SwePub - sökning: hsv:(NATURVETENSKAP) hsv:(Mate...

Numrering	Referens	Omslagsbild	Hitta
1.	Berndtsson, Bo, 1950 (författare) Probability measures associated to geodesics in the space of kähler metrics 2018 Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 269, s. 395-419 Konferensbidrag (refereegranskat)abstract We associate certain probability measures on R to geodesics in the space HL of positively curved metrics on a line bundle L, and to geodesics in the finite dimensional symmetric space of hermitian norms on H0(X, kL). We prove that the measures associated to the finite dimensional spaces converge weakly to the measures related to geodesics in HL as k goes to infinity. The convergence of second order moments implies a recent result of Chen and Sun on geodesic distances in the respective spaces, while the convergence of first order moments gives convergence of Donaldson’s Z-functional to the Aubin–Yau energy. We also include a result on approximation of infinite dimensional geodesics by Bergman kernels which generalizes work of Phong and Sturm.
2.	Xia, Jiacheng, 1991 (författare) Vector-valued Eisenstein series of congruence types and their products 2019 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
3.	Kurujyibwami, Celestin (författare) Admissible transformations and the group classification of Schrödinger equations 2017 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
4.	Berman, Robert, 1976 (författare) On the strict convexity of the K-energy 2019 Ingår i: Pure and Applied Mathematics Quarterly. - 1558-8599 .- 1558-8602. ; 15:4, s. 983-999 Tidskriftsartikel (refereegranskat)abstract Let (X, L) be a polarized projective complex manifold. We show, by a simple toric one-dimensional example, that Mabuchi's K-energy functional on the geodesically complete space of bounded positive (1, 1)-forms in c(1)(L), endowed with the Mabuchi-Donaldson-Semmes metric, is not strictly convex modulo automorphisms. However, under some further assumptions the strict convexity in question does hold in the toric case. This leads to a uniqueness result saying that a finite energy minimizer of the K-energy (which exists on any toric polarized manifold (X, L) which is uniformly K-stable) is uniquely determined modulo automorphisms under the assumption that there exists some minimizer with strictly positive curvature current.
5.	Kim, Inkang, et al. (författare) Toledo invariant of lattices in SU(2,1) via symmetric square 2020 Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 1089-7658 .- 0022-2488. ; 61:11 Tidskriftsartikel (refereegranskat)abstract In this paper, we address the issue of the quaternionic Toledo invariant to study the character variety of two-dimensional complex hyperbolic uniform lattices into SU(n, 2), n ≥ 4. We construct four distinct representations to prove that the character variety contains at least seven distinct components. We also show the existence of holomorphic horizontal lift to various period domains of SU(n, 2).
6.	Beckwith, O., et al. (författare) Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers 2020 Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : Proceedings of the National Academy of Sciences. - 0027-8424 .- 1091-6490. ; 117:36, s. 21953-21961 Tidskriftsartikel (refereegranskat)abstract In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on nonholomorphic generating series. We establish a divisibility result for such nonholomorphic congruences of Hurwitz class numbers. The two key tools in our proof are the holomorphic projection of products of theta series with a Hurwitz class number generating series and a theorem by Serre, which allows us to rule out certain congruences.
7.	Brandes, Julia, 1986 (författare) The density of rational lines on hypersurfaces: a bihomogeneous perspective 2021 Ingår i: Monatshefte für Mathematik. - : Springer Science and Business Media LLC. - 1436-5081 .- 0026-9255. ; 195:2, s. 191-231 Tidskriftsartikel (refereegranskat)abstract Let F be a non-singular homogeneous polynomial of degree d in n variables. We give an asymptotic formula of the pairs of integer points (x, y) with \| x\| ⩽ X and \| y\| ⩽ Y which generate a line lying in the hypersurface defined by F, provided that n> 2 d-1d4(d+ 1) (d+ 2). In particular, by restricting to Zariski-open subsets we are able to avoid imposing any conditions on the relative sizes of X and Y.
