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  • Walter's theorem for fusion systems
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-10-23
    Michael Aschbacher

    We determine the saturated 2‐fusion systems in which the centralizer of some fully centralized involution contains a component that is the 2‐fusion system of a large group of Lie type over a field of odd order.

    更新日期:2020-10-26
  • A geometric approach to the sup‐norm problem for automorphic forms: the case of newforms on GL2(Fq(T)) with squarefree level
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-10-20
    Will Sawin

    The sup‐norm problem in analytic number theory asks for the largest value taken by a given automorphic form. We observe that the function‐field version of this problem can be reduced to the geometric problem of finding the largest dimension of the i th stalk cohomology group of a given Hecke eigensheaf at any point. This problem, in turn, can be reduced to the intersection‐theoretic problem of bounding

    更新日期:2020-10-20
  • Moduli of weighted stable elliptic surfaces and invariance of log plurigenera
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-10-20
    Kenneth Ascher; Dori Bejleri

    Motivated by Hassett's weighted pointed stable curves, we use the log minimal model program to construct compact moduli spaces parameterizing weighted stable elliptic surfaces — elliptic fibrations with section and marked fibers each weighted between zero and one. Moreover, we show that the domain of weights admits a wall and chamber structure, describe the induced wall‐crossing morphisms on the moduli

    更新日期:2020-10-20
  • E8 and the average size of the 3‐Selmer group of the Jacobian of a pointed genus‐2 curve
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-10-20
    Beth Romano; Jack A. Thorne

    We prove that the average size of the 3‐Selmer group of a genus‐2 curve with a marked Weierstrass point is 4. We accomplish this by studying rational and integral orbits in the representation associated to a stably Z / 3 Z ‐graded simple Lie algebra of type E 8 . We give new techniques to construct integral orbits, inspired by the proof of the fundamental lemma and by the twisted vertex operator realisation

    更新日期:2020-10-20
  • Grothendieck–Witt groups of some singular schemes
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-09-20
    Max Karoubi; Marco Schlichting; Charles Weibel

    We establish some structural results for the Witt and Grothendieck–Witt groups of schemes over Z [ 1 / 2 ] , including homotopy invariance for Witt groups and a formula for the Witt and Grothendieck–Witt groups of punctured affine spaces over a scheme. All these results hold for singular schemes and at the level of spectra.

    更新日期:2020-09-21
  • Strong solution for Korteweg system in bmo−1(RN) with initial density in L∞
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-09-16
    Boris Haspot

    In this paper we investigate the question of the local existence of strong solution for the Korteweg system in critical spaces in dimension N ⩾ 1 provided that the initial data are small (we restrict our analysis to the case of the so‐called compressible quantum Navier–Stokes equations which corresponds to the capillary coefficient κ ( ρ ) = κ 2 ρ with κ 2 > 0 ). More precisely the initial momentum

    更新日期:2020-09-16
  • Homotopy type of the complex of free factors of a free group
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-09-02
    Benjamin Brück, Radhika Gupta

    We show that the complex of free factors of a free group of rank n ⩾ 2 is homotopy equivalent to a wedge of spheres of dimension n − 2 . We also prove that for n ⩾ 2 , the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is ( n − 2 ) ‐connected. In addition, we show that for every non‐trivial free factor system

    更新日期:2020-09-02
  • Sobolev inequalities with jointly concave weights on convex cones
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-27
    Zoltán M. Balogh; Cristian E. Gutiérrez; Alexandru Kristály

    Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form ∫ E | u ( x ) | q ω ( x ) d x 1 / q ⩽ K 0 ∫ E | ∇ u ( x ) | p σ ( x ) d x 1 / p , u ∈ C 0 ∞ ( R n ) , (WSI)where p ⩾ 1 and q > 0 is the corresponding Sobolev critical exponent. Here E ⊆ R n is an open convex cone, and ω , σ : E → ( 0 , ∞ ) are two homogeneous weights verifying a general concavity‐type structural

