样式: 排序: IF: - GO 导出 标记为已读
-
Signed permutohedra, delta-matroids, and beyond Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-03-17 Christopher Eur, Alex Fink, Matt Larson, Hunter Spink
We establish a connection between the algebraic geometry of the type B$B$ permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the volume and lattice point counts of type B$B$ generalized permutohedra. Applying tropical Hodge theory to a new framework of “tautological classes of delta-matroids,” modeled after certain vector bundles associated to realizable
-
Logarithmic bounds on Fujita's conjecture Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-03-15 Luca Ghidelli, Justin Lacini
Let X$X$ be a smooth complex projective variety of dimension n$n$. We prove bounds on Fujita's basepoint freeness conjecture that grow as nloglog(n)$n\operatorname{log}\operatorname{log}(n)$, where log$\operatorname{log}$ is the logarithm with natural base.
-
Bilinear sums with GL(2) coefficients and the exponent of distribution of d3 Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-03-15 Prahlad Sharma
We obtain the exponent of distribution 1/2+1/30$1/2+1/30$ for the ternary divisor function d3$d_3$ to square-free and prime power moduli, improving the previous results of Fouvry–Kowalski–Michel, Heath-Brown and Friedlander–Iwaniec. The key input is certain estimates on bilinear sums with GL(2)$GL(2)$ coefficients obtained using the delta symbol approach.
-
Liouville theorems and optimal regularity in elliptic equations Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-03-12 Giorgio Tortone
The objective of this paper is to establish a connection between the problem of optimal regularity among solutions to elliptic partial differential equations with measurable coefficients and the Liouville property at infinity. Initially, we address the two-dimensional case by proving an Alt–Caffarelli–Friedman-type monotonicity formula, enabling the proof of optimal regularity and the Liouville property
-
Tollmien–Schlichting waves in the subsonic regime Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-03-14 Nader Masmoudi, Yuxi Wang, Di Wu, Zhifei Zhang
The Tollmien–Schlichting (T-S) waves play a key role in the early stages of boundary layer transition. In a breakthrough work, Grenier, Guo, and Nguyen gave the first rigorous construction of the T-S waves of temporal mode for the incompressible fluid. Yang and Zhang recently made an important contribution by constructing the compressible T-S waves of temporal mode for certain boundary layer profiles
-
Minimal surfaces with symmetries Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-03-12 Franc Forstnerič
Let G$G$ be a finite group acting on a connected open Riemann surface X$X$ by holomorphic automorphisms and acting on a Euclidean space Rn$\mathbb {R}^n$ (n⩾3)$(n\geqslant 3)$ by orthogonal transformations. We identify a necessary and sufficient condition for the existence of a G$G$-equivariant conformal minimal immersion F:X→Rn$F:X\rightarrow \mathbb {R}^n$. We show in particular that such a map F$F$
-
Boundary current fluctuations for the half-space ASEP and six-vertex model Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-02-18 Jimmy He
We study fluctuations of the current at the boundary for the half-space asymmetric simple exclusion process (ASEP) and the height function of the half-space six-vertex model at the boundary at large times. We establish a phase transition depending on the effective density of particles at the boundary, with Gaussian symplectic ensemble (GSE) and Gaussian orthogonal ensemble (GOE) limits as well as the
-
Simple spines of homotopy 2-spheres are unique Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-02-14 Patrick Orson, Mark Powell
A locally flatly embedded 2-sphere in a compact 4-manifold X$X$ is called a spine if the inclusion map is a homotopy equivalence. A spine is called simple if the complement of the 2-sphere has abelian fundamental group. We prove that if two simple spines represent the same generator of H2(X)$H_2(X)$ then they are ambiently isotopic. In particular, the theorem applies to simple shake-slicing 2-spheres
-
On the number of high-dimensional partitions Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-02-14 Cosmin Pohoata, Dmitrii Zakharov