8.	Brannan, Michael, et al. (författare) Synchronicity for quantum non-local games 2023 Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 284:2 Tidskriftsartikel (refereegranskat)abstract We introduce concurrent quantum non-local games, quantum output mirror games and concurrent classical-to-quantum non-local games, as quantum versions of synchronous non-local games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes. We define -algebras and C-algebras of concurrent classical-to-quantum and concurrent quantum non-local games, and algebraic versions of the orthogonal rank of a graph. We show that quantum homomorphisms of quantum graphs can be viewed as entanglement assisted classical homomorphisms of the graphs, and give descriptions of the perfect quantum commuting and the perfect approximately quantum strategies for the quantum graph homomorphism game. We specialise the latter results to the case where the inputs of the game are based on a classical graph.
9.	Algebra, Geometry, and Mathematical Physics 2010 2012 Ingår i: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6596 .- 1742-6588. Samlingsverk (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract This proceedings volume presents results obtained by the participants of the 6th Baltic–Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25–30, 2010. The Baltic–Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic–Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic–Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers.
10.	Almquist, Martin, et al. (författare) Order-preserving interpolation for summation-by-parts operators at nonconforming grid interfaces 2019 Ingår i: SIAM Journal of Scientific Computing. - : Society for Industrial and Applied Mathematics Publications. - 1064-8275 .- 1095-7197. ; 41:2, s. A1201-A1227 Tidskriftsartikel (refereegranskat)abstract We study nonconforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a reduction of the global convergence rate by one order, due to large truncation errors at the nonconforming interface. We avoid the order reduction by generalizing the interface treatment and introducing order-preserving interpolation operators. We prove that, given two diagonal-norm summation-by-parts schemes, order-preserving interpolation operators with the necessary properties are guaranteed to exist, regardless of the grid-point distributions along the interface. The new methods retain the stability and global accuracy properties of the underlying schemes for conforming interfaces.
11.	Arkeryd, Leif, 1940, et al. (författare) On stationary solutions to normal, coplanar discrete Boltzmann equation models 2020 Ingår i: Communications in Mathematical Sciences. - 1539-6746 .- 1945-0796. ; 18:8, s. 2215-2234 Tidskriftsartikel (refereegranskat)abstract The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with L-1- compactness for the integrated collision frequency and gain term. L-1-compactness of a sequence of approximations is obtained using the Kolmogorov-Riesz theorem and replaces the L-1-compactness of velocity averages in the continuous velocity case, not available when the velocities are discrete.
12.	Bandara, L., et al. (författare) Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary 2021 Ingår i: Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze. - : Scuola Normale Superiore - Edizioni della Normale. - 0391-173X .- 2036-2145. ; 22:4, s. 1843-1878 Tidskriftsartikel (refereegranskat)abstract Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This is known as a rough Riemannian manifold. For a large class of boundary conditions we demonstrate a Weyl law for the asymptotics of the eigenvalues of the Laplacian associated to a rough metric. Moreover, we obtain eigenvalue asymptotics for weighted Laplace equations associated to a rough metric. Of particular novelty is that the weight function is not assumed to be of fixed sign, and thus the eigenvalues may be both positive and negative. Key ingredients in the proofs were demonstrated by Birman and Solomjak nearly fifty years ago in their seminal work on eigenvalue asymptotics. In addition to determining the eigenvalue asymptotics in the rough Riemannian manifold setting for weighted Laplace equations, we also wish to promote their achievements which may have further applications to modern problems.
13.	Bandara, L., et al. (författare) Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric 2018 Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 370:1-2, s. 863-915 Tidskriftsartikel (refereegranskat)abstract We prove that the Atiyah-Singer Dirac operator D-g in L-2 depends Riesz continuously L-infinity on perturbations of complete metrics on a smooth manifold. The Lipschitz bound for the map g -> D-g(1 + D-g(2))(-1/2) depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Caldern's first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles.
14.	Bandara, Lashi, et al. (författare) Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of local boundary conditions 2019 Ingår i: Communications in Partial Differential Equations. - : Informa UK Limited. - 0360-5302 .- 1532-4133. ; 44:12, s. 1253-1284 Tidskriftsartikel (refereegranskat)abstract On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah–Singer Dirac operator /DB in L2 depends Riesz continuously on L∞ perturbations of local boundary conditions B. The Lipschitz bound for the map B→/DB(1+/D2B)−12 depends on Lipschitz smoothness and ellipticity of B and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.