    更新日期:2020-08-27
  • Non‐vanishing theorems for central L‐values of some elliptic curves with complex multiplication
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-20
    John Coates, Yongxiong Li

    The paper uses Iwasawa theory at the prime p = 2 to prove non‐vanishing theorems for the value at s = 1 of the complex L ‐series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field K = Q ( − q ) , where q is any prime ≡ 7 mod 8 . Our results establish some broad generalizations of the non‐vanishing theorem first proven by Rohrlich using complex

    更新日期:2020-08-20
  • On the birational geometry of spaces of complete forms I: collineations and quadrics
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-19
    Alex Massarenti

    Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduli spaces of complete collineations and quadrics from the point of view of Mori theory. We compute their effective, nef and movable cones, the generators of their Cox rings, and their groups of pseudo‐automorphisms

    更新日期:2020-08-19
  • Injectivity results for coarse homology theories
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-19
    Ulrich Bunke, Alexander Engel, Daniel Kasprowski, Christoph Winges

    We show injectivity results for assembly maps using equivariant coarse homology theories with transfers. Our method is based on the descent principle and applies to a large class of linear groups or, more generally, groups with finite decomposition complexity.

    更新日期:2020-08-19
  • Elusive extremal graphs
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-19
    Andrzej Grzesik, Daniel Král, László Miklós Lovász

    We study the uniqueness of optimal solutions to extremal graph theory problems. Lovász conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the resulting set is satisfied by an asymptotically unique graph. This statement is often referred to as saying that ‘every extremal graph theory problem has a finitely

    更新日期:2020-08-19
  • Complete moduli of cubic threefolds and their intermediate Jacobians
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-17
    Sebastian Casalaina‐Martin; Samuel Grushevsky; Klaus Hulek; Radu Laza

    The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds, not even as a map to the Satake compactification of the moduli space of principally polarized abelian fivefolds. A better ‘wonderful’ compactification M ∼ of the space of cubic threefolds was constructed by the first and

    更新日期:2020-08-18
  • From Hardy to Rellich inequalities on graphs
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-16
    Matthias Keller; Yehuda Pinchover; Felix Pogorzelski

    We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrödinger operators afterwards

    更新日期:2020-08-17
  • A local‐global principle for isogenies of composite degree
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-17
    Isabel Vogt

    Let E be an elliptic curve defined over a number field K . If for almost all primes of K , the reduction of E has a rational cyclic isogeny of fixed degree, then we can ask whether E has a cyclic isogeny over K of that degree. Building upon the works of Sutherland, Anni, and Banwait‐Cremona in the case of prime degree, we consider this question for cyclic isogenies of arbitrary degree.

    更新日期:2020-08-17
  • Motivic Chern classes and K‐theoretic stable envelopes
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-08-06
    László M. Fehér; Richárd Rimányi; Andrzej Weber

    We consider a smooth algebraic variety with an action of a linear algebraic group acting with finitely many orbits. We study equivariant characteristic classes of the orbits, namely the equivariant motivic Chern classes , in the K‐theory of the ambient space. We prove that the motivic Chern class satisfies the axiom system inspired by that of ‘K‐theoretic stable envelopes’, recently defined by Okounkov

    更新日期:2020-08-06
  • Asymptotic period relations for Jacobian elliptic surfaces
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-14
    N. I. Shepherd‐Barron

    We describe the image of the locus of hyperelliptic curves of genus g under the period mapping in a neighbourhood of the diagonal locus Diag g . There is just one branch for each of the alkanes C g H 2 g + 2 of elementary organic chemistry, and each branch has a simple linear description in terms of the entries of the period matrix.

    更新日期:2020-07-24
  • Heegner points in Coleman families
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-06
    Dimitar Jetchev; David Loeffler; Sarah Livia Zerbes

    We construct two‐parameter analytic families of Galois cohomology classes interpolating the étale Abel–Jacobi images of generalised Heegner cycles, with both the modular form and Grössencharacter varying in p ‐adic families.

