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The restricted quantum double of the Yangian Can. J. Math. (IF 0.7) Pub Date : 2024-02-16 Curtis Wendlandt
Let $\mathfrak {g}$ be a complex semisimple Lie algebra with associated Yangian $Y_{\hbar }\mathfrak {g}$. In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts that the algebra $\mathrm {D}Y_{\hbar }\mathfrak {g}$ obtained by doubling the generators of $Y_{\hbar }\mathfrak {g}$, called the Yangian double, provides a realization of the quantum double of the Yangian. We provide
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Shi arrangements and low elements in affine Coxeter groups Can. J. Math. (IF 0.7) Pub Date : 2024-02-12 Nathan Chapelier-Laget, Christophe Hohlweg
Given an affine Coxeter group W, the corresponding Shi arrangement is a refinement of the corresponding Coxeter hyperplane arrangements that was introduced by Shi to study Kazhdan–Lusztig cells for W. Shi showed that each region of the Shi arrangement contains exactly one element of minimal length in W. Low elements in W were introduced to study the word problem of the corresponding Artin–Tits (braid)
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On restricted Falconer distance sets Can. J. Math. (IF 0.7) Pub Date : 2024-02-05 José Gaitan, Allan Greenleaf, Eyvindur Ari Palsson, Georgios Psaromiligkos
We introduce a class of Falconer distance problems, which we call of restricted type, lying between the classical version and its pinned variant. Prototypical restricted distance sets are the diagonal distance sets, k-point configuration sets given by $$ \begin{align*}\Delta^{\mathrm{diag}}(E)= \{ \,|(x,x,\dots,x)-(y_1,y_2,\dots,y_{k-1})| : x, y_1, \dots,y_{k-1} \in E\, \}\end{align*} $$for a compact
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Electrical networks and the grove algebra Can. J. Math. (IF 0.7) Pub Date : 2024-02-01 Yibo Gao, Thomas Lam, Zixuan Xu
We study the ring of regular functions on the space of planar electrical networks, which we coin the grove algebra. This algebra is an electrical analog of the Plücker ring studied classically in invariant theory. We develop the combinatorics of double groves to study the grove algebra, and find a quadratic Gröbner basis for the grove ideal.
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Tracial oscillation zero and stable rank one Can. J. Math. (IF 0.7) Pub Date : 2024-01-24 Xuanlong Fu, Huaxin Lin
Let A be a separable (not necessarily unital) simple $C^*$-algebra with strict comparison. We show that if A has tracial approximate oscillation zero, then A has stable rank one and the canonical map $\Gamma $ from the Cuntz semigroup of A to the corresponding lower-semicontinuous affine function space is surjective. The converse also holds. As a by-product, we find that a separable simple $C^*$-algebra
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Heights and quantitative arithmetic on stacky curves Can. J. Math. (IF 0.7) Pub Date : 2024-01-19 Brett Nasserden, Stanley Yao Xiao
In this paper, we investigate the theory of heights in a family of stacky curves following recent work of Ellenberg, Satriano, and Zureick-Brown. We first give an elementary construction of a height which is seen to be dual to theirs. We count rational points having bounded ESZ-B height on a particular stacky curve, answering a question of Ellenberg, Satriano, and Zureick-Brown. We also show that when
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On the cross-product conjecture for the number of linear extensions Can. J. Math. (IF 0.7) Pub Date : 2024-01-19 Swee Hong Chan, Igor Pak, Greta Panova
We prove a weak version of the cross-product conjecture: $\textrm {F}(k+1,\ell ) \hskip .06cm \textrm {F}(k,\ell +1) \ge (\frac 12+\varepsilon ) \hskip .06cm \textrm {F}(k,\ell ) \hskip .06cm \textrm {F}(k+1,\ell +1)$, where $\textrm {F}(k,\ell )$ is the number of linear extensions for which the values at fixed elements $x,y,z$ are k and $\ell $ apart, respectively, and where $\varepsilon>0$ depends
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On definable groups and D-groups in certain fields with a generic derivation Can. J. Math. (IF 0.7) Pub Date : 2024-01-15 Ya’acov Peterzil, Anand Pillay, Françoise Point