15.	Bauer, M., et al. (författare) Semi-invariant Riemannian metrics in hydrodynamics 2020 Ingår i: Calculus of Variations and Partial Differential Equations. - : Springer Science and Business Media LLC. - 0944-2669 .- 1432-0835. ; 59:2 Tidskriftsartikel (refereegranskat)abstract Many models in mathematical physics are given as non-linear partial differential equation of hydrodynamic type; the incompressible Euler, KdV, and Camassa-Holm equations are well-studied examples. A beautiful approach to well-posedness is to go from the Eulerian to a Lagrangian description. Geometrically it corresponds to a geodesic initial value problem on the infinite-dimensional group of diffeomorphisms with a right invariant Riemannian metric. By establishing regularity properties of the Riemannian spray one can then obtain local, and sometimes global, existence and uniqueness results. There are, however, many hydrodynamic-type equations, notably shallow water models and compressible Euler equations, where the underlying infinite-dimensional Riemannian structure is not fully right invariant, but still semi-invariant with respect to the subgroup of volume preserving diffeomorphisms. Here we study such metrics. For semi-invariant metrics of Sobolev Hk-type we give local and some global well-posedness results for the geodesic initial value problem. We also give results in the presence of a potential functional (corresponding to the fluid's internal energy). Our study reveals many pitfalls in going from fully right invariant to semi-invariant Sobolev metrics; the regularity requirements, for example, are higher. Nevertheless the key results, such as no loss or gain in regularity along geodesics, can be adopted.
16.	Bogfjellmo, Geir, 1987, et al. (författare) A Numerical Algorithm for C-2-Splines on Symmetric Spaces 2018 Ingår i: SIAM Journal on Numerical Analysis. - : Siam Publications. - 1095-7170 .- 0036-1429. ; 56:4, s. 2623-2647 Tidskriftsartikel (refereegranskat)abstract Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example, computer vision and quantum control, there is a growing need for spline interpolation on curved, non-Euclidean space. The generalization of cubic splines to manifolds is not self-evident, with several distinct approaches. One possibility is to mimic the acceleration minimizing property, which leads to Riemannian cubics. This, however, requires the solution of a coupled set of nonlinear boundary value problems that cannot be integrated explicitly, even if formulae for geodesics are available. Another possibility is to mimic De Casteljau's algorithm, which leads to generalized .Bezier curves. To construct C-2-splines from such curves is a complicated nonlinear problem, until now lacking numerical methods. Here we provide an iterative algorithm for C-2-splines on Riemannian symmetric spaces, and we prove convergence of linear order. In terms of numerical tractability and computational efficiency, the new method surpasses those based on Riemannian cubics. Each iteration is parallel and thus suitable for multicore implementation. We demonstrate the algorithm for three geometries of interest: the n-sphere, complex projective space, and the real Grassmannian.
17.	Elfverson, Daniel, et al. (författare) Multiscale methods for problems with complex geometry 2017 Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 321, s. 103-123 Tidskriftsartikel (refereegranskat)abstract We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We construct corrected coarse test and trail spaces which takes the fine scale features of the computational domain into account. The corrections only need to be computed in regions surrounding fine scale geometric features. We achieve linear convergence rate in the energy norm for the multiscale solution. Moreover, the conditioning of the resulting matrices is not affected by the way the domain boundary cuts the coarse elements in the background mesh. The analytical findings are verified in a series of numerical experiments.
18.	Frahm, J., et al. (författare) An extension problem related to the fractional Branson-Gover operators 2020 Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 278:5 Tidskriftsartikel (refereegranskat)abstract The Branson-Gover operators are conformally invariant differential operators of even degree acting on differential forms. They can be interpolated by a holomorphic family of conformally invariant integral operators called fractional Branson-Gover operators. For Euclidean spaces we show that the fractional Branson-Gover operators can be obtained as Dirichlet-to-Neumann operators of certain conformally invariant boundary value problems, generalizing the work of Caffarelli-Silvestre for the fractional Laplacians to differential forms. The relevant boundary value problems are studied in detail and we find appropriate Sobolev type spaces in which there exist unique solutions and obtain the explicit integral kernels of the solution operators as well as some of their properties. (C) 2019 Elsevier Inc. All rights reserved.