    更新日期:2020-07-24
  • Relative regular Riemann–Hilbert correspondence
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-03
    Luisa Fiorot; Teresa Monteiro Fernandes; Claude Sabbah

    On the product of a complex manifold X by a complex curve S considered as a parameter space, we show a Riemann–Hilbert correspondence between regular holonomic relative D ‐modules (respectively, complexes) on the one hand and relative perverse complexes (respectively, S ‐ C ‐constructible complexes) on the other hand.

    更新日期:2020-07-24
  • An arithmetic Lefschetz–Riemann–Roch theorem
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-06-25
    Shun Tang

    In this article, we consider regular projective arithmetic schemes in the context of Arakelov geometry, any of which is endowed with an action of the diagonalizable group scheme associated to a finite cyclic group and with an equivariant very ample invertible sheaf. For any equivariant morphism between such arithmetic schemes, which is smooth over the generic fiber, we define a direct image map between

    更新日期:2020-07-24
  • On quint‐canonical birationality of irregular threefolds
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-06-09
    Jheng‐Jie Chen; Jungkai Alfred Chen; Meng Chen; Zhi Jiang

    Let X be a complex smooth projective threefold of general type. Assume q ( X ) > 0 . We show that the m ‐canonical map of X is birational for all m ⩾ 5 .

    更新日期:2020-07-24
  • Rigid connections on P1 via the Bruhat–Tits building
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-19
    Masoud Kamgarpour; Daniel S. Sage

    We apply the theory of fundamental strata of Bremer and Sage to find cohomologically rigid G ‐connections on the projective line, generalising the work of Frenkel and Gross. In this theory, one studies the leading term of a formal connection with respect to the Moy–Prasad filtration associated to a point in the Bruhat–Tits building. If the leading term is regular semisimple with centraliser a (not

    更新日期:2020-07-24
  • On the weak relative Dixmier property
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-15
    Amine Marrakchi

    We show that every inclusion of von Neumann algebras with a faithful normal conditional expectation has the weak relative Dixmier property. This answers a question of Popa (J. Funct. Anal . 171 (2000) 139–154). The proof uses an improvement of Ellis's lemma for compact convex semigroups.

    更新日期:2020-07-24
  • Hypergraph expanders of all uniformities from Cayley graphs
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-21
    David Conlon, Jonathan Tidor, Yufei Zhao

    Hypergraph expanders are hypergraphs with surprising, non‐intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, of 3‐uniform hypergraph expanders with polylogarithmic degree. We generalize this construction, giving a simple construction of r ‐uniform hypergraph expanders for all r ⩾ 3 .

    更新日期:2020-07-21
  • Quotient theorems in polyfold theory and S1‐equivariant transversality
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-21
    Zhengyi Zhou

    We introduce group actions on polyfolds and polyfold bundles. We prove quotient theorems for polyfolds, when the group action has finite isotropy. We prove that the sc‐Fredholm property is preserved under quotient if the base polyfold is infinite dimensional. The quotient construction is the main technical tool in the construction of equivariant fundamental class in our future work. We also analyze

    更新日期:2020-07-21
  • The boundary of chaos for interval mappings
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-21
    Trevor Clark, Sofía Trejo

    A goal in the study of dynamics on the interval is to understand the transition to positive topological entropy. There is a conjecture from the 1980s that the only route to positive topological entropy is through a cascade of period doubling bifurcations. We prove this conjecture in natural families of smooth interval maps, and use it to study the structure of the boundary of mappings with positive

    更新日期:2020-07-21
  • Almost all Steiner triple systems have perfect matchings
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-21
    Matthew Kwan

    We show that for any n divisible by 3, almost all order‐ n Steiner triple systems have a perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of perfect matchings in a Steiner triple system and show that almost all Steiner triple systems essentially attain this maximum. We accomplish this via a general theorem comparing a uniformly

