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Virtual χ−y‐genera of Quot schemes on surfaces J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-04-15 Woonam Lim
This paper studies the virtual χ − y ‐genera of Grothendieck's Quot schemes on surfaces, thus refining the calculations of the virtual Euler characteristics by Oprea–Pandharipande. We first prove a structural result expressing the equivariant virtual χ − y ‐genera of Quot schemes universally in terms of the Seiberg–Witten invariants. The formula is simpler for curve classes of Seiberg–Witten length
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On CM points away from the Torelli locus J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-04-15 Ke Chen, Xin Lu, Kang Zuo
In this paper we prove that certain points in the Hecke orbit of a CM point in the Siegel modular variety do not lie in the open Torelli locus under suitable conditions on the field of definition and the CM factors that arise in the corresponding CM abelian variety. The proof is a combination of properties of stable Faltings height and known cases of the Sato–Tate equidistribution, and is motivated
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Infinity‐operads and Day convolution in Goodwillie calculus J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-04-14 Michael Ching
We prove two theorems about Goodwillie calculus and use those theorems to describe new models for Goodwillie derivatives of functors between pointed compactly generated ∞ ‐categories. The first theorem says that the construction of higher derivatives for spectrum‐valued functors is a Day convolution of copies of the first derivative construction. The second theorem says that the derivatives of any
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On the structure of double complexes J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-03-25 Jonas Stelzig
We study consequences and applications of the folklore statement that every double complex over a field decomposes into so‐called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences easy to understand. We describe a notion of ‘universal’ quasi‐isomorphism and the behaviour of the decomposition under tensor product and compute the Grothendieck
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Functional inequalities for the heat flow on time‐dependent metric measure spaces J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-03-18 Eva Kopfer, Karl‐Theodor Sturm
We prove that synthetic lower Ricci bounds for metric measure spaces — both in the sense of Bakry–Émery and in the sense of Lott–Sturm–Villani — can be characterized by various functional inequalities including local Poincaré inequalities, local logarithmic Sobolev inequalities, dimension independent Harnack inequality, and logarithmic Harnack inequality.
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On the small rigid body limit in 3D incompressible flows J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-03-02 Jiao He, Dragoş Iftimie
We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space R 3 . The motion of the fluid is modeled by the Navier–Stokes equations, whereas the motion of the rigid body is described by the conservation law of linear and angular momentum. Under the assumption that the diameter of the rigid body tends to zero and that the density of the rigid body goes
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Abstract crystals for quantum Borcherds–Bozec algebras J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-03-02 Zhaobing Fan, Seok‐Jin Kang, Young Rock Kim, Bolun Tong
In this paper, we develop the theory of abstract crystals for quantum Borcherds–Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crystal embedding theorem and provide a characterization of B ( ∞ ) and B ( λ ) as its application, where B ( ∞ ) and B ( λ ) are the crystals of the negative half part of the quantum Borcherds–Bozec algebra U q ( g ) and its
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The generality of a section of a curve J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-03-01 Eric Larson
This paper considers the following fundamental problem about intersections in projective space: When is the intersection of a (varying) curve with a (fixed) hypersurface a general set of points on the hypersurface?