We continue our study from Peterzil et al. (2022, Preprint, arXiv:2208.08293) of finite-dimensional definable groups in models of the theory $T_{\partial }$, the model companion of an o-minimal ${\mathcal {L}}$-theory T expanded by a generic derivation $\partial $ as in Fornasiero and Kaplan (2021, Journal of Mathematical Logic 21, 2150007). We generalize Buium’s notion of an algebraic D-group to ${\mathcal
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Faltings’ main p-adic comparison theorems for non-smooth schemes Can. J. Math. (IF 0.7) Pub Date : 2024-01-12 Tongmu He
To understand the p-adic étale cohomology of a proper smooth variety over a p-adic field, Faltings compared it to the cohomology of his ringed topos, by the so-called Faltings’ main p-adic comparison theorem, and then deduced various comparisons with p-adic cohomologies originating from differential forms. In this article, we generalize the former to any proper and finitely presented morphism of coherent
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Refinements of Katz–Sarnak theory for the number of points on curves over finite fields Can. J. Math. (IF 0.7) Pub Date : 2024-01-09 Jonas Bergström, Everett W. Howe, Elisa Lorenzo García, Christophe Ritzenthaler
This paper goes beyond Katz–Sarnak theory on the distribution of curves over finite fields according to their number of rational points, theoretically, experimentally, and conjecturally. In particular, we give a formula for the limits of the moments measuring the asymmetry of this distribution for (non-hyperelliptic) curves of genus $g\geq 3$. The experiments point to a stronger notion of convergence
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Trigonometric convexity of the multidimensional indicator Can. J. Math. (IF 0.7) Pub Date : 2024-01-05 Aleksandr Mkrtchyan, Armen Vagharshakyan
The notion of indicator of an analytic function, that describes the function’s growth along rays, was introduced by Phragmen and Lindelöf. Trigonometric convexity is a defining property of the indicator. For multivariate cases, an analogous property of trigonometric convexity was not known so far. We prove the property of trigonometric convexity for the indicator of multivariate analytic functions
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Systems involving mean value formulas on trees Can. J. Math. (IF 0.7) Pub Date : 2024-01-03 Alfredo Miranda, Carolina A. Mosquera, Julio D. Rossi
In this paper, we study the Dirichlet problem for systems of mean value equations on a regular tree. We deal both with the directed case (the equations verified by the components of the system at a node in the tree only involve values of the unknowns at the successors of the node in the tree) and the undirected case (now the equations also involve the predecessor in the tree). We find necessary and
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Meridional rank and bridge number of knotted 2-spheres Can. J. Math. (IF 0.7) Pub Date : 2023-12-27 Jason Joseph, Puttipong Pongtanapaisan
The meridional rank conjecture asks whether the bridge number of a knot in $S^3$ is equal to the minimal number of meridians needed to generate the fundamental group of its complement. In this paper, we investigate the analogous conjecture for knotted spheres in $S^4$. Towards this end, we give a construction to produce classical knots with quotients sending meridians to elements of any finite order
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Multi-linear forms, graphs, and Can. J. Math. (IF 0.7) Pub Date : 2023-12-27 Pablo Bhowmik, Alex Iosevich, Doowon Koh, Thang Pham
The purpose of this paper is to introduce and study the following graph-theoretic paradigm. Let $$ \begin{align*}T_Kf(x)=\int K(x,y) f(y) d\mu(y),\end{align*} $$where $f: X \to {\Bbb R}$, X a set, finite or infinite, and K and $\mu $ denote a suitable kernel and a measure, respectively. Given a connected ordered graph G on n vertices, consider the multi-linear form $$ \begin{align*}\Lambda_G(f_1,f_2
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Symmetric and antisymmetric tensor products for the function-theoretic operator theorist Can. J. Math. (IF 0.7) Pub Date : 2023-12-22 Stephan Ramon Garcia, Ryan O’Loughlin, Jiahui Yu
We study symmetric and antisymmetric tensor products of Hilbert-space operators, focusing on norms and spectra for some well-known classes favored by function-theoretic operator theorists. We pose many open questions that should interest the field.