    更新日期:2020-07-21
  • Degree bounds for local cohomology
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-14
    Andrew R. Kustin, Claudia Polini, Bernd Ulrich

    It has long been known how to read information about the socle degrees of the local cohomology H m 0 ( M ) of a graded module over a polynomial ring R from the twists in position d = dim R , in a resolution of M by free R ‐modules. It has also long been known how to use local cohomology to read valuable information from complexes which approximate resolutions in the sense that they have positive homology

    更新日期:2020-07-14
  • Degrees of iterates of rational maps on normal projective varieties
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-14
    Nguyen‐Bac Dang

    Let X be a normal projective variety defined over an algebraically closed field of arbitrary characteristic. We study the sequence of intermediate degrees of the iterates of a dominant rational selfmap of X , recovering former results by Dinh and Sibony (Ann. Sci. Éc. Norm. Supér. (4) 37 (2004) 959–971), and by Truong (J. Reine Angew. Math. 758 (2020) 139–182). Precisely, we give a new proof of the

    更新日期:2020-07-14
  • Ambidexterity and the universality of finite spans
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-04
    Yonatan Harpaz

    Pursuing the notions of ambidexterity and higher semiadditivity as developed by Hopkins and Lurie, we prove that the span ∞ ‐category of m ‐finite spaces is the free m ‐semiadditive ∞ ‐category generated by a single object. Passing to presentable ∞ ‐categories we obtain a description of the free presentable m ‐semiadditive ∞ ‐category in terms of a new notion of m ‐commutative monoids, which can be

    更新日期:2020-07-04
  • On Dℓ‐extensions of odd prime degree ℓ
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-04
    Henri Cohen, Frank Thorne

    Generalizing the work of Morra and the authors, we give explicit formulas for the Dirichlet series generating function of D ℓ ‐extensions of odd prime degree ℓ with given quadratic resolvent. Over the course of our proof, we explain connections between our formulas and the Ankeny–Artin–Chowla conjecture, the Ohno–Nakagawa relation for binary cubic forms, and other topics. We also obtain improved upper

    更新日期:2020-07-04
  • Logarithmic compactification of the Abel–Jacobi section
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-07-04
    Steffen Marcus, Jonathan Wise

    Given a smooth curve with weighted marked points, the Abel–Jacboi map produces a line bundle on the curve. This map fails to extend to the full boundary of the moduli space of stable pointed curves. Using logarithmic and tropical geometry, we describe a modular modification of the moduli space of curves over which the Abel–Jacobi map extends. We also describe the attendant deformation theory and virtual

    更新日期:2020-07-04
  • On depth zero L‐packets for classical groups
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-06-28
    Jaime Lust, Shaun Stevens

    By computing reducibility points of parabolically induced representations, we construct, to within at most two unramified quadratic characters, the Langlands parameter of an arbitrary depth zero irreducible cuspidal representation π of a classical group (which may be not‐quasi‐split) over a non‐archimedean local field of odd residual characteristic. From this, we can explicitly describe all the irreducible

    更新日期:2020-06-28
  • E8 spectral curves
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-19
    Andrea Brini

    I provide an explicit construction of spectral curves for the affine E 8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the representation ring of E 8 for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of both integrals of motion and the action‐angle map for the

    更新日期:2020-05-19
  • Cohen–Macaulay modules over the algebra of planar quasi–invariants and Calogero–Moser systems
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-19
    Igor Burban, Alexander Zheglov

    In this paper, we study properties of the algebras of planar quasi‐invariants. These algebras are Cohen–Macaulay and Gorenstein in codimension one. Using the technique of matrix problems, we classify all Cohen–Macaulay modules of rank one over them and determine their Picard groups. In terms of this classification, we describe the spectral modules of the planar rational Calogero–Moser systems. Finally

    更新日期:2020-05-19
  • On class groups of random number fields
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-18
    Alex Bartel, Hendrik W. Lenstra

    The main aim of this paper is to disprove the Cohen–Lenstra–Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in terms of Arakelov class groups, giving an explanation for the probability weights appearing in the general form of the heuristics. We conclude by proposing a rigorously formulated Cohen–Lenstra–Martinet conjecture.

