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  • Fano quiver moduli
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-12-28
    Hans Franzen; Markus Reineke; Silvia Sabatini

    We exhibit a large class of quiver moduli spaces, which are Fano varieties, by studying line bundles on quiver moduli and their global sections in general, and work out several classes of examples, comprising moduli spaces of point configurations, Kronecker moduli, and toric quiver moduli.

  • A weak Lefschetz result for Chow groups of complete intersections
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-12-28
    James Lewis; Jenan Shtayat

    We introduce a weak Lefschetz-type result on Chow groups of complete intersections. As an application, we can reproduce some of the results in [P]. The purpose of this paper is not to reproduce all of [P] but rather illustrate why the aforementioned weak Lefschetz result is an interesting idea worth exploiting in itself. We hope the reader agrees.

  • A characterization of singular Schrödinger operators on the half-line
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-12-07
    Raffaele Scandone; Lorenzo Luperi Baglini; Kyrylo Simonov

    We study a class of delta-like perturbations of the Laplacian on the half-line, characterized by Robin boundary conditions at the origin. Using the formalism of nonstandard analysis, we derive a simple connection with a suitable family of Schrödinger operators with potentials of very large (infinite) magnitude and very short (infinitesimal) range. As a consequence, we also derive a similar result for

  • Prescribed k-symmetric curvature hypersurfaces in de Sitter space
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-11-26
    Daniel Ballesteros-Chávez; Wilhelm Klingenberg; Ben Lambert

    We prove the existence of compact spacelike hypersurfaces with prescribed k-curvature in de Sitter space, where the prescription function depends on both space and the tilt function.

  • On the decay of singular inner functions
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-12-02
    Thomas Ransford

    It is known that if $S(z)$ is a non-constant singular inner function defined on the unit disk, then $\min _{|z|\le r}|S(z)|\to 0$ as $r\to 1^-$. We show that the convergence can be arbitrarily slow.

  • A Pólya–Vinogradov inequality for short character sums
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-12-02
    Matteo Bordignon

    In this paper, we obtain a variation of the Pólya–Vinogradov inequality with the sum restricted to a certain height. Assume $\chi $ to be a primitive character modulo q, $ \epsilon>0$ and $N\le q^{1-\gamma }$, with $0\le \gamma \le 1/3$. We prove that $$ \begin{align*} |\sum_{n=1}^N \chi(n) |\le c (\tfrac{1}{3} -\gamma+\epsilon )\sqrt{q}\log q \end{align*} $$with $c=2/\pi ^2$ if $\chi $ is even and

  • On the degree of repeated radical extensions
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-11-23
    Fernando Szechtman

    We answer a question posed by Mordell in 1953, in the case of repeated radical extensions, and find necessary and sufficient conditions for $[F[\sqrt [m_1]{N_1},\dots ,\sqrt [m_\ell ]{N_\ell }]:F]=m_1\cdots m_\ell $, where F is an arbitrary field of characteristic not dividing any $m_i$.

  • Degree gaps for multipliers and the dynamical André–Oort conjecture
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-11-13
    Patrick Ingram

    We demonstrate how recent work of Favre and Gauthier, together with a modification of a result of the author, shows that a family of polynomials with infinitely many post-critically finite specializations cannot have any periodic cycles with multiplier of very low degree, except those that vanish, generalizing results of Baker and DeMarco, and Favre and Gauthier.

  • Autocorrelation functions for quantum particles in supersymmetric Pöschl-Teller potentials
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-10-28
    Francesco Cellarosi

    We consider autocorrelation functions for supersymmetric quantum mechanical systems (consisting of a fermion and a boson) confined in trigonometric Pöschl–Teller partner potentials. We study the limit of rescaled autocorrelation functions (at random time) as the localization of the initial state goes to infinity. The limiting distribution can be described using pairs of Jacobi theta functions on a

  • Sharp affine Trudinger–Moser inequalities: A new argument
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-10-22
    Nguyen Tuan Duy; Nguyen Lam; Phi Long Le

    We set up the sharp Trudinger–Moser inequality under arbitrary norms. Using this result and the $L_{p}$ Busemann-Petty centroid inequality, we will provide a new proof to the sharp affine Trudinger–Moser inequalities without using the well-known affine Pólya–Szegö inequality.