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Higher dimensional algebraic fiberings for pro-p groups Can. J. Math. (IF 0.7) Pub Date : 2023-12-22 Dessislava H. Kochloukova
We prove some conditions for higher-dimensional algebraic fibering of pro-p group extensions, and we establish corollaries about incoherence of pro-p groups. In particular, if $1 \to K \to G \to \Gamma \to 1$ is a short exact sequence of pro-p groups, such that $\Gamma $ contains a finitely generated, non-abelian, free pro-p subgroup, K a finitely presented pro-p group with N a normal pro-p subgroup
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Affine isoperimetric inequalities on flag manifolds Can. J. Math. (IF 0.7) Pub Date : 2023-12-19 Susanna Dann, Grigoris Paouris, Peter Pivovarov
Building on work of Furstenberg and Tzkoni, we introduce $\mathbf {r}$-flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermassintegrals as averages on flag manifolds (where the Grassmannian can be considered as a special case). We establish affine and linear invariance properties and extend fundamental results to this new setting. In particular
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Extension of monotone operators and Lipschitz maps invariant for a group of isometries Can. J. Math. (IF 0.7) Pub Date : 2023-12-18 Giulia Cavagnari, Giuseppe Savaré, Giacomo Enrico Sodini
We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms, and we show that they always admit a maximal extension which preserves the same invariance. A similar result applies to Lipschitz maps in Hilbert spaces, thus providing an invariant version of Kirszbraun–Valentine extension theorem. We then provide a relevant application
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Linear maps preserving -norms of tensor products of matrices Can. J. Math. (IF 0.7) Pub Date : 2023-12-15 Zejun Huang, Nung-Sing Sze, Run Zheng
Let $m,n\ge 2$ be integers. Denote by $M_n$ the set of $n\times n$ complex matrices and $\|\cdot \|_{(p,k)}$ the $(p,k)$ norm on $M_{mn}$ with a positive integer $k\leq mn$ and a real number $p>2$. We show that a linear map $\phi :M_{mn}\rightarrow M_{mn}$ satisfies $$ \begin{align*}\|\phi(A\otimes B)\|_{(p,k)}=\|A\otimes B\|_{(p,k)} \mathrm{\quad for~ all\quad}A\in M_m\ \mathrm{and}\ B\in M_n\end{align*}
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Solvability of Hessian quotient equations in exterior domains Can. J. Math. (IF 0.7) Pub Date : 2023-12-14 Limei Dai, Jiguang Bao, Bo Wang
In this paper, we study the Dirichlet problem of Hessian quotient equations of the form $S_k(D^2u)/S_l(D^2u)=g(x)$ in exterior domains. For $g\equiv \mbox {const.}$, we obtain the necessary and sufficient conditions on the existence of radially symmetric solutions. For g being a perturbation of a generalized symmetric function at infinity, we obtain the existence of viscosity solutions by Perron’s
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Unified bounds for the independence number of graphs Can. J. Math. (IF 0.7) Pub Date : 2023-12-11 Jiang Zhou
The Hoffman ratio bound, Lovász theta function, and Schrijver theta function are classical upper bounds for the independence number of graphs, which are useful in graph theory, extremal combinatorics, and information theory. By using generalized inverses and eigenvalues of graph matrices, we give bounds for independence sets and the independence number of graphs. Our bounds unify the Lovász theta function
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Equivariant -correspondences and compact quantum group actions on Pimsner algebras Can. J. Math. (IF 0.7) Pub Date : 2023-12-05 Suvrajit Bhattacharjee, Soumalya Joardar
Let G be a compact quantum group. We show that given a G-equivariant $\textrm {C}^*$-correspondence E, the Pimsner algebra $\mathcal {O}_E$ can be naturally made into a G-$\textrm {C}^*$-algebra. We also provide sufficient conditions under which it is guaranteed that a G-action on the Pimsner algebra $\mathcal {O}_E$ arises in this way, in a suitable precise sense. When G is of Kac type, a KMS state
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Combinatorial proofs of properties of double-point enhanced grid homology Can. J. Math. (IF 0.7) Pub Date : 2023-12-05 Ollie Thakar
We provide a purely combinatorial proof of a skein exact sequence obeyed by double-point enhanced grid homology. We also extend the theory to coefficients over $\mathbb {Z},$ and discuss alternatives to the Ozsváth–Szabó $\tau $ invariant.