    更新日期:2020-05-18
  • Graphons, permutons and the Thoma simplex: three mod‐Gaussian moduli spaces
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-16
    Valentin Féray, Pierre‐Loïc Méliot, Ashkan Nikeghbali

    In this paper, we show how to use the framework of mod‐Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three frameworks, a generic homogeneous observable of a generic random model is mod‐Gaussian under an appropriate renormalization. This implies a central limit theorem with

    更新日期:2020-05-16
  • Existence of common zeros for commuting vector fields on 3‐manifolds II. Solving global difficulties
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-13
    Sébastien Alvarez, Christian Bonatti, Bruno Santiago

    We address the following conjecture about the existence of common zeros for commuting vector fields in dimension 3: if X , Y are two C 1 commuting vector fields on a 3‐manifold M , and U is a relatively compact open such that X does not vanish on the boundary of U and has a non‐vanishing Poincaré–Hopf index in U , then X and Y have a common zero inside U . We prove this conjecture when X and Y are

    更新日期:2020-05-13
  • Unfriendly colorings of graphs with finite average degree
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-09
    Clinton T. Conley; Omer Tamuz

    In an unfriendly coloring of a graph the color of every node mismatches that of the majority of its neighbors. We show that every probability measure preserving Borel graph with finite average degree admits a Borel unfriendly coloring almost everywhere. We also show that every bounded degree Borel graph of subexponential growth admits a Borel unfriendly coloring.

    更新日期:2020-05-09
  • Solvability of systems of diagonal equations over p‐adic local fields
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-04
    Christopher Skinner

    We prove that a system of R diagonal equations of degree d over a finite extension K of Q p has a non‐trivial solution in K if the number of variables exceeds 3 R 2 d 2 (if p > 2 ) or 8 R 2 d 2 (if p = 2 ). As a consequence, a system of R homogeneous equations of degree d over K has a non‐trivial solution in K if the number of variables exceeds ( 8 R 2 d 2 ) 2 d − 1 .

    更新日期:2020-05-04
  • Absence of eigenvalues of non‐self‐adjoint Robin Laplacians on the half‐space
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-02
    L. Cossetti, D. Krejčiřík

    By developing the method of multipliers, we establish sufficient conditions which guarantee the total absence of eigenvalues of the Laplacian in the half‐space, subject to variable complex Robin boundary conditions. As a further application of this technique, uniform resolvent estimates are derived under the same assumptions on the potential. Some of the results are new even in the self‐adjoint setting

    更新日期:2020-05-02
  • Relative semi‐ampleness in positive characteristic
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-02
    Paolo Cascini, Hiromu Tanaka

    Given an invertible sheaf on a fibre space between projective varieties of positive characteristic, we show that fibrewise semi‐ampleness implies relative semi‐ampleness. The same statement fails in characteristic zero.

    更新日期:2020-05-02
  • Blob algebra approach to modular representation theory
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-02
    Nicolas Libedinsky, David Plaza

    Two decades ago, Martin and Woodcock made a surprising and prophetic link between statistical mechanics and representation theory. They observed that the decomposition numbers of the blob algebra (that appeared in the context of transfer matrix algebras) are Kazhdan–Lusztig polynomials in type A ∼ 1 . In this paper, we take that observation far beyond its original scope. We conjecture that for A ∼

    更新日期:2020-05-02
  • Forbidden vector‐valued intersections
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-02
    Peter Keevash, Eoin Long

    We solve a generalised form of a conjecture of Kalai motivated by attempts to improve the bounds for Borsuk's problem. The conjecture can be roughly understood as asking for an analogue of the Frankl–Rödl forbidden intersection theorem in which set intersections are vector‐valued. We discover that the vector world is richer in surprising ways: in particular, Kalai's conjecture is false, but we prove