  • On isomorphisms between weighted $L^p$ -algebras
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-10-30
    Yulia Kuznetsova; Safoura Zadeh

    Let G be a locally compact group and let $\omega $ be a continuous weight on G. In this paper, we first characterize bicontinuous biseparating algebra isomorphisms between weighted $L^p$ -algebras. As a result, we extend previous results of Edwards, Parrott, and Strichartz on algebra isomorphisms between $L^p$ -algebras to the setting of weighted $L^p$ -algebras. We then study the automorphisms of

  • Surjective isometries of metric geometries
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-10-28
    A. F. Beardon; D. Minda

    Many authors define an isometry of a metric space to be a distance-preserving map of the space onto itself. In this note, we discuss spaces for which surjectivity is a consequence of the distance-preserving property rather than an initial assumption. These spaces include, for example, the three classical (Euclidean, spherical, and hyperbolic) geometries of constant curvature that are usually discussed

  • Relations between modular invariants of a vector and a covector in dimension two
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-10-28
    Yin Chen

    We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.

  • Erratum: Limiting properties of the distribution of primes in an arbitrarily large number of residue classes
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-11-05
    Lucile Devin

    As pointed out by Alexandre Bailleul, the paper mentioned in the title contains a mistake in Theorem 2.2. The hypothesis on the linear relation of the almost periods is not sufficient. In this note, we fix the problem and its minor consequences on other results in the same paper.

  • Brill-Noether generality of binary curves
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-10-13
    Xiang He

    We show that the space $G^r_{\underline d}(X)$ of linear series of certain multi-degree $\underline d=(d_1,d_2)$ (including the balanced ones) and rank r on a general genus-g binary curve X has dimension $\rho _{g,r,d}=g-(r+1)(g-d+r)$ if nonempty, where $d=d_1+d_2$ . This generalizes Caporaso’s result from the case $r\leq 2$ to arbitrary rank, and shows that the space of Osserman-limit linear series

  • A note on the phase retrieval of holomorphic functions
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-10-08
    Rolando Perez

    We prove that if f and g are holomorphic functions on an open connected domain, with the same moduli on two intersecting segments, then $f=g$ up to the multiplication of a unimodular constant, provided the segments make an angle that is an irrational multiple of $\pi $ . We also prove that if f and g are functions in the Nevanlinna class, and if $|f|=|g|$ on the unit circle and on a circle inside the

  • Homology supported in Lagrangian submanifolds in mirror quintic threefolds
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-11
    Daniel López Garcia

    In this note, we study homology classes in the mirror quintic Calabi–Yau threefold that can be realized by special Lagrangian submanifolds. We have used Picard–Lefschetz theory to establish the monodromy action and to study the orbit of Lagrangian vanishing cycles. For many prime numbers $p,$ we can compute the orbit modulo p. We conjecture that the orbit in homology with coefficients in $\mathbb {Z}$

  • The virtually generating graph of a profinite group
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-10-15
    Andrea Lucchini

    We consider the graph $\Gamma _{\text {virt}}(G)$ whose vertices are the elements of a finitely generated profinite group G and where two vertices x and y are adjacent if and only if they topologically generate an open subgroup of G. We investigate the connectivity of the graph $\Delta _{\text {virt}}(G)$ obtained from $\Gamma _{\text {virt}}(G)$ by removing its isolated vertices. In particular, we

  • The Clifford-cyclotomic group and Euler–Poincaré characteristics
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-02
    Colin Ingalls; Bruce W. Jordan; Allan Keeton; Adam Logan; Yevgeny Zaytman