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Ubiquity of entropies of intermediate factors J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-02-25 Kevin McGoff, Ronnie Pavlov
We consider topological dynamical systems ( X , T ) , where X is a compact metrizable space and T denotes an action of a countable amenable group G on X by homeomorphisms. For two such systems ( X , T ) and ( Y , S ) and a factor map π : X → Y , an intermediate factor is a topological dynamical system ( Z , R ) for which π can be written as a composition of factor maps ψ : X → Z and φ : Z → Y . In
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Estimates of Dirichlet heat kernels for unimodal Lévy processes with low intensity of small jumps J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-02-23 Soobin Cho, Jaehoon Kang, Panki Kim
In this paper, we study transition density functions for pure jump unimodal Lévy processes killed upon leaving an open set D . Under some mild assumptions on the Lévy density, we establish two‐sided Dirichlet heat kernel estimates when the open set D is C 1 , 1 . Our result covers the case that the Lévy densities of unimodal Lévy processes are regularly varying functions whose indices are equal to
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Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-02-22 Dohyun Kwon, Alpár Richárd Mészáros
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in particular on gradient flows in the space of probability measures equipped with the distance arising in the Monge–Kantorovich optimal transport problem. The associated
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Deformed Hermitian Yang–Mills connections, extended gauge group and scalar curvature J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-02-21 Enrico Schlitzer, Jacopo Stoppa
The deformed Hermitian Yang‐Mills (dHYM) equation is a special Lagrangian type condition in complex geometry. It requires the complex analogue of the Lagrangian phase, defined for Chern connections on holomorphic line bundles using a background Kähler metric, to be constant. In this paper, we introduce and study dHYM equations with variable Kähler metric. These are coupled equations involving both
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Affine diffeomorphism groups are undistorted J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-02-20 Robert Tang
The affine diffeomorphism group Aff ( S , q ) of a half‐translation surface ( S , q ) comprise the self‐diffeomorphisms with constant differential away from the singularities. This group coincides with the stabiliser of the associated Teichmüller disc under the action of the mapping class group on Teichmüller space. We prove that any finitely generated subgroup of Aff ( S , q ) is undistorted in the
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Equivariant stable categories for incomplete systems of transfers J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-02-07 Andrew J. Blumberg, Michael A. Hill
In this paper, we construct incomplete versions of the equivariant stable category; that is, equivariant stabilizations of the category of G ‐spaces with respect to incomplete systems of transfers encoded by an N ∞ operad O . These categories are built from the categories of O ‐algebras in G ‐spaces. Using this operadic formulation, we establish incomplete versions of the usual structural properties
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On the formality of the little disks operad in positive characteristic J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-02-02 Pedro Boavida de Brito, Geoffroy Horel
Using a variant of the Boardman–Vogt tensor product, we construct an action of the Grothendieck–Teichmüller group on the completion of the little n ‐disks operad E n . This action is used to establish a partial formality theorem for E n with mod p coefficients and to give a new proof of the formality theorem in characteristic zero.
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On the determination of nonlinear terms appearing in semilinear hyperbolic equations J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-22 Yavar Kian
We consider the inverse problem of determining the shape of a general nonlinear term appearing in a semilinear hyperbolic equation on a Riemannian manifold with boundary ( M , g ) of dimension n = 2 , 3 . We prove results of unique recovery of the nonlinear term F ( t , x , u ) , appearing in the equation ∂ t 2 u − Δ g u + F ( t , x , u ) = 0 on ( 0 , T ) × M with T > 0 , from partial knowledge of
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Instantons and some concordance invariants of knots J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-22 P. B. Kronheimer, T. S. Mrowka
Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1‐parameter family of homomorphisms f r , from the knot concordance group to R . Prima facie, these concordance invariants have the potential to provide independent bounds on the genus and number of double points
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Concentration phenomena for the fractional Q‐curvature equation in dimension 3 and fractional Poisson formulas J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-21 Azahara DelaTorre, María del Mar González, Ali Hyder, Luca Martinazzi
We study the compactness properties of metrics of prescribed fractional Q ‐curvature of order 3 in R 3 . We will use an approach inspired from conformal geometry, seeing a metric on a subset of R 3 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
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The automorphism group and limit set of a bounded domain II: the convex case J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-21 Andrew Zimmer
For convex domains with C 1 , ε boundary we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different closed complex faces of the boundary, then the automorphism group has finitely many components and the connected component of the identity is the almost direct product of a compact group and a non‐compact connected simple Lie group
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Stark–Heegner cycles attached to Bianchi modular forms J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-20 Guhan Venkat, Chris Williams
Let f be a Bianchi modular form, that is, an automorphic form for GL ( 2 ) over an imaginary quadratic field F , and let p be a prime of F at which f is new. Let K be a quadratic extension of F , and L ( f / K , s ) the L ‐function of the base‐change of f to K . Under certain hypotheses on f and K , the functional equation of L ( f / K , s ) ensures that it vanishes at the central point. The Bloch–Kato
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Schauder theorems for a class of (pseudo‐)differential operators on finite‐ and infinite‐dimensional state spaces J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-19 Alessandra Lunardi, Michael Röckner
We prove maximal regularity results in Hölder and Zygmund spaces for linear stationary and evolution equations driven by a class of differential and pseudo‐differential operators L , both in finite and in infinite dimension. The assumptions are given in terms of the semigroup generated by L . We cover the cases of fractional Laplacians and Ornstein–Uhlenbeck operators with fractional diffusion in finite