    更新日期:2020-05-02
  • Degree and birationality of multi‐graded rational maps
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-02
    Laurent Busé, Yairon Cid‐Ruiz, Carlos D'Andrea

    We give formulas and effective sharp bounds for the degree of multi‐graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian dual criterion to the multi‐graded setting. Our approach is based on the study of blow‐up algebras, including syzygies, of the ideal generated by the defining polynomials

    更新日期:2020-05-02
  • Stone duality and quasi‐orbit spaces for generalised C∗‐inclusions
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-02
    Bartosz Kosma Kwaśniewski, Ralf Meyer

    Let A be a C ∗ ‐subalgebra of the multiplier algebra M ( B ) of a C ∗ ‐algebra B . Exploiting the duality between sober spaces and spatial locales, and the adjunction between restriction and induction for ideals in A and B , we identify conditions that allow to define a quasi‐orbit space and a quasi‐orbit map for A ⊆ M ( B ) . These objects generalise classical notions for group actions. We characterise

    更新日期:2020-05-02
  • Polynomial to exponential transition in Ramsey theory
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-01
    Dhruv Mubayi; Alexander Razborov

    Given s ⩾ k ⩾ 3 , let h ( k ) ( s ) be the minimum t such that there exist arbitrarily large k ‐uniform hypergraphs H whose independence number is at most polylogarithmic in the number of vertices and in which every s vertices span at most t edges. Erdős and Hajnal conjectured (1972) that h ( k ) ( s ) can be calculated precisely using a recursive formula and Erdős offered $500 for a proof of this

    更新日期:2020-05-01
  • Anomalous Anosov flows revisited
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-01
    Thomas Barthelmé; Christian Bonatti; Andrey Gogolev; Federico Rodriguez Hertz

    This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3‐dimensional Anosov flows. We provide a dichotomy result for such flows — they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In particular, this proves

    更新日期:2020-05-01
  • On the Assouad dimension of projections
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-01
    Tuomas Orponen

    Let F ⊂ R 2 , and let dim A stand for Assouad dimension. I prove that dim A π e ( F ) ⩾ min { dim A F , 1 } for all e ∈ S 1 outside of a set of Hausdorff dimension zero. This is a strong variant of Marstrand's projection theorem for Assouad dimension, whose analogue is not true for other common notions of fractal dimension, such as Hausdorff or packing dimension.

    更新日期:2020-05-01
  • Boundary spike‐layer solutions of the singular Keller–Segel system: existence and stability
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-05-01
    Jose A. Carrillo; Jingyu Li; Zhi‐An Wang

    We explore the existence and nonlinear stability of boundary spike‐layer solutions of the Keller–Segel system with logarithmic singular sensitivity in the half space, where the physical zero‐flux and Dirichlet boundary conditions are prescribed. We first prove that, under above boundary conditions, the Keller–Segel system admits a unique boundary spike‐layer steady state where the first solution component

    更新日期:2020-05-01
  • Decomposing tournaments into paths
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-04-29
    Allan Lo, Viresh Patel, Jozef Skokan, John Talbot

    We consider a generalisation of Kelly's conjecture which is due to Alspach, Mason, and Pullman from 1976. Kelly's conjecture states that every regular tournament has an edge decomposition into Hamilton cycles, and this was proved by Kühn and Osthus for large tournaments. The conjecture of Alspach, Mason, and Pullman asks for the minimum number of paths needed in a path decomposition of a general tournament

    更新日期:2020-04-29
  • Littlewood–Richardson coefficients via mirror symmetry for cluster varieties
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-04-29
    Timothy Magee

    I prove that the full Fock–Goncharov conjecture holds for Conf 3 × ( F ℓ ∼ ) — the configuration space of triples of decorated flags in generic position. As a key ingredient of this proof, I exhibit a maximal green sequence for the quiver of the initial seed. I compute the Landau–Ginzburg potential W on Conf 3 × ( F ℓ ∼ ) ∨ associated to the partial minimal model Conf 3 × ( F ℓ ∼ ) ⊂ Conf 3 ( F ℓ ∼