    For an integer $n\geq 8$ divisible by $4$ , let $R_n={\mathbb Z}[\zeta _n,1/2]$ and let $\operatorname {\mathrm {U_{2}}}(R_n)$ be the group of $2\times 2$ unitary matrices with entries in $R_n$ . Set $\operatorname {\mathrm {U_2^\zeta }}(R_n)=\{\gamma \in \operatorname {\mathrm {U_{2}}}(R_n)\mid \det \gamma \in \langle \zeta _n\rangle \}$ . Let $\mathcal {G}_n\subseteq \operatorname {\mathrm {U_2^\zeta

  • Left orderable surgeries of double twist knots II
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-27
    Vu The Khoi; Masakazu Teragaito; Anh T. Tran

    A slope r is called a left orderable slope of a knot $K \subset S^3$ if the 3-manifold obtained by r-surgery along K has left orderable fundamental group. Consider double twist knots $C(2m, \pm 2n)$ and $C(2m+1, -2n)$ in the Conway notation, where $m \ge 1$ and $n \ge 2$ are integers. By using continuous families of hyperbolic ${\mathrm {SL}}_2(\mathbb {R})$ -representations of knot groups, it was

  • On framings of links in 3-manifolds
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-21
    Rhea Palak Bakshi; Dionne Ibarra; Gabriel Montoya-Vega; Józef H. Przytycki; Deborah Weeks

    We show that the only way of changing the framing of a link by ambient isotopy in an oriented $3$ -manifold is when the manifold has a properly embedded non-separating $S^{2}$ . This change of framing is given by the Dirac trick, also known as the light bulb trick. The main tool we use is based on McCullough’s work on the mapping class groups of $3$ -manifolds. We also relate our results to the theory

  • $C^*$ -algebra structure on certain Banach algebra products
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-07
    Fatemeh Abtahi

    Let $\mathcal A$ and $\mathcal B$ be commutative and semisimple Banach algebras and let $\theta \in \Delta (\mathcal B)$ . In this paper, we prove that $\mathcal A\times _{\theta }\mathcal B$ is a type I-BSE algebra if and only if ${\mathcal A}_e$ and $\mathcal B$ are so. As a main application of this result, we prove that $\mathcal A\times _{\theta }\mathcal B$ is isomorphic with a $C^*$ -algebra

  • On a rationality problem for fields of cross-ratios II
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-04
    Tran-Trung Nghiem; Zinovy Reichstein

    Let k be a field, $x_1, \dots , x_n$ be independent variables and let $L_n = k(x_1, \dots , x_n)$ . The symmetric group $\operatorname {\Sigma }_n$ acts on $L_n$ by permuting the variables, and the projective linear group $\operatorname {PGL}_2$ acts by $$ \begin{align*} \begin{pmatrix} a & b \\ c & d \end{pmatrix}\, \colon x_i \longmapsto \frac{a x_i + b}{c x_i + d} \end{align*} $$ for each $i = 1

  • Dyson’s rank, overpartitions, and universal mock theta functions
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-07
    Helen W. J. Zhang

    In this paper, we decompose $\overline {D}(a,M)$ into modular and mock modular parts, so that it gives as a straightforward consequencethe celebrated results of Bringmann and Lovejoy on Maass forms. Let $\overline {p}(n)$ be the number of partitions of n and $\overline {N}(a,M,n)$ be the number of overpartitions of n with rank congruent to a modulo M. Motivated by Hickerson and Mortenson, we find and

  • Regularity theory of Kolmogorov operator revisited
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-24
    Damir Kinzebulatov

    We consider Kolmorogov operator $-\Delta +b \cdot \nabla $ with drift b in the class of form-bounded vector fields (containing vector fields having critical-order singularities). We characterize quantitative dependence of the Sobolev and Hölder regularity of solutions to the corresponding elliptic equation on the value of the form-bound of b.