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Linear homeomorphisms of function spaces and the position of a space in its compactification Can. J. Math. (IF 0.7) Pub Date : 2023-11-28 Mikołaj Krupski
An old question of Arhangel’skii asks if the Menger property of a Tychonoff space X is preserved by homeomorphisms of the space $C_p(X)$ of continuous real-valued functions on X endowed with the pointwise topology. We provide affirmative answer in the case of linear homeomorphisms. To this end, we develop a method of studying invariants of linear homeomorphisms of function spaces $C_p(X)$ by looking
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Anisotropic flow, entropy, and -Minkowski problem Can. J. Math. (IF 0.7) Pub Date : 2023-11-28 Károly J. Böröczky, Pengfei Guan
We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak’s $L^p$-Minkowski problem on $S^n$ which were obtained by other methods.
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Graphical methods and rings of invariants on the symmetric algebra Can. J. Math. (IF 0.7) Pub Date : 2023-11-28 Rebecca Bourn, William Q. Erickson, Jeb F. Willenbring
Let G be a complex classical group, and let V be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of G-invariant polynomial functions on the space $\mathcal P^m(V)$ of degree-m homogeneous polynomial functions on V. In this paper, we replace $\mathcal P^m(V)$ with the full polynomial
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More Ramsey theory for highly connected monochromatic subgraphs Can. J. Math. (IF 0.7) Pub Date : 2023-11-24 Michael Hrušák, Saharon Shelah, Jing Zhang
An infinite graph is said to be highly connected if the induced subgraph on the complement of any set of vertices of smaller size is connected. We continue the study of weaker versions of Ramsey’s theorem on uncountable cardinals asserting that if we color edges of the complete graph, we can find a large highly connected monochromatic subgraph. In particular, several questions of Bergfalk, Hrušák,
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Tangle equations, the Jones conjecture, slopes of surfaces in tangle complements, and q-deformed rationals Can. J. Math. (IF 0.7) Pub Date : 2023-11-14 Adam S. Sikor
We study systems of two-tangle equations $$ \begin{align*}\begin{cases} N(X+T_1)=L_1,\\ N(X+T_2)=L_2, \end{cases}\end{align*} $$which play an important role in the analysis of enzyme actions on DNA strands. We show that every system of framed tangle equations has at most one-framed rational solution. Furthermore, we show that the Jones unknot conjecture implies that if a system of tangle equations
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Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability Can. J. Math. (IF 0.7) Pub Date : 2023-11-13 Junyan Zhao
In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with sum of lines as boundary divisors, and prove that for $d=2,3,4$, these K-moduli of pairs are isomorphic to the K-moduli spaces of del Pezzo surfaces. For $d=1$, we prove that they are different by exhibiting some walls.