Let Pd(n)$P_{d}(n)$ denote the number of n×…×nd$n \times \ldots \times n \ d$-dimensional partitions with entries from {0,1,…,n}$\lbrace 0,1,\ldots,n\rbrace$. Building upon the works of Balogh–Treglown–Wagner and Noel–Scott–Sudakov, we show that when d→∞$d \rightarrow \infty$,
-
A p-adic approach to the existence of level-raising congruences Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-02-13 Jack A. Thorne
We construct level-raising congruences between p$p$-ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the nth$n\text{th}$ symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer n=1,3,⋯,25$n = 1, 3, \dots, 25$. In a future work with James Newton,
-
The Loewner–Kufarev energy and foliations by Weil–Petersson quasicircles Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-02-13 Fredrik Viklund, Yilin Wang
We study foliations by chord–arc Jordan curves of the twice punctured Riemann sphere C∖{0}$\mathbb {C} \setminus \lbrace 0\rbrace$ using the Loewner–Kufarev equation. We associate to such a foliation a function on the plane that describes the “local winding” along each leaf. Our main theorem is that this function has finite Dirichlet energy if and only if the Loewner driving measure ρ$\rho$ has finite
-
Diophantine approximation, large intersections and geodesics in negative curvature Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-02-10 Anish Ghosh, Debanjan Nandi
In this paper, we prove quantitative results about geodesic approximations to submanifolds in negatively curved spaces. Among the main tools is a new and general Jarník–Besicovitch type theorem in Diophantine approximation. Our framework allows manifolds of variable negative curvature, a variety of geometric targets, and logarithm laws as well as spiraling phenomena in both measure and dimension aspect
-
Geometry of canonical genus 4 curves Proc. London Math. Soc. (IF 1.8) Pub Date : 2024-01-15 Fatemeh Rezaee
We apply the machinery of Bridgeland stability conditions on derived categories of coherent sheaves to describe the geometry of classical moduli spaces associated with canonical genus 4 space curves via an effective control over its wall-crossing. This article provides the first description of a moduli space of Pandharipande–Thomas stable pairs that is used as an intermediate step toward the description
-
The spectrum of a twisted commutative algebra Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-12-22 Andrew Snowden
A twisted commutative algebra is (for us) a commutative Q $\mathbf {Q}$ -algebra equipped with an action of the infinite general linear group. In such algebras, the “ GL $\mathbf {GL}$ -prime” ideals assume the duties fulfilled by prime ideals in ordinary commutative algebra, and so it is crucial to understand them. Unfortunately, distinct GL $\mathbf {GL}$ -primes can have the same radical, which
-
On the existence of harmonic metrics on non-Hermitian Yang–Mills bundles Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-12-25 Changpeng Pan, Zhenghan Shen, Xi Zhang
In this paper, we study the non-Hermitian Yang–Mills (NHYM) bundles over compact Kähler manifolds. We show that the existence of harmonic metrics is equivalent to the semisimplicity of NHYM bundles, which confirms the Conjecture 8.7 in Kaledin and Verbitsky (Selecta Math. (N.S.) 4 (1998) 279–320).
-
Waring identifiability for powers of forms via degenerations Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-12-19 Alex Casarotti, Elisa Postinghel
We discuss an approach to the secant non-defectivity of the varieties parametrising k $k$ th powers of forms of degree d $d$ . It employs a Terracini-type argument along with certain degeneration arguments, some of which are based on toric geometry. This implies a result on the identifiability of the Waring decompositions of general forms of degree kd as a sum of k $k$ th powers of degree d $d$ forms
-
Birational maps with transcendental dynamical degree Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-12-19 Jason P. Bell, Jeffrey Diller, Mattias Jonsson, Holly Krieger
We give examples of birational selfmaps of Pd,d⩾3$\mathbb {P}^d, d \geqslant 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.
-
Slowly recurrent Collet–Eckmann maps with non-empty Fatou set Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-12-19 Magnus Aspenberg, Mats Bylund, Weiwei Cui
In this paper, we study rational Collet–Eckmann maps for which the Julia set is not the whole sphere and for which the critical points are recurrent at a slow rate. In families where the orders of the critical points are fixed, we prove that such maps are Lebesgue density points of hyperbolic maps. In particular, if all critical points are simple, these maps are Lebesgue density points of hyperbolic
-
Row-Hamiltonian Latin squares and Falconer varieties Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-12-19 Jack Allsop, Ian M. Wanless
A Latin square is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square L $L$ is row-Hamiltonian if the permutation induced by each pair of distinct rows of L $L$ is a full cycle permutation. Row-Hamiltonian Latin squares are equivalent to perfect 1-factorisations of complete bipartite graphs. For the first time, we exhibit a family of Latin squares that
-
Rates of mixing for the measure of maximal entropy of dispersing billiard maps Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-12-20 Mark F. Demers, Alexey Korepanov
In a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli. We show that this measure enjoys natural probabilistic properties for Hölder continuous observables, such as at least polynomial decay of correlations and the Central Limit Theorem. The results of Baladi and Demers are
-
An upper bound on the mean value of the Erdős–Hooley Delta function Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-11-09 Dimitris Koukoulopoulos, Terence Tao
The Erdős–Hooley Delta function is defined for n ∈ N $n\in \mathbb {N}$ as Δ ( n ) = sup u ∈ R # { d | n : e u < d ⩽ e u + 1 } $\Delta (n)=\sup _{u\in \mathbb {R}} \#\lbrace d|n : e^u
-
The Calkin algebra, Kazhdan's property (T), and strongly self-absorbing C∗$\mathrm{C}^*$-algebras Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-11-04 Ilijas Farah
It is well known that the relative commutant of every separable nuclear C ∗ $\mathrm{C}^*$ -subalgebra of the Calkin algebra has a unital copy of Cuntz algebra O ∞ $\mathcal {O}_\infty$ . We prove that the Calkin algebra has a separable C ∗ $\mathrm{C}^*$ -subalgebra whose relative commutant has no simple, unital, and noncommutative C ∗ $\mathrm{C}^*$ -subalgebra. On the other hand, the corona of every
-
Realizability and tameness of fusion systems Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-11-02 Carles Broto, Jesper M. Møller, Bob Oliver, Albert Ruiz
A saturated fusion system over a finite p $p$ -group S $S$ is a category whose objects are the subgroups of S $S$ and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over S $S$ is realized by a finite group G $G$ if S $S$ is a Sylow p $p$ -subgroup of G $G$ and morphisms in the category are those induced by conjugation in G $G$ . One recurrent
-
Anticyclotomic Euler systems for unitary groups Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-11-01 Andrew Graham, Syed Waqar Ali Shah
Let n ⩾ 1 $n \geqslant 1$ be an odd integer. We construct an anticyclotomic Euler system for certain cuspidal automorphic representations of unitary groups with signature ( 1 , 2 n − 1 ) $(1, 2n-1)$ .
-
Joint integrability and spectral rigidity for Anosov diffeomorphisms Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-10-25 Andrey Gogolev, Yi Shi
Let f : T d → T d $f\colon \mathbb {T}^d\rightarrow \mathbb {T}^d$ be an Anosov diffeomorphism whose linearization A ∈ GL ( d , Z ) $A\in {\rm GL}(d,\mathbb {Z})$ is irreducible. Assume that f $f$ is also absolutely partially hyperbolic where a weak stable subbundle is considered as the center subbundle. We show that if the strong stable subbundle and the unstable subbundle are jointly integrable,
-
Conjugacy of transitive SFTs minus periodic points Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-10-25 Ville Salo
It is a question of Hochman whether any two one-dimensional topologically mixing subshifts of finite type (SFTs) with the same entropy are topologically conjugate when their periodic points are removed. We give a negative answer, and, in fact, we prove the stronger result that there is a canonical correspondence between topological conjugacies of transitive SFTs and topological conjugacies between
-
Functions tiling simultaneously with two arithmetic progressions Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-10-24 Mark Mordechai Etkind, Nir Lev
We consider measurable functions f $f$ on R $\mathbb {R}$ that tile simultaneously by two arithmetic progressions α Z $\alpha \mathbb {Z}$ and β Z $\beta \mathbb {Z}$ at respective tiling levels p $p$ and q $q$ . We are interested in two main questions: what are the possible values of the tiling levels p , q $p,q$ , and what is the least possible measure of the support of f $f$ ? We obtain sharp results
-
Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell–Lang conjecture Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-10-04 Pietro Corvaja, Umberto Zannier
We offer some theorems, mainly finiteness results, for certain patterns in elliptical billiards, related to periodic trajectories; these seem to be the first finiteness results in this context. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in ( 0 , π ) $(0,\pi )$ , there are only finitely many directions for both trajectories being periodic. Another
-
L-theory of C∗$C^*$-algebras Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-10-03 Markus Land, Thomas Nikolaus, Marco Schlichting
We establish a formula for the L-theory spectrum of real C ∗ $C^*$ -algebras from which we deduce a presentation of the L-groups in terms of the topological K-groups, extending all previously known results of this kind. Along the way, we extend the integral comparison map τ : k → L $\tau \colon \mathrm{k}\rightarrow \mathrm{L}$ obtained in previous work by the first two authors to real C ∗ $C^*$ -algebras
-
2-Selmer parity for hyperelliptic curves in quadratic extensions Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-09-30 Adam Morgan
We study the 2-parity conjecture for Jacobians of hyperelliptic curves over number fields. Under some mild assumptions on their reduction, we prove the conjecture over quadratic extensions of the base field. The proof proceeds via a generalisation of a formula of Kramer and Tunnell relating local invariants of the curve, which may be of independent interest. A new feature of this generalisation is
-
An intrinsic approach to relative braid group symmetries on ı$\imath$quantum groups Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-09-29 Weiqiang Wang, Weinan Zhang
We initiate a general approach to the relative braid group symmetries on (universal) ı $\imath$ quantum groups, arising from quantum symmetric pairs of arbitrary finite types, and their modules. Our approach is built on new intertwining properties of quasi K $K$ -matrices which we develop and braid group symmetries on (Drinfeld double) quantum groups. Explicit formulas for these new symmetries on ı
-
Asymptotic enumeration of graphical regular representations Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-09-25 Binzhou Xia, Shasha Zheng
We estimate the number of graphical regular representations (GRRs) of a given group with large enough order. As a consequence, we show that almost all finite Cayley graphs have full automorphism groups ‘as small as possible’. This confirms a conjecture of Babai–Godsil–Imrich–Lovász on the proportion of GRRs, as well as a conjecture of Xu on the proportion of normal Cayley graphs, among Cayley graphs
-
An identity in the Bethe subalgebra of C[Sn]$\mathbb {C}[\mathfrak {S}_n]$ Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-09-20 Kevin Purbhoo
As part of the proof of the Bethe ansatz conjecture for the Gaudin model for gl n $\mathfrak {gl}_n$ , Mukhin, Tarasov, and Varchenko described a correspondence between inverse Wronskians of polynomials and eigenspaces of the Gaudin Hamiltonians. Notably, this correspondence afforded the first proof of the Shapiro–Shapiro conjecture. In this paper, we give an identity in the group algebra of the symmetric
-
Pointed Hopf algebras over nonabelian groups with nonsimple standard braidings Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-09-01 Iván Angiono, Simon Lentner, Guillermo Sanmarco
We construct finite-dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Lie algebra together with a Dynkin diagram automorphism. We show conversely that every finite-dimensional pointed Hopf algebra over a nonabelian group with nonsimple infinitesimal braiding of rank at least 4 is of this form
-
Lax monoidal adjunctions, two-variable fibrations and the calculus of mates Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-08-24 Rune Haugseng, Fabian Hebestreit, Sil Linskens, Joost Nuiten
We provide a calculus of mates for functors to the ∞ $\infty$ -category of ∞ $\infty$ -categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformations correspond to maps of (co)cartesian fibrations that do not necessarily preserve (co)cartesian edges. As a sample application, we obtain an equivalence between lax symmetric monoidal structures on right adjoint
-
Localizations for quiver Hecke algebras II Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-08-22 Masaki Kashiwara, Myungho Kim, Se-jin Oh, Euiyong Park
We prove that the localization C ∼ w $ \widetilde{\mathcal {C}}_w$ of the monoidal category C w $ \mathcal {C}_w$ is rigid, and the category C w , v $ \mathcal {C}_{w,v}$ admits a localization via a real commuting family of central objects. For a quiver Hecke algebra R $R$ and an element w $w$ in the Weyl group, the subcategory C w $ \mathcal {C}_w$ of the category R - gmod $R\text{-}\mathrm{gmod}$
-
The polynomials X2+(Y2+1)2$X^2+(Y^2+1)^2$ and X2+(Y3+Z3)2$X^{2} + (Y^3+Z^3)^2$ also capture their primes Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-08-19 Jori Merikoski
We show that there are infinitely many primes of the form X 2 + ( Y 2 + 1 ) 2 $X^2+(Y^2+1)^2$ and X 2 + ( Y 3 + Z 3 ) 2 $X^2+(Y^3+Z^3)^2$ . This extends the work of Friedlander and Iwaniec showing that there are infinitely many primes of the form X 2 + Y 4 $X^2+Y^4$ . More precisely, Friedlander and Iwaniec obtained an asymptotic formula for the number of primes of this form. For the sequences X 2
-
Arithmetic and metric aspects of open de Rham spaces Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-08-16 Tamás Hausel, Michael Lennox Wong, Dimitri Wyss
In this paper, we determine the motivic class — in particular, the weight polynomial and conjecturally the Poincaré polynomial — of the open de Rham space, defined and studied by Boalch, of certain moduli spaces of irregular meromorphic connections on the trivial rank n $n$ bundle on P 1 $\mathbb {P}^1$ . The computation is by motivic Fourier transform. We show that the result satisfies the purity
-
Expansion of the fundamental solution of a second-order elliptic operator with analytic coefficients Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-08-10 Federico Franceschini, Federico Glaudo
Let L $L$ be a second-order elliptic operator with analytic coefficients defined in B 1 ⊆ R n $B_1\subseteq \mathbb {R}^n$ . We construct explicitly and canonically a fundamental solution for the operator, that is, a function u : B r 0 → R $u:B_{r_0}\rightarrow \mathbb {R}$ such that L u = δ 0 $Lu=\delta _0$ . As a consequence of our construction, we obtain an expansion of the fundamental solution
-
Associahedra for finite-type cluster algebras and minimal relations between g-vectors Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-08-09 Arnau Padrol, Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon
We show that the mesh mutations are the minimal relations among the g ${\bm{g}}$ -vectors with respect to any initial seed in any finite-type cluster algebra. We then use this algebraic result to derive geometric properties of the g ${\bm{g}}$ -vector fan: we show that the space of all its polytopal realizations is a simplicial cone, and we then observe that this property implies that all its realizations
-
Local constancy of pro-unipotent Kummer maps Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-08-03 Luke Alexander Betts
It is a theorem of Kim–Tamagawa that the Q ℓ ${\mathbb {Q}}_\ell$ -pro-unipotent Kummer map associated to a smooth projective curve Y $Y$ over a finite extension of Q p ${\mathbb {Q}}_p$ is locally constant when ℓ ≠ p $\ell \ne p$ . This paper establishes two generalisations of this result. First, we extend the Kim–Tamagawa theorem to the case that Y $Y$ is a smooth variety of any dimension. Second
-
Irreducibility of periodic curves in cubic polynomial moduli space Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-07-28 Matthieu Arfeux, Jan Kiwi
In the moduli space of complex cubic polynomials with a marked critical point, given any p ⩾ 1 $p \geqslant 1$ , we prove that the loci formed by polynomials with the marked critical point periodic of period p $p$ is an irreducible curve. Thus, answering a question posed by Milnor in the 1990s.
-
Quantitative bounds on vortex fluctuations in 2d$2d$ Coulomb gas and maximum of the integer-valued Gaussian free field Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-07-23 Christophe Garban, Avelio Sepúlveda
In this paper, we study the influence of the vortices on the fluctuations of 2 d $2d$ systems such as the Coulomb gas, the Villain model, or the integer-valued Gaussian free field (GFF). In the case of the 2 d $2d$ Villain model, we prove that the fluctuations induced by the vortices are at least of the same order of magnitude as the ones produced by the spin wave. We obtain the following quantitative
-
On sufficient conditions for spanning structures in dense graphs Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-07-21 Richard Lang, Nicolás Sanhueza-Matamala
We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and, excluding the bipartite case, contains an odd cycle. A simple consequence of the Robust Expander Theorem of Kühn, Osthus and Treglown tells us that any large enough graph
-
On the parity conjecture for abelian surfaces Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-07-19 Vladimir Dokchitser, Céline Maistret
Assuming finiteness of the Tate–Shafarevich group, we prove that the Birch–Swinnerton–Dyer conjecture correctly predicts the parity of the rank of semistable principally polarised abelian surfaces. If the surface in question is the Jacobian of a curve, we require that the curve has good ordinary reduction at 2-adic places.
-
The 2-fusion system of the Monster Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-07-19 Michael Aschbacher
This paper is part of an effort to determine a certain class of simple 2-fusion systems, and to use that result to simplify the proof of the classification of the finite simple groups. The main theorem proves that the 2-fusion system of the Monster is the unique simple system with a fully centralized involution whose centralizer is the fusion system of the universal covering group of the Baby Monster
-
Counting and boundary limit theorems for representations of Gromov-hyperbolic groups Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-07-17 Stephen Cantrell, Cagri Sert
Given a Gromov-hyperbolic group G $G$ endowed with a finite symmetric generating set, we study the statistics of counting measures on the spheres of the associated Cayley graph under linear representations of G $G$ . More generally, we obtain a weak law of large numbers for subadditive functions, echoing the classical Fekete lemma. For strongly irreducible and proximal representations, we prove a counting
-
A type I conjecture and boundary representations of hyperbolic groups Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-07-02 Pierre-Emmanuel Caprace, Mehrdad Kalantar, Nicolas Monod
We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group G $G$ associated with nonsingular G $G$ -spaces. We deduce that any two boundary representations of a hyperbolic locally compact group are weakly equivalent. We also show that nonamenable hyperbolic locally compact groups with a cocompact amenable subgroup are characterized
-
Multiplicative functions in short arithmetic progressions Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-06-25 Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen
We study for bounded multiplicative functions f $f$ sums of the form
-
Determination of a class of permutation quadrinomials Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-06-20 Zhiguo Ding, Michael E. Zieve
We determine all permutation polynomials over F q 2 $\mathbb {F}_{q^2}$ of the form X r A ( X q − 1 ) $X^r A(X^{q-1})$ where, for some Q $Q$ that is a power of the characteristic of F q $\mathbb {F}_q$ , we have r ≡ Q + 1 ( mod q + 1 ) $r\equiv Q+1\pmod {q+1}$ and all terms of A ( X ) $A(X)$ have degrees in { 0 , 1 , Q , Q + 1 } $\lbrace 0,1,Q,Q+1\rbrace$ . We use this classification to resolve eight
-
Moments of moments of primes in arithmetic progressions Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-06-18 R. de la Bretèche, D. Fiorilli
We establish unconditional Ω $\Omega$ -results for all weighted even moments of primes in arithmetic progressions. We also study the moments of these moments and establish lower bounds under the Generalized Riemann Hypothesis (GRH). Finally, under GRH and the Linear Independence Hypothesis (LI), we prove an asymptotic for all moments of the associated limiting distribution, which, in turn, indicates
-
Local types of (Γ,G)$(\Gamma ,G)$-bundles and parahoric group schemes Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-06-14 Chiara Damiolini, Jiuzu Hong
Let G $G$ be a simple algebraic group over an algebraically closed field k $k$ . Let Γ $\Gamma$ be a finite group acting on G $G$ . We classify and compute the local types of ( Γ , G ) $(\Gamma , G)$ -bundles on a smooth projective Γ $\Gamma$ -curve in terms of the first nonabelian group cohomology of the stabilizer groups at the tamely ramified points with coefficients in G $G$ . When char ( k ) =
-
Affine deformations of quasi-divisible convex cones Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-06-06 Xin Nie, Andrea Seppi
We study subgroups of SL ( 3 , R ) ⋉ R 3 $\mathrm{SL}(3,\mathbb {R})\ltimes \mathbb {R}^3$ obtained by adding a translation part to the holonomy of a finite-volume convex projective surface. Under a natural condition on the translations added to the peripheral parabolic elements, we show that the affine action of the group on R 3 $\mathbb {R}^3$ has convex domains of discontinuity which are regular
-
Massey products and elliptic curves Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-06-01 Frauke M. Bleher, Ted Chinburg, Jean Gillibert
We study the vanishing of Massey products of order at least 3 for absolutely irreducible smooth projective curves over a field with coefficients in Z / ℓ $\mathbb {Z}/\ell$ . We mainly focus on elliptic curves, for which we obtain a complete characterization of when triple Massey products do not vanish.
-
Transversals in quasirandom latin squares Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-05-31 Sean Eberhard, Freddie Manners, Rudi Mrazović
A transversal in an n × n $n \times n$ latin square is a collection of n $n$ entries not repeating any row, column, or symbol. Kwan showed that almost every n × n $n \times n$ latin square has ( 1 + o ( 1 ) ) n / e 2 n $\bigl ((1 + o(1)) n / e^2\bigr )^n$ transversals as n → ∞ $n \rightarrow \infty$ . Using a loose variant of the circle method we sharpen this to ( e − 1 / 2 + o ( 1 ) ) n ! 2 / n n
-
Applications of the algebraic geometry of the Putman–Wieland conjecture Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-05-29 Aaron Landesman, Daniel Litt
We give two applications of our prior work toward the Putman–Wieland conjecture. First, we deduce a strengthening of a result of Marković–Tošić on virtual mapping class group actions on the homology of covers. Second, let g ⩾ 2 $g\geqslant 2$ and let Σ g ′ , n ′ → Σ g , n $\Sigma _{g^{\prime },n^{\prime }}\rightarrow \Sigma _{g, n}$ be a finite H $H$ -cover of topological surfaces. We show the virtual
-
Regularity of viscosity solutions of the σk$\sigma _k$-Loewner–Nirenberg problem Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-05-24 YanYan Li, Luc Nguyen, Jingang Xiong
We study the regularity of the viscosity solution u $u$ of the σ k $\sigma _k$ -Loewner–Nirenberg problem on a bounded smooth domain Ω ⊂ R n $\Omega \subset \mathbb {R}^n$ for k ⩾ 2 $k \geqslant 2$ . It was known that u $u$ is locally Lipschitz in Ω $\Omega$ . We prove that, with d $d$ being the distance function to ∂ Ω $\partial \Omega$ and δ > 0 $\delta > 0$ sufficiently small, u $u$ is smooth in
-
The elliptic sieve and Brauer groups Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-05-11 Subham Bhakta, Daniel Loughran, Simon L. Rydin Myerson, Masahiro Nakahara
A theorem of Serre states that almost all plane conics over Q ${{\mathbb {Q}}}$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve for elliptic curves. We also give more general results for specialisations of Brauer groups, which yields applications to norm form equations
-
The trace of the affine Hecke category Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-04-30 Eugene Gorsky, Andrei Neguț
We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an “affine” version of the construction of Gorsky et al. (Int. Math. Res. Not. IMRN 2022 (2022) 11304–11400). Explicitly, we show that the aforementioned trace is generated by the objects E d = Tr ( Y 1 d 1 ⋯ Y n d n T 1 ⋯ T n − 1 ) $E_{\mathbf {d}} = {\rm Tr}(Y_1^{d_1} \dots Y_n^{d_n} T_1
-
Square function estimates and local smoothing for Fourier integral operators Proc. London Math. Soc. (IF 1.8) Pub Date : 2023-04-24 Chuanwei Gao, Bochen Liu, Changxing Miao, Yakun Xi
We prove a variable coefficient version of the square function estimate of Guth–Wang–Zhang. By a classical argument of Mockenhaupt–Seeger–Sogge, it implies the full range of sharp local smoothing estimates for 2 + 1 $2+1$ -dimensional Fourier integral operators satisfying the cinematic curvature condition. In particular, the local smoothing conjecture for wave equations on compact Riemannian surfaces