  • Mixing and average mixing times for general Markov processes
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-14
    Robert M. Anderson; Haosui Duanmu; Aaron Smith

    Yuval Peres and Perla Sousi showed that the mixing times and average mixing times of reversible Markov chains on finite state spaces are equal up to some universal multiplicative constant. We use tools from nonstandard analysis to extend this result to reversible Markov chains on compact state spaces that satisfy the strong Feller property.

  • Small trees in supercritical random forests
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-29
    Tao Lei

    We study the scaling limit of a random forest with prescribed degree sequence in the regime that the largest tree consists of all but a vanishing fraction of nodes. We give a description of the limit of the forest consisting of the small trees, by relating a plane forest to a marked cyclic forest and its corresponding skip-free walk.

  • Lineability, continuity, and antiderivatives in the non-Archimedean setting
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-02
    J. Khodabandehlou; S. Maghsoudi; J. B. Seoane-Sepúlveda

    This work focuses on the ongoing research of lineability (the search for large linear structures within certain non-linear sets) in non-Archimedean frameworks. Among several other results, we show that there exist large linear structures inside each of the following sets: (i) functions with a fixed closed subset of continuity, (ii) all continuous functions that are not Darboux continuous (or vice versa)

  • The Klein bottle group is not strongly verbally closed, though awfully close to being so
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-03
    Anton A. Klyachko

    According to Mazhuga’s theorem, the fundamental group H of anyconnected surface, possibly except for the Klein bottle, is a retract of each finitely generated group containing H as a verbally closed subgroup. We prove that the Klein bottle group is indeed an exception but has a very close property.

  • Equivalence of codes for countable sets of reals
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-20
    William Chan

    A set $U \subseteq {\mathbb {R}} \times {\mathbb {R}}$ is universal for countable subsets of ${\mathbb {R}}$ if and only if for all $x \in {\mathbb {R}}$ , the section $U_x = \{y \in {\mathbb {R}} : U(x,y)\}$ is countable and for all countable sets $A \subseteq {\mathbb {R}}$ , there is an $x \in {\mathbb {R}}$ so that $U_x = A$ . Define the equivalence relation $E_U$ on ${\mathbb {R}}$ by $x_0 \ E_U

  • Some results on Ricci-Bourguignon solitons and almost solitons
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-20
    Shubham Dwivedi

    We prove some results for the solitons of the Ricci–Bourguignon flow, generalizing the corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci–Bourguignon almost solitons and prove some results about them that generalize previous results for Ricci almost solitons. We also derive integral formulas for compact gradient Ricci–Bourguignon

  • Variational principles for symplectic eigenvalues
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-20
    Rajendra Bhatia; Tanvi Jain

    If A is a real $2n \times 2n$ positive definite matrix, then there exists a symplectic matrix M such that $M^TAM=\text {diag}(D, D),$ where D is a positive diagonal matrix with diagonal entries $d_1(A)\leqslant \cdots \leqslant d_n(A).$ We prove a maxmin principle for $d_k(A)$ akin to the classical Courant–Fisher–Weyl principle for Hermitian eigenvalues and use it to derive an analogue of the Weyl

  • Rigidity of diagonally embedded triangle groups
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-20
    Jean-Philippe Burelle

    We show local rigidity of hyperbolic triangle groups generated by reflections in pairs of n-dimensional subspaces of $\mathbb {R}^{2n}$ obtained by composition of the geometric representation in $\mathsf {PGL}(2,\mathbb {R})$ with the diagonal embeddings into $\mathsf {PGL}(2n,\mathbb {R})$ and $\mathsf {PSp}^\pm (2n,\mathbb {R})$ .

  • Beyond Beatty sequences: Complementary lattices
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-06
    Sam Vandervelde

    By taking square lattices as a two-dimensional analogue to Beatty sequences, we are motivated to define and explore the notion of complementary lattices. In particular, we present a continuous one-parameter family of complementary lattices. This main result then yields several novel examples of complementary sequences, along with a geometric proof of the fundamental property of Beatty sequences.