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The blowup-polynomial of a metric space: connections to stable polynomials, graphs and their distance spectra Can. J. Math. (IF 0.7) Pub Date : 2023-11-09 Projesh Nath Choudhury, Apoorva Khare
To every finite metric space X, including all connected unweighted graphs with the minimum edge-distance metric, we attach an invariant that we call its blowup-polynomial $p_X(\{ n_x : x \in X \})$. This is obtained from the blowup $X[\mathbf {n}]$ – which contains $n_x$ copies of each point x – by computing the determinant of the distance matrix of $X[\mathbf {n}]$ and removing an exponential factor
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A new way to tackle a conjecture of Rémond Can. J. Math. (IF 0.7) Pub Date : 2023-10-31 Arnaud Plessis
Let $\Gamma \subset \overline {\mathbb {Q}}^*$ be a finitely generated subgroup. Denote by $\Gamma _{\mathrm {div}}$ its division group. A recent conjecture due to Rémond, related to the Zilber–Pink conjecture, predicts that the absolute logarithmic Weil height of an element of $\mathbb {Q}(\Gamma _{\mathrm {div}})^*\backslash \Gamma _{\mathrm {div}}$ is bounded from below by a positive constant depending
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Prime representations in the Hernandez–Leclerc category: classical decompositions Can. J. Math. (IF 0.7) Pub Date : 2023-10-27 Leon Barth, Deniz Kus
We use the dual functional realization of loop algebras to study the prime irreducible objects in the Hernandez–Leclerc (HL) category for the quantum affine algebra associated with $\mathfrak {sl}_{n+1}$. When the HL category is realized as a monoidal categorification of a cluster algebra (Hernandez and Leclerc (2010, Duke Mathematical Journal 154, 265–341); Hernandez and Leclerc (2013, Symmetries
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Webs of type P Can. J. Math. (IF 0.7) Pub Date : 2023-10-27 Nicholas Davidson, Jonathan R. Kujawa, Robert Muth
This paper introduces type P web supercategories. They are defined as diagrammatic monoidal ${\mathbb {k}}$-linear supercategories via generators and relations. We study the structure of these categories and provide diagrammatic bases for their morphism spaces. We also prove these supercategories provide combinatorial models for the monoidal supercategory generated by the symmetric powers of the natural
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The Frobenius semiradical, generic stabilizers, and Poisson center for nilradicals Can. J. Math. (IF 0.7) Pub Date : 2023-10-27 Dmitri I. Panyushev
Let ${\mathfrak g}$ be a complex simple Lie algebra and ${\mathfrak n}$ the nilradical of a parabolic subalgebra of ${\mathfrak g}$. We consider some properties of the coadjoint representation of ${\mathfrak n}$ and related algebras of invariants. This includes (i) the problem of existence of generic stabilizers, (ii) a description of the Frobenius semiradical of ${\mathfrak n}$ and the Poisson center
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Lower bounds on Bourgain’s constant for harmonic measure Can. J. Math. (IF 0.7) Pub Date : 2023-10-27 Matthew Badger, Alyssa Genschaw
For every $n\geq 2$, Bourgain’s constant $b_n$ is the largest number such that the (upper) Hausdorff dimension of harmonic measure is at most $n-b_n$ for every domain in $\mathbb {R}^n$ on which harmonic measure is defined. Jones and Wolff (1988, Acta Mathematica 161, 131–144) proved that $b_2=1$. When $n\geq 3$, Bourgain (1987, Inventiones Mathematicae 87, 477–483) proved that $b_n>0$ and Wolff (1995
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Isogeny graphs on superspecial abelian varieties: eigenvalues and connection to Bruhat–Tits buildings Can. J. Math. (IF 0.7) Pub Date : 2023-10-20 Yusuke Aikawa, Ryokichi Tanaka, Takuya Yamauchi
We study for each fixed integer $g \ge 2$, for all primes $\ell $ and p with $\ell \neq p$, finite regular directed graphs associated with the set of equivalence classes of $\ell $-marked principally polarized superspecial abelian varieties of dimension g in characteristic p, and show that the adjacency matrices have real eigenvalues with spectral gaps independent of p. This implies a rapid mixing
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Category for truncated current Lie algebras Can. J. Math. (IF 0.7) Pub Date : 2023-10-19 Matthew Chaffe, Lewis Topley
In this paper, we study an analogue of the Bernstein–Gelfand–Gelfand category ${\mathcal {O}}$ for truncated current Lie algebras $\mathfrak {g}_n$ attached to a complex semisimple Lie algebra. This category admits Verma modules and simple modules, each parametrized by the dual space of the truncated currents on a choice of Cartan subalgebra in $\mathfrak {g}$. Our main result describes an inductive
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Infinite families of Artin–Schreier function fields with any prescribed class group rank Can. J. Math. (IF 0.7) Pub Date : 2023-10-19 Jinjoo Yoo, Yoonjin Lee
We study the Galois module structure of the class groups of the Artin–Schreier extensions K over k of extension degree p, where $k:={\mathbb F}_q(T)$ is the rational function field and p is a prime number. The structure of the p-part $Cl_K(p)$ of the ideal class group of K as a finite G-module is determined by the invariant ${\lambda }_n$, where $G:=\operatorname {\mathrm {Gal}}(K/k)=\langle {\sigma