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Tangle addition and the knots‐quivers correspondence J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-18 Marko Stošić, Paul Wedrich
We prove that the generating functions for the one row/column colored HOMFLY‐PT invariants of arborescent links are specializations of the generating functions of the motivic Donaldson–Thomas invariants of appropriate quivers that we naturally associate with these links. Our approach extends the previously established tangles‐quivers correspondence for rational tangles to algebraic tangles by developing
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Geometry of weighted Lorentz–Finsler manifolds I: singularity theorems J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-18 Yufeng Lu, Ettore Minguzzi, Shin‐ichi Ohta
We develop the theory of weighted Ricci curvature in a weighted Lorentz–Finsler framework and extend the classical singularity theorems of general relativity. In order to reach this result, we generalize the Jacobi, Riccati and Raychaudhuri equations to weighted Finsler spacetimes and study their implications for the existence of conjugate points along causal geodesics. We also show a weighted Lorentz–Finsler
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The Kodaira dimension of some moduli spaces of elliptic K3 surfaces J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-18 Mauro Fortuna, Giacomo Mezzedimi
We study the moduli spaces of elliptic K3 surfaces of Picard number at least 3, that is, U ⊕ ⟨ − 2 k ⟩ ‐polarized K3 surfaces. Such moduli spaces are proved to be of general type for k ⩾ 220 . The proof relies on the low‐weight cusp form trick developed by Gritsenko, Hulek and Sankaran. Furthermore, explicit geometric constructions of some elliptic K3 surfaces lead to the unirationality of these moduli
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Quasi‐geodesics in Out(Fn) and their shadows in sub‐factors J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-18 Yulan Qing, Kasra Rafi
We study the behaviour of quasi‐geodesics in Out ( F n ) . Given an element ϕ in Out ( F n ) , there are several natural paths connecting the origin to ϕ in Out ( F n ) ; for example, paths given by Stallings' folding algorithm and paths induced by the shadow of greedy folding paths in Outer Space. We show that none of these paths is, in general, a quasi‐geodesic in Out ( F n ) . In fact, in contrast
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AF‐embeddability for Lie groups with T1 primitive ideal spaces J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-14 Ingrid Beltiţă, Daniel Beltiţă
We study simply connected Lie groups G for which the hull‐kernel topology of the primitive ideal space Prim ( G ) of the group C ∗ ‐algebra C ∗ ( G ) is T 1 , that is, the finite subsets of Prim ( G ) are closed. Thus, we prove that C ∗ ( G ) is AF‐embeddable. To this end, we show that if G is solvable and its action on the centre of [ G , G ] has at least one imaginary weight, then Prim ( G ) has
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Strengthened inequalities for the mean width and the ℓ‐norm J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-13 Károly J. Böröczky, Ferenc Fodor, Daniel Hug
Barthe proved that the regular simplex maximizes the mean width of convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball; or equivalently, the regular simplex maximizes the ℓ ‐norm of convex bodies whose Löwner ellipsoid (minimal volume ellipsoid containing the body) is the Euclidean unit ball. Schmuckenschläger verified the reverse statement;
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The Strong Maximal Rank conjecture and higher rank Brill–Noether theory J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-13 Ethan Cotterill, Adrián Alonso Gonzalo, Naizhen Zhang
In this paper, we compute the cohomology class of certain ‘special maximal‐rank loci’ originally defined by Aprodu and Farkas. By showing that such classes are non‐zero, we are able to verify the non‐emptiness portion of the Strong Maximal Rank Conjecture in a wide range of cases. As an application, we obtain new evidence for the existence portion of a well‐known conjecture due to Bertram, Feinberg
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Homogenization of random convolution energies J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-12 Andrea Braides, Andrey Piatnitski
We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity, we prove that the Γ ‐limit of such energy is almost surely a deterministic quadratic Dirichlet‐type integral functional, whose integrand can be characterized through an asymptotic formula. The proof of this characterization relies
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Optimization results for the higher eigenvalues of the p‐Laplacian associated with sign‐changing capacitary measures J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-12 Marco Degiovanni, Dario Mazzoleni
In this paper we prove the existence of an optimal set for the minimization of the k th variational eigenvalue of the p ‐Laplacian among p ‐quasi open sets of fixed measure included in a box of finite measure. An analogous existence result is obtained for eigenvalues of the p ‐Laplacian associated with Schrödinger potentials. In order to deal with these nonlinear shape optimization problems, we develop
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On the L‐invariant of the adjoint of a weight one modular form J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-12 Marti Roset, Victor Rotger, Vinayak Vatsal
The purpose of this article is proving the equality of two natural L ‐invariants attached to the adjoint representation of a weight one cusp form, each defined by purely analytic, respectively, algebraic means. The proof departs from Greenberg's definition of the algebraic L ‐invariant as a universal norm of a canonical Z p ‐extension of Q p associated to the representation. We relate it to a certain
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C1,1 regularity of geodesics of singular Kähler metrics J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-09 Jianchun Chu, Nicholas McCleerey
We show the optimal C 1 , 1 regularity of geodesics in nef and big cohomology class on Kähler manifolds away from the non‐Kähler locus, assuming sufficiently regular initial data. As a special case, we prove the C 1 , 1 regularity of geodesics of Kähler metrics on compact Kähler varieties away from the singular locus. Our main novelty is an improved boundary estimate for the complex Monge–Ampère equation
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Oscillating wandering domains for functions with escaping singular values J. Lond. Math. Soc. (IF 1.121) Pub Date : 2021-01-09 Kirill Lazebnik
We construct a transcendental entire f : C → C such that (1) f has bounded singular set, (2) f has a wandering domain, and (3) each singular value of f escapes to infinity under iteration by f .