  • Criteria for periodicity and an application to elliptic functions
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-14
    Ehud de Shalit

    Let P and Q be relatively prime integers greater than 1, and let f be a real valued discretely supported function on a finite dimensional real vector space V. We prove that if $f_{P}(x)=f(Px)-f(x)$ and $f_{Q}(x)=f(Qx)-f(x)$ are both $\Lambda $ -periodic for some lattice $\Lambda \subset V$ , then so is f (up to a modification at $0$ ). This result is used to prove a theorem on the arithmetic of elliptic

  • On intersections of polynomial semigroups orbits with plane lines
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-17
    Jorge Mello

    We study intersections of orbits in polynomial semigroup dynamics with lines on the affine plane over a number field, extending previous work of D. Ghioca, T. Tucker, and M. Zieve (2008).

  • Geography of simply connected nonspin symplectic 4-manifolds with positive signature. II
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-10
    Anar Akhmedov; B. Doug Park

    Building upon our earlier work with M. C. Hughes, we construct many new smooth structures on closed simply connected nonspin $4$ -manifolds with positive signature. We also provide numerical and asymptotic upper bounds on the function $\lambda (\sigma )$ that was defined in our earlier work.

  • Optimal free export/import regions
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-17
    Samer Dweik

    We consider the problem of finding two free export/import sets $E^+$ and $E^-$ that minimize the total cost of some export/import transportation problem (with export/import taxes $g^\pm $), between two densities $f^+$ and $f^-$, plus penalization terms on $E^+$ and $E^-$. First, we prove the existence of such optimal sets under some assumptions on $f^\pm $ and $g^\pm $. Then we study some properties

  • Embedding of Dirichlet type spaces into tent spaces and Volterra operators
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-09-08
    Ruishen Qian; Xiangling Zhu

    In this paper, we study the boundedness and compactness of the inclusion mapping from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to tent spaces. Meanwhile, the boundedness, compactness, and essential norm of Volterra integral operators from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to general function spaces are also investigated.

  • The Nef Cone of the Hilbert Scheme of Points on Rational Elliptic Surfaces and the Cone Conjecture
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-08
    John Kopper

    We compute the nef cone of the Hilbert scheme of points on a general rational elliptic surface. As a consequence of our computation, we show that the Morrison–Kawamata cone conjecture holds for these nef cones.

  • Approximation via Hausdorff operators
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-08-13
    Alberto Debernardi; Elijah Liflyand

    Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate functions and the adjoint to that Hausdorff operator of the given function. We find estimates for the rate of approximation in various metrics in terms of the parameter of truncation and the components of the Hausdorff operator. Explicit rates of approximation of functions and comparison with approximate

  • The Number of Non-cyclic Sylow Subgroups of the Multiplicative Group Modulo n
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-08
    Paul Pollack

    For each positive integer n, let $U(\mathbf {Z}/n\mathbf {Z})$ denote the group of units modulo n, which has order $\phi (n)$ (Euler’s function) and exponent $\lambda (n)$ (Carmichael’s function). The ratio $\phi (n)/\lambda (n)$ is always an integer, and a prime p divides this ratio precisely when the (unique) Sylow p-subgroup of $U(\mathbf {Z}/n\mathbf {Z})$ is noncyclic. Write W(n) for the number

  • On Single-Distance Graphs on the Rational Points in Euclidean Spaces
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-29
    Sheng Bau; Peter Johnson; Matt Noble

    For positive integers n and d > 0, let $G(\mathbb {Q}^n,\; d)$ denote the graph whose vertices are the set of rational points $\mathbb {Q}^n$ , with $u,v \in \mathbb {Q}^n$ being adjacent if and only if the Euclidean distance between u and v is equal to d. Such a graph is deemed “non-trivial” if d is actually realized as a distance between points of $\mathbb {Q}^n$ . In this paper, we show that a space