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The second fundamental form of the real Kaehler submanifolds Can. J. Math. (IF 0.7) Pub Date : 2023-10-18 Sergio Chion, Marcos Dajczer
Let $f\colon M^{2n}\to \mathbb {R}^{2n+p}$, $2\leq p\leq n-1$, be an isometric immersion of a Kaehler manifold into Euclidean space. Yan and Zheng (2013, Michigan Mathematical Journal 62, 421–441) conjectured that if the codimension is $p\leq 11$, then, along any connected component of an open dense subset of $M^{2n}$, the submanifold is as follows: it is either foliated by holomorphic submanifolds
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The solvability for a nonlinear degenerate hyperbolic–parabolic coupled system arising from nematic liquid crystals Can. J. Math. (IF 0.7) Pub Date : 2023-10-13 Yanbo Hu
This paper focuses on the Cauchy problem for a one-dimensional quasilinear hyperbolic–parabolic coupled system with initial data given on a line of parabolicity. The coupled system is derived from the Poiseuille flow of full Ericksen–Leslie model in the theory of nematic liquid crystals, which incorporates the crystal and liquid properties of the materials. The main difficulty comes from the degeneracy
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Lambert series of logarithm, the derivative of Deninger’s function Can. J. Math. (IF 0.7) Pub Date : 2023-10-11 Soumyarup Banerjee, Atul Dixit, Shivajee Gupta
An explicit transformation for the series $\sum \limits _{n=1}^{\infty }\displaystyle \frac {\log (n)}{e^{ny}-1}$, or equivalently, $\sum \limits _{n=1}^{\infty }d(n)\log (n)e^{-ny}$ for Re$(y)>0$, which takes y to $1/y$, is obtained for the first time. This series transforms into a series containing the derivative of $R(z)$, a function studied by Christopher Deninger while obtaining an analog of the
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Weighted nonlinear flag manifolds as coadjoint orbits Can. J. Math. (IF 0.7) Pub Date : 2023-10-09 Stefan Haller, Cornelia Vizman
A weighted nonlinear flag is a nested set of closed submanifolds, each submanifold endowed with a volume density. We study the geometry of Fréchet manifolds of weighted nonlinear flags, in this way generalizing the weighted nonlinear Grassmannians. When the ambient manifold is symplectic, we use these nonlinear flags to describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms
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Asymptotics for symmetrized positive moments of odd ranks Can. J. Math. (IF 0.7) Pub Date : 2023-10-09 Edward Y. S. Liu
In 2007, Andrews introduced Durfee symbols and k-marked Durfee symbols so as to give a combinatorial interpretation for the symmetrized moment function $\eta _{2k}(n)$ of ranks of partitions. He also considered the relations between odd Durfee symbols and the mock theta function $\omega (q)$, and proved that the $2k$th moment function $\eta _{2k}^0(n)$ of odd ranks of odd Durfee symbols counts $(k+1)$-marked
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The Kudla–Millson form via the Mathai–Quillen formalism Can. J. Math. (IF 0.7) Pub Date : 2023-10-05 Romain Branchereau
A crucial ingredient in the theory of theta liftings of Kudla and Millson is the construction of a $q$-form $\varphi_{KM}$ on an orthogonal symmetric space, using Howe's differential operators. This form can be seen as a Thom form of a real oriented vector bundle. We show that the Kudla-Millson form can be recovered from a canonical construction of Mathai and Quillen. A similar result was obtaind by
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Tensor algebras of subproduct systems and noncommutative function theory Can. J. Math. (IF 0.7) Pub Date : 2023-10-02 Michael Hartz, Orr Moshe Shalit
We revisit tensor algebras of subproduct systems with Hilbert space fibers, resolving some open questions in the case of infinite-dimensional fibers. We characterize when a tensor algebra can be identified as the algebra of uniformly continuous noncommutative functions on a noncommutative homogeneous variety or, equivalently, when it is residually finite-dimensional: this happens precisely when the
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Examples of dHYM connections in a variable background Can. J. Math. (IF 0.7) Pub Date : 2023-10-02 Enrico Schlitzer, Jacopo Stoppa
We study deformed Hermitian Yang–Mills (dHYM) connections on ruled surfaces explicitly, using the momentum construction. As a main application, we provide many new examples of dHYM connections coupled to a variable background Kähler metric. These are solutions of the moment map partial differential equations given by the Hamiltonian action of the extended gauge group, coupling the dHYM equation to
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Shifted moments of the Riemann zeta function Can. J. Math. (IF 0.7) Pub Date : 2023-09-25 Nathan Ng, Quanli Shen, Peng-Jie Wong
In this article, we prove that the Riemann hypothesis implies a conjecture of Chandee on shifted moments of the Riemann zeta function. The proof is based on ideas of Harper concerning sharp upper bounds for the $2k$th moments of the Riemann zeta function on the critical line.
