater than 5 has o(n3/2) edges. Every subset of [n] without a nontrivial solution to the equation x1+x2+2x3=x4+3x5 has size o(n).
  • On the Number of Rational Points of Bounded Height on Smooth Bilinear Hypersurfaces in Biprojective Space
    Item type: Journal Article
    Robbiani, Marcello (2001)
    Journal of the London Mathematical Society
  • Higher genus relative Gromov–Witten theory and double ramification cycles
    Item type: Journal Article
    Fan, Honglu; Wu, Longting; You, Fenglong (2021)
    Journal of the London Mathematical Society
    We extend the definition of relative Gromov–Witten invariants with negative contact orders to all genera. Then we show that relative Gromov–Witten theory forms a partial CohFT. Some cycle relations on the moduli space of stable maps are also proved.
  • Patchworking oriented matroids
    Item type: Journal Article
    Celaya, Marcel; Loho, Georg; Yuen, Chi Ho (2022)
    Journal of the London Mathematical Society
    In a previous work, we gave a construction of (not necessarily realisable) oriented matroids from a triangulation of a product of two simplices. In this follow-up paper, we use a combinatorial analogue of Viro's patchworking to derive a topological representation of the oriented matroid directly from the polyhedral structure of the triangulation. This provides a combinatorial manifestation of patchworking besides tropical algebraic geometry. We achieve this by defining a general homeomorphism-preserving operation on regular cell complexes which acts by merging adjacent cells in the complex together. We then rephrase the patchworking procedure in terms of this process using the theory of tropical oriented matroids.
  • Solutions of the Ginzburg–Landau equations concentrating on codimension‐2 minimal submanifolds
    Item type: Journal Article
    Badran, Marco; del Pino, Manuel (2024)
    Journal of the London Mathematical Society
  • The joint spectrum
    Item type: Journal Article
    Breuillard, Emmanuel; Sert, Çagri (2021)
    Journal of the London Mathematical Society
    We introduce the notion of joint spectrum of a compact set of matrices S⊂GLd (C) , which is a multi‐dimensional generalization of the joint spectral radius. We begin with a thorough study of its properties (under various assumptions: irreducibility, Zariski‐density, and domination). Several classical properties of the joint spectral radius are shown to hold in this generalized setting and an analogue of the Lagarias–Wang finiteness conjecture is discussed. Then we relate the joint spectrum to matrix valued random processes and study what points of it can be realized as Lyapunov vectors. We also show how the joint spectrum encodes all word metrics on reductive groups. Several examples are worked out in detail. This paper relies extensively on colour figures. Some references to colour may not be meaningful in the printed version, and we refer the reader to the online version which includes the colour figures.
  • Sparse Kneser graphs are Hamiltonian
    Item type: Journal Article
    Mütze, Torsten; Nummenpalo, Jerri; Walczak, Bartosz (2021)
    Journal of the London Mathematical Society
    For integers k > 1 and n > 2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1, horizontal ellipsis ,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k > 3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k > 3 and a > 0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k-6 distinct Hamilton cycles for k > 6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words.
  • Genus 0 logarithmic and tropical fixed-domain counts for Hirzebruch surfaces
    Item type: Journal Article
    Cela, Alessio; Iribar López, Aitor (2024)
    Journal of the London Mathematical Society
    For a non-singular projective toric variety (Formula presented.), the virtual logarithmic Tevelev degrees are defined as the virtual degree of the morphism from the moduli stack of logarithmic stable maps (Formula presented.) to the product (Formula presented.). In this paper, after proving that Mikhalkin's correspondence theorem holds in genus 0 for logarithmic virtual Tevelev degrees, we use tropical methods to provide closed formulas for the case in which (Formula presented.) is a Hirzebruch surface. In order to do so, we explicitly list all the tropical curves contributing to the count.
  • New bounds on the size of nearly perfect matchings in almost regular hypergraphs
    Item type: Journal Article
    Kang, Dong Yeap; Kühn, Daniela; Methuku, Abhishek; et al. (2023)
    Journal of the London Mathematical Society
    Let H be a k-uniform D-regular simple hypergraph on N vertices. Based on an analysis of the Rödl nibble, in 1997, Alon, Kim and Spencer proved that if k ≥ 3, then H contains a matching covering all but at most N D⁻¹/⁽ᵏ⁻¹⁾⁺⁰⁽¹⁾ vertices, and asked whether this bound is tight. In this paper we improve their bound by showing that for all k > 3, H contains a matching covering all but at most N D⁻¹/⁽ᵏ⁻¹⁾⁻η vertices for some η = Θ (k⁻³) > 0, when N and D are sufficiently large. Our approach consists of showing that the Rödl nibble process not only constructs a large matching but it also produces many well-distributed ‘augmenting stars’ which can then be used to significantly improve the matching constructed by the Rödl nibble process. Based on this, we also improve the results of Kostochka and Rödl from 1998 and Vu from 2000 on the size of matchings in almost regular hypergraphs with small codegree. As a consequence, we improve the best known bounds on the size of large matchings in combinatorial designs with general parameters. Finally, we improve the bounds of Molloy and Reed from 2000 on the chromatic index of hypergraphs with small codegree (which can be applied to improve the best known bounds on the chromatic index of Steiner triple systems and more general designs).
Publications 1 - 10 of 19