  • Complete boundedness of multiple operator integrals
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-27
    Clément Coine

    In this paper, we characterize the multiple operator integrals mappings that are bounded on the Haagerup tensor product of spaces of compact operators. We show that such maps are automatically completely bounded and prove that this is equivalent to a certain factorization property of the symbol associated with the operator integral mapping. This generalizes a result by Juschenko-Todorov-Turowska on

  • Finite descent obstruction for Hilbert modular varieties
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-22
    Gregorio Baldi; Giada Grossi

    Let S be a finite set of primes. We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of $\mathbb {Z}_{S}$ -points on integral models of Hilbert modular varieties, extending a result of D. Helm and F. Voloch about modular curves. Let L be a totally real field. Under (a special case of) the absolute Hodge conjecture and a weak Serre’s conjecture for mod

  • On cohesive almost zero-dimensional spaces
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-15
    Jan J. Dijkstra; David S. Lipham

    We investigate C-sets in almost zero-dimensional spaces, showing that closed $\sigma $ C-sets are C-sets. As corollaries, we prove that every rim- $\sigma $ -compact almost zero-dimensional space is zero-dimensional and that each cohesive almost zero-dimensional space is nowhere rational. To show that these results are sharp, we construct a rim-discrete connected set with an explosion point. We also

  • Almost Gorenstein rings arising from fiber products
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-10
    Naoki Endo; Shiro Goto; Ryotaro Isobe

    The purpose of this paper is, as part of the stratification of Cohen–Macaulay rings, to investigate the question of when the fiber products are almost Gorenstein rings. We show that the fiber product $R \times _T S$ of Cohen–Macaulay local rings R, S of the same dimension $d>0$ over a regular local ring T with $\dim T=d-1$ is an almost Gorenstein ring if and only if so are R and S. In addition, the

  • A question for iterated Galois groups in arithmetic dynamics
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-10
    Andrew Bridy; John R. Doyle; Dragos Ghioca; Liang-Chung Hsia; Thomas J. Tucker

    We formulate a general question regarding the size of the iterated Galois groups associated with an algebraic dynamical system and then we discuss some special cases of our question. Our main result answers this question for certain split polynomial maps whose coordinates are unicritical polynomials.

  • Explicit symmetric DGLA models of 3-cells
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-07-01
    Itay Griniasty; Ruth Lawrence

    We give explicit formulae for differential graded Lie algebra (DGLA) models of 3-cells. In particular, for a cube and an n-faceted banana-shaped 3-cell with two vertices, n edges each joining those two vertices, and n bi-gon 2-cells, we construct a model symmetric under the geometric symmetries of the cell fixing two antipodal vertices. The cube model is to be used in forthcoming work for discrete

  • Continuity of condenser capacity under holomorphic motions
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-29
    Stamatis Pouliasis

    We show that condenser capacity varies continuously under holomorphic motions, and the corresponding family of the equilibrium measures of the condensers is continuous with respect to the weak-star convergence. We also study the behavior of uniformly perfect sets under holomorphic motions.

  • Deligne–Lusztig varieties and basic EKOR strata
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-29
    Haining Wang

    Using the axioms of He and Rapoport for the stratifications of Shimura varieties, we explain a result of Görtz, He, and Nie that the EKOR strata contained in the basic loci can be described as a disjoint union of Deligne–Lusztig varieties. In the special case of Siegel modular varieties, we compare their descriptions to that of Görtz and Yu for the supersingular Kottwitz-Rapoport strata and to the

  • Injective modules over the Jacobson algebra $K\langle X, Y \ | \ XY=1\rangle $
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-22
    Gene Abrams; Francesca Mantese; Alberto Tonolo