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On some multiplicative properties of large difference sets Can. J. Math. (IF 0.7) Pub Date : 2023-09-08 Ilya D. Shkredov
In our paper, we study multiplicative properties of difference sets $A-A$ for large sets $A \subseteq {\mathbb {Z}}/q{\mathbb {Z}}$ in the case of composite q. We obtain a quantitative version of a result of A. Fish about the structure of the product sets $(A-A)(A-A)$. Also, we show that the multiplicative covering number of any difference set is always small.
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An approximation formula for the shifted cubic moment of automorphic L-functions in the weight aspect Can. J. Math. (IF 0.7) Pub Date : 2023-09-06 Olga Balkanova, John Brian Conrey, Dmitry Frolenkov
Consider the family of automorphic L-functions associated with primitive cusp forms of level one, ordered by weight k. Assuming that k tends to infinity, we prove a new approximation formula for the cubic moment of shifted L-values over this family which relates it to the fourth moment of the Riemann zeta function. More precisely, the formula includes a conjectural main term, the fourth moment of the
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Sub-Bergman Hilbert spaces on the unit disk III Can. J. Math. (IF 0.7) Pub Date : 2023-08-22 Shuaibing Luo, Kehe Zhu
For a bounded analytic function $\varphi $ on the unit disk $\mathbb {D}$ with $\|\varphi \|_\infty \le 1$, we consider the defect operators $D_\varphi $ and $D_{\overline \varphi }$ of the Toeplitz operators $T_{\overline \varphi }$ and $T_\varphi $, respectively, on the weighted Bergman space $A^2_\alpha $. The ranges of $D_\varphi $ and $D_{\overline \varphi }$, written as $H(\varphi )$ and $H(\overline
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Simple eigenvalues of cubic vertex-transitive graphs Can. J. Math. (IF 0.7) Pub Date : 2023-08-10 Krystal Guo, Bojan Mohar
If ${\mathbf v} \in {\mathbb R}^{V(X)}$ is an eigenvector for eigenvalue $\lambda $ of a graph X and $\alpha $ is an automorphism of X, then $\alpha ({\mathbf v})$ is also an eigenvector for $\lambda $. Thus, it is rather exceptional for an eigenvalue of a vertex-transitive graph to have multiplicity one. We study cubic vertex-transitive graphs with a nontrivial simple eigenvalue, and discover remarkable
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On the period of Li, Pertusi, and Zhao’s symplectic variety Can. J. Math. (IF 0.7) Pub Date : 2023-08-04 Franco Giovenzana, Luca Giovenzana, Claudio Onorati
We extend classical results of Perego and Rapagnetta on moduli spaces of sheaves of type OG10 to moduli spaces of Bridgeland semistable objects on the Kuznetsov component of a cubic fourfold. In particular, we determine the period of this class of varieties and use it to understand when they become birational to moduli spaces of sheaves on a K3 surface.