    更新日期:2020-04-29
  • Sign changing solutions of Poisson's equation
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-04-29
    M. van den Berg, D. Bucur

    Let Ω be an open, possibly unbounded, set in Euclidean space R m with boundary ∂ Ω , let A be a measurable subset of Ω with measure | A | and let γ ∈ ( 0 , 1 ) . We investigate whether the solution v Ω , A , γ of − Δ v = γ 1 Ω ∖ A − ( 1 − γ ) 1 A with v = 0 on ∂ Ω changes sign. Bounds are obtained for | A | in terms of geometric characteristics of Ω (bottom of the spectrum of the Dirichlet Laplacian

    更新日期:2020-04-29
  • Homological stability for Artin monoids
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-04-29
    Rachael Boyd

    We prove that certain sequences of Artin monoids containing the braid monoid as a submonoid satisfy homological stability. When the K ( π , 1 ) conjecture holds for the associated family of Artin groups, this establishes homological stability for these groups. In particular, this recovers and extends Arnol'd's proof of stability for the Artin groups of type A , B and D .

    更新日期:2020-04-29
  • Dimension of ergodic measures projected onto self‐similar sets with overlaps
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-04-29
    Thomas Jordan; Ariel Rapaport

    For self‐similar sets on R satisfying the exponential separation condition we show that the dimension of natural projections of shift invariant ergodic measures is equal to min { 1 , h − χ } , where h and χ are the entropy and Lyapunov exponent, respectively. The proof relies on Shmerkin's recent result on the L q dimension of self‐similar measures. We also use the same method to give results on convolutions

    更新日期:2020-04-29
  • On classical solutions of the KdV equation
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-04-04
    Sergei Grudsky, Alexei Rybkin

    We show that if the initial profile q ( x ) for the Korteweg‐de Vries (KdV) equation is essentially semibounded from below and ∫ ∞ x 5 / 2 | q ( x ) | d x < ∞ , (no decay at − ∞ is required) then the KdV has a unique global classical solution given by a determinant formula. This result is best known to date.

    更新日期:2020-04-04
  • Linear correlations of multiplicative functions
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-04-04
    Lilian Matthiesen

    We prove a Green–Tao type theorem for multiplicative functions.

    更新日期:2020-04-04
  • Real Lagrangians in Calabi–Yau threefolds
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-03-20
    Hülya Argüz, Thomas Prince

    We compute the mod 2 cohomology groups of real Lagrangians in torus fibrations on Calabi–Yau threefolds constructed by Gross. To do this we study a long exact sequence introduced by Castaño‐Bernard–Matessi, which relates the cohomology of the Lagrangians to the cohomology of the Calabi–Yau. We show that the connecting homomorphism in this sequence is given by the map squaring divisor classes in the

    更新日期:2020-03-20
  • Slicing theorems and rigidity phenomena for self‐affine carpets
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-03-20
    Amir Algom

    Let F be a Bedford–McMullen carpet defined by independent exponents. We prove that dim ¯ B ( ℓ ∩ F ) ⩽ max { dim ∗ F − 1 , 0 } for all lines ℓ not parallel to the principal axes, where dim ∗ is Furstenberg's star dimension (maximal dimension of a microset). We also prove several rigidity results for incommensurable Bedford–McMullen carpets, that is, carpets F and E such that all defining exponents

    更新日期:2020-03-20
  • Polygonal Z2‐subshifts
    Proc. London Math. Soc. (IF 1.366) Pub Date : 2020-03-19
    John Franks, Bryna Kra

    Let P ⊂ Z 2 be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex v ∈ P is uniquely determined by the labeling of all other points in the polygon. We introduce a class of Z 2 ‐shift systems, the polygonal shifts, determined by such a polygon: These are shift systems such that the restriction of any x ∈ X to some polygon P has this

    更新日期:2020-03-19
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