    For a field K, let $\mathcal {R}$ denote the Jacobson algebra $K\langle X, Y \ | \ XY=1\rangle $ . We give an explicit construction of the injective envelope of each of the (infinitely many) simple left $\mathcal {R}$ -modules. Consequently, we obtain an explicit description of a minimal injective cogenerator for $\mathcal {R}$ . Our approach involves realizing $\mathcal {R}$ up to isomorphism as the

  • Positive definite functions and cut-off for discrete groups
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-22
    Amaury Freslon

    We consider the sequence of powers of a positive definite function on a discrete group. Taking inspiration from random walks on compact quantum groups, we give several examples of situations where a cut-off phenomenon occurs for this sequence, including free groups and infinite Coxeter groups. We also give examples of absence of cut-off using free groups again.

  • Relative vertex asphericity
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-16
    Jens Harlander; Stephan Rosebrock

    Diagrammatic reducibility DR and its generalization, vertex asphericity VA, are combinatorial tools developed for detecting asphericity of a 2-complex. Here we present tests for a relative version of VA that apply to pairs of 2-complexes $(L,K)$ , where K is a subcomplex of L. We show that a relative weight test holds for injective labeled oriented trees, implying that they are VA and hence aspherical

  • On Pisier’s inequality for UMD targets
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-15
    Alexandros Eskenazis

    We prove an extension of Pisier’s inequality (1986) with a dimension-independent constant for vector-valued functions whose target spaces satisfy a relaxation of the UMD property.

  • Faltings extension and Hodge-Tate filtration for abelian varieties over p-adic local fields with imperfect residue fields
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-11
    Tongmu He

    Let K be a complete discrete valuation field of characteristic $0$ , with not necessarily perfect residue field of characteristic $p>0$ . We define a Faltings extension of $\mathcal {O}_K$ over $\mathbb {Z}_p$ , and we construct a Hodge-Tate filtration for abelian varieties over K by generalizing Fontaine’s construction [Fon82] where he treated the perfect residue field case.

  • Growth of frequently hypercyclic functions for some weighted Taylor shifts on the unit disc
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-11
    Augustin Mouze; Vincent Munnier

    For any $\alpha \in \mathbb {R},$ we consider the weighted Taylor shift operators $T_{\alpha }$ acting on the space of analytic functions in the unit disc given by $T_{\alpha }:H(\mathbb {D})\rightarrow H(\mathbb {D}),$ $ \begin{align*}f(z)=\sum_{k\geq 0}a_{k}z^{k}\mapsto T_{\alpha}(f)(z)=a_1+\sum_{k\geq 1}\Big(1+\frac{1}{k}\Big)^{\alpha}a_{k+1}z^{k}.\end{align*}$ We establish the optimal growth of

  • Euler characteristics and their congruences in the positive rank setting
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-06-11
    Anwesh Ray; R. Sujatha

    The notion of the truncated Euler characteristic for Iwasawa modules is an extension of the notion of the usual Euler characteristic to the case when the homology groups are not finite. This article explores congruence relations between the truncated Euler characteristics for dual Selmer groups of elliptic curves with isomorphic residual representations, over admissible p-adic Lie extensions. Our results

  • Möbius Randomness Law for Frobenius Traces of Ordinary Curves
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-05-15
    Min Sha; Igor E. Shparlinski

    Recently E. Bombieri and N. M. Katz (2010) demonstrated that several well-known results about the distribution of values of linear recurrence sequences lead to interesting statements for Frobenius traces of algebraic curves. Here we continue this line of study and establish the Möbius randomness law quantitatively for the normalised form of Frobenius traces.

  • Finsler Warped Product Metrics with Relatively Isotropic Landsberg Curvature
    Can. Math. Bull. (IF 0.655) Pub Date : 2020-05-12
    Zhao Yang; Xiaoling Zhang

    In this paper, we study Finsler warped product metrics with relatively isotropic Landsberg curvature. We obtain the differential equations that characterize such metrics. Then we give some examples.

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