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Assembling RKHS with Pick kernels and assembling polyhedra in Can. J. Math. (IF 0.7) Pub Date : 2023-08-03 Richard Rochberg
We study the geometry of Hilbert spaces with complete Pick kernels and the geometry of sets in complex hyperbolic space, taking advantage of the correspondence between the two topics. We focus on questions of assembling Hilbert spaces into larger spaces and of assembling sets into larger sets. Model questions include describing the possible three-dimensional subspaces of four-dimensional Hilbert spaces
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Sliding methods for tempered fractional parabolic problem Can. J. Math. (IF 0.7) Pub Date : 2023-07-28 Shaolong Peng
In this article, we are concerned with the tempered fractional parabolic problem $$ \begin{align*}\frac{\partial u}{\partial t}(x, t)-\left(\Delta+\lambda\right)^{\frac{\alpha}{2}} u(x, t)=f(u(x, t)), \end{align*} $$ where $-\left (\Delta +\lambda \right )^{\frac {\alpha }{2}}$ is a tempered fractional operator with $\alpha \in (0,2)$ and $\lambda $ is a sufficiently small positive constant. We first
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Sensitivity of mixing times of Cayley graphs Can. J. Math. (IF 0.7) Pub Date : 2023-07-18 Jonathan Hermon, Gady Kozma
We show that the total variation mixing time is not quasi-isometry invariant, even for Cayley graphs. Namely, we construct a sequence of pairs of Cayley graphs with maps between them that twist the metric in a bounded way, while the ratio of the two mixing times goes to infinity. The Cayley graphs serving as an example have unbounded degrees. For non-transitive graphs, we construct bounded degree graphs
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Some asymptotic formulae for torsion in homotopy groups Can. J. Math. (IF 0.7) Pub Date : 2023-06-29 Guy Boyde, Ruizhi Huang
Inspired by a remarkable work of Félix, Halperin, and Thomas on the asymptotic estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors on local hyperbolicity, we prove two asymptotic formulae for torsion rank of homotopy groups, one using ordinary homology and one using K-theory. We use these to obtain explicit quantitative asymptotic lower bounds on the torsion
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Cobordism distance on the projective space of the knot concordance group Can. J. Math. (IF 0.7) Pub Date : 2023-06-27 Charles Livingston
We use the cobordism distance on the smooth knot concordance group $\mathcal {C}$ to measure how close two knots are to being linearly dependent. Our measure, $\Delta (\mathcal {K}, \mathcal {J})$, is built by minimizing the cobordism distance between all pairs of knots, $\mathcal {K}'$ and $\mathcal {J}'$, in cyclic subgroups containing $\mathcal {K}$ and $\mathcal {J}$. When made precise, this leads
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Radius of comparison and mean topological dimension: -actions Can. J. Math. (IF 0.7) Pub Date : 2023-06-19 Zhuang Niu
Consider a minimal-free topological dynamical system $(X, \mathbb Z^d)$. It is shown that the radius of comparison of the crossed product C*-algebra $\mathrm {C}(X) \rtimes \mathbb Z^d$ is at most half the mean topological dimension of $(X, \mathbb Z^d)$. As a consequence, the C*-algebra $\mathrm {C}(X) \rtimes \mathbb Z^d$ is classified by the Elliott invariant if the mean dimension of $(X, \mathbb
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Quantitative inverse theorem for Gowers uniformity norms Can. J. Math. (IF 0.7) Pub Date : 2023-06-15 Luka Milićević
We prove quantitative bounds for the inverse theorem for Gowers uniformity norms $\mathsf {U}^5$ and $\mathsf {U}^6$ in $\mathbb {F}_2^n$. The proof starts from an earlier partial result of Gowers and the author which reduces the inverse problem to a study of algebraic properties of certain multilinear forms. The bulk of the work in this paper is a study of the relationship between the natural actions
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Schreier families and -(almost) greedy bases Can. J. Math. (IF 0.7) Pub Date : 2023-06-14 Kevin Beanland, Hùng Việt Chu
Let $\mathcal {F}$ be a hereditary collection of finite subsets of $\mathbb {N}$. In this paper, we introduce and characterize $\mathcal {F}$-(almost) greedy bases. Given such a family $\mathcal {F}$, a basis $(e_n)_n$ for a Banach space X is called $\mathcal {F}$-greedy if there is a constant $C\geqslant 1$ such that for each $x\in X$, $m \in \mathbb {N}$, and $G_m(x)$, we have $$ \begin{align*} \|x