19.	Jensen, M., et al. (författare) Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions 2022 Ingår i: Ima Journal of Numerical Analysis. - : Oxford University Press (OUP). - 0272-4979 .- 1464-3642. ; 42:1, s. 199-228 Tidskriftsartikel (refereegranskat)abstract We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the spatial discretization and the backward Euler scheme for the temporal discretization. Furthermore, we prove uniqueness and higher regularity of the solution on creased domains and additional regularity in the interior of the domain. Due to a variational formulation with a cut-off functional, the convergence analysis does not require a discrete maximum principle, permitting approximation spaces suitable for adaptive mesh refinement, responding to the difference in regularity within the domain.
20.	Khesin, Boris, et al. (författare) Newton's Equation on Diffeomorphisms and Densities 2017 Ingår i: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - Cham : Springer International Publishing. - 1611-3349 .- 0302-9743. - 9783319684451 ; 10589, s. 873-873 Konferensbidrag (refereegranskat)abstract We develop a geometric framework for Newton-type equations on the infinite-dimensional configuration space of probability densities. It can be viewed as a second order analogue of the "Otto calculus" framework for gradient flow equations. Namely, for an n-dimensional manifold M we derive Newton's equations on the group of diffeomorphisms Diff(M) and the space of smooth probability densities Dens(M), as well as describe the Hamiltonian reduction relating them. For example, the compressible Euler equations are obtained by a Poisson reduction of Newton's equation on Diff(M) with the symmetry group of volume-preserving diffeomorphisms, while the Hamilton-Jacobi equation of fluid mechanics corresponds to potential solutions. We also prove that the Madelung transform between Schrodinger-type and Newton's equations is a symplectomorphism between the corresponding phase spaces T* Dens(M) and PL2 (M, C). This improves on the previous symplectic submersion result of von Renesse [1]. Furthermore, we prove that the Madelung transform is a Kahler map provided that the space of densities is equipped with the (prolonged) Fisher-Rao information metric and describe its dynamical applications. This geometric setting for the Madelung transform sheds light on the relation between the classical Fisher-Rao metric and its quantum counterpart, the Bures metric. In addition to compressible Euler, Hamilton-Jacobi, and linear and nonlinear Schrodinger equations, the framework for Newton equations encapsulates Burgers' inviscid equation, shallow water equations, two-component and mu-Hunter-Saxton equations, the Klein-Gordon equation, and infinite-dimensional Neumann problems.
21.	Maurelli, M., et al. (författare) Incompressible Euler equations with stochastic forcing: A geometric approach 2023 Ingår i: Stochastic Processes and Their Applications. - : Elsevier BV. - 0304-4149. ; 159, s. 101-148 Tidskriftsartikel (refereegranskat)abstract We consider a stochastic version of Euler equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden (1970). For the Euler equations on a compact manifold (possibly with smooth boundary) we establish local existence and uniqueness of a strong solution in spaces of Sobolev mappings (of high enough regularity). Our approach combines techniques from stochastic analysis and infinite-dimensional geometry and provides a novel toolbox to establish local well-posedness of stochastic non-linear partial differential equations.(c) 2023 Elsevier B.V. All rights reserved.
22.	Modin, Klas, 1979, et al. (författare) Integrability of Point-Vortex Dynamics via Symplectic Reduction: A Survey 2021 Ingår i: Arnold Mathematical Journal. - : Springer Science and Business Media LLC. - 2199-6792 .- 2199-6806. ; 7:3, s. 357-385 Tidskriftsartikel (refereegranskat)abstract Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on two-dimensional manifolds. Integrability results for few point-vortices on various domains is a vivid topic, with many results and techniques scattered in the literature. Here, we give a unified framework for proving integrability results for N= 2 , 3, or 4 point-vortices (and also more general Hamiltonian systems), based on symplectic reduction theory. The approach works on any two-dimensional manifold with a symmetry group; we illustrate it on the sphere, the plane, the hyperbolic plane