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On arithmetic sums of fractal sets in Rd J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-29 De‐Jun Feng, Yu‐Feng Wu
A compact set E ⊂ R d is said to be arithmetically thick if there exists a positive integer n so that the n ‐fold arithmetic sum of E has non‐empty interior. We prove the arithmetic thickness of E , if E is uniformly non‐flat, in the sense that there exists ε 0 > 0 such that for x ∈ E and 0 < r ⩽ diam ( E ) , E ∩ B ( x , r ) never stays ε 0 r ‐close to a hyperplane in R d . Moreover, we prove the arithmetic
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The size‐Ramsey number of powers of bounded degree trees J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-27 Sören Berger, Yoshiharu Kohayakawa, Giulia Satiko Maesaka, Taísa Martins, Walner Mendonça, Guilherme Oliveira Mota, Olaf Parczyk
Given a positive integer s , the s ‐colour size‐Ramsey number of a graph H is the smallest integer m such that there exists a graph G with m edges with the property that, in any colouring of E ( G ) with s colours, there is a monochromatic copy of H . We prove that, for any positive integers k and s , the s ‐colour size‐Ramsey number of the k th power of any n ‐vertex bounded degree tree is linear
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The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-16 Sebastian Casalaina‐Martin, Zheng Zhang
We study the moduli space of pairs consisting of a smooth cubic surface and a smooth hyperplane section, via a Hodge theoretic period map due to Laza, Pearlstein, and the second‐named author. The construction associates to such a pair a so‐called Eckardt cubic threefold, admitting an involution, and the period map sends the pair to the anti‐invariant part of the intermediate Jacobian of this cubic
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Real Springer fibers and odd arc algebras J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-11 Jens Niklas Eberhardt, Grégoire Naisse, Arik Wilbert
We give a topological description of the two‐row Springer fiber over the real numbers. We show its cohomology ring coincides with the oddification of the cohomology ring of the complex Springer fiber introduced by Lauda–Russell. We also realize Ozsváth–Rasmussen–Szabó's odd TQFT from pullbacks and exceptional pushforwards along inclusion and projection maps between hypertori. Using these results, we
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Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-10 Marco Aymone, Winston Heap, Jing Zhao
We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high moments of this object. Using these we determine the likely maximum of T log T independently sampled copies of our sum and find that this is in agreement with a conjecture of Farmer–Gonek–Hughes on the maximum of the Riemann
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Sparse Kneser graphs are Hamiltonian J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-10 Torsten Mütze, Jerri Nummenpalo, Bartosz Walczak
For integers k ⩾ 1 and n ⩾ 2 k + 1 , the Kneser graph K ( n , k ) is the graph whose vertices are the k ‐element subsets of { 1 , … , n } and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K ( 2 k + 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
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Delayed blow‐up for chemotaxis models with local sensing J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-10 Martin Burger, Philippe Laurençot, Ariane Trescases
The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller–Segel model. The model we study has the same entropy as the minimal Keller–Segel model, but a different dynamics to minimize this entropy. Consequently, the conditions on the mass for the existence of stationary solutions or blow‐up
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Compatible Poisson brackets associated with 2‐splittings and Poisson commutative subalgebras of S(g) J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-07 Dmitri I. Panyushev, Oksana S. Yakimova
Let S ( g ) be the symmetric algebra of a reductive Lie algebra g equipped with the standard Poisson structure. If C ⊂ S ( g ) is a Poisson‐commutative subalgebra, then tr . deg C ⩽ b ( g ) , where b ( g ) = ( dim g + rk g ) / 2 . We present a method for constructing the Poisson‐commutative subalgebra Z ⟨ h , r ⟩ of transcendence degree b ( g ) via a vector space decomposition g = h ⊕ r into a sum
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Higher genus relative Gromov–Witten theory and double ramification cycles J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-06 H. Fan, L. Wu, F. You
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.
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On the monoidal center of Deligne's category Re̲p(St) J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-04 Johannes Flake, Robert Laugwitz
We explicitly compute a monoidal subcategory of the monoidal center of Deligne's interpolation category Re ̲ p ( S t ) , for t not necessarily a natural number, and we show that this subcategory is a ribbon category. For t = n , a natural number, there exists a functor onto the braided monoidal category of modules over the Drinfeld double of S n which is essentially surjective and full. Hence the new
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Nonlinear stability of phase transition steady states to a hyperbolic–parabolic system modeling vascular networks J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-02 Guangyi Hong, Hongyun Peng, Zhi‐An Wang, Changjiang Zhu
This paper is concerned with the existence and stability of phase transition steady states to a quasi‐linear hyperbolic–parabolic system of chemotactic aggregation, which was proposed in [Ambrosi, Bussolino and Preziosi, J. Theoret. Med. 6 (2005) 1–19; Gamba et al., Phys. Rev. Lett. 90 (2003) 118101.] to describe the coherent vascular network formation observed in vitro experiment. Considering the
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The double point formula with isolated singularities and canonical embeddings J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-10-07 Fabrizio Catanese, Keiji Oguiso
Motivated by the embedding problem of canonical models in small codimension, we extend Severi's double point formula to the case of surfaces with rational double points, and we give more general double point formulae for varieties with isolated singularities. A concrete application is for surfaces with geometric genus p g = 5 : the canonical model is embedded in P 4 if and only if we have a complete
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Open and discrete maps with piecewise linear branch set images are piecewise linear maps J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-02 Rami Luisto, Eden Prywes
The image of the branch set of a piecewise linear (PL)‐branched cover between PL n ‐manifolds is a simplicial ( n − 2 ) ‐complex. We demonstrate that the reverse implication also holds: an open and discrete map f : S n → S n with the image of the branch set contained in a simplicial ( n − 2 ) ‐complex is equivalent up to homeomorphism to a PL‐branched cover.
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Infinite families of hyperbolic 3‐manifolds with finite‐dimensional skein modules J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-01 Renaud Detcherry
The Kauffman bracket skein module K ( M ) of a 3‐manifold M is the quotient of the Q ( A ) ‐vector space spanned by isotopy classes of links in M by the Kauffman relations. A conjecture of Witten states that if M is closed, then K ( M ) is finite dimensional. We introduce a version of this conjecture for manifolds with boundary and prove a stability property for generic Dehn filling of knots. As a
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Orders of units in integral group rings and blocks of defect 1 J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-12-01 Mauricio Caicedo, Leo Margolis
We show that if a Sylow p ‐subgroup of a finite group G is of order p , then the normalized unit group of the integral group ring of G contains a normalized unit of order p q if and only if G contains an element of order p q , where q is any prime. We use this result to answer the Prime Graph Question for most sporadic simple groups and some simple groups of Lie type, including seven new infinite series'
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Nondiscrete parabolic characters of the free group F2: supergroup density and Nielsen classes in the complement of the Riley slice J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-29 Gaven J. Martin
A parabolic representation of the free group F 2 is one in which the images of both generators are parabolic elements of P S L ( 2 , C ) . Roughly the Riley slice is an open subset R ⊂ C which is a model for the parabolic, discrete and faithful characters of F 2 . The complement of the closure of the Riley slice is a bounded Jordan domain within which there are isolated points, accumulating only at
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On singularity properties of convolutions of algebraic morphisms ‐ the general case J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-29 Itay Glazer, Yotam I. Hendel
Let K be a field of characteristic zero, X and Y be smooth K ‐varieties, and let G be an algebraic K ‐group. Given two algebraic morphisms φ : X → G and ψ : Y → G , we define their convolution φ ∗ ψ : X × Y → G by φ ∗ ψ ( x , y ) = φ ( x ) · ψ ( y ) . We then show that this operation yields morphisms with improved smoothness properties. More precisely, we show that for any morphism φ : X → G which
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Resolutions of standard modules over KLR algebras of type A J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-30 Doeke Buursma, Alexander Kleshchev, David J. Steinberg
Khovanov–Lauda–Rouquier algebras R θ of finite Lie type are affine quasi‐hereditary with standard modules Δ ( π ) labeled by Kostant partitions π of θ . In type A , we construct explicit projective resolutions of standard modules Δ ( π ) .
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Synchronicity phenomenon in cluster patterns J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-29 Tomoki Nakanishi
It has been known that several objects such as cluster variables, coefficients, seeds, and Y ‐seeds in different cluster patterns with common exchange matrices share the same periodicity under mutations. We call it synchronicity phenomenon in cluster patterns. In this expository note we explain the mechanism of synchronicity based on several fundamental results on cluster algebra theory such as separation
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Some new results in random matrices over finite fields J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-26 Kyle Luh, Sean Meehan, Hoi H. Nguyen
In this note, we give various characterizations of random walks with possibly different steps that have relatively large discrepancy from the uniform distribution modulo a prime p , and use these results to study the distribution of the rank of random matrices over F p and the equi‐distribution behavior of normal vectors of random hyperplanes. We also study the probability that a random square matrix
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Constructing convex projective 3‐manifolds with generalized cusps J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-24 Samuel A. Ballas
We prove that non‐compact finite volume hyperbolic 3‐manifolds that satisfy a mild cohomological condition (infinitesimal rigidity) admit a family of properly convex deformations of their complete hyperbolic structure where the ends become generalized cusps of type 1 or type 2. We also discuss methods for controlling which types of cusps occur. Using these methods we produce the first known example
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On affine invariant and local Loomis–Whitney type inequalities J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-24 David Alonso‐Gutiérrez, Julio Bernués, Silouanos Brazitikos, Anthony Carbery
We prove various extensions of the Loomis–Whitney inequality and its dual, where the subspaces on which the projections (or sections) are considered are either spanned by vectors w i of a not necessarily orthonormal basis of R n , or their orthogonal complements. In order to prove such inequalities, we estimate the constant in the Brascamp–Lieb inequality in terms of the vectors w i . Restricted and
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On the counting problem in inverse Littlewood–Offord theory J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-23 Asaf Ferber, Vishesh Jain, Kyle Luh, Wojciech Samotij
Let ε 1 , … , ε n be independent and identically distributed Rademacher random variables taking values ± 1 with probability 1 / 2 each. Given an integer vector a = ( a 1 , … , a n ) , its concentration probability is the quantity ρ ( a ) : = sup x ∈ Z Pr ( ε 1 a 1 + ⋯ + ε n a n = x ) . The Littlewood–Offord problem asks for bounds on ρ ( a ) under various hypotheses on a , whereas the inverse Littlewood–Offord
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Almost everywhere convergence of Bochner–Riesz means on Heisenberg‐type groups J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-23 Adam D. Horwich, Alessio Martini
We prove an almost everywhere convergence result for Bochner–Riesz means of L p functions on Heisenberg‐type groups, yielding the existence of a p > 2 for which convergence holds for means of arbitrarily small order. The proof hinges on a reduction of weighted L 2 estimates for the maximal Bochner–Riesz operator to corresponding estimates for the non‐maximal operator, and a ‘dual Sobolev trace lemma’
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Algebraic criteria for Lipschitz equivalence of dust‐like self‐similar sets J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-22 Li‐Feng Xi, Ying Xiong
This paper concerns the Lipschitz equivalence of dust‐like self‐similar sets with commensurable ratios. We obtain an algebraic criterion of Falconer–Marsh type to check whether such two self‐similar sets are Lipschitz equivalent, and prove that it is a sufficient and necessary condition.
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Applications of the moduli continuity method to log K‐stable pairs J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-11-04 Patricio Gallardo, Jesus Martinez‐Garcia, Cristiano Spotti
The ‘moduli continuity method’ permits an explicit algebraisation of the Gromov–Hausdorff compactification of Kähler–Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the ‘log setting’ to describe explicitly some compact moduli spaces of K‐polystable log Fano pairs. We focus on situations when the angle of singularities is perturbed in an interval
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The joint spectrum J. Lond. Math. Soc. (IF 1.121) Pub Date : 2020-10-29 Emmanuel Breuillard, Cagri Sert
We introduce the notion of joint spectrum of a compact set of matrices S ⊂ GL d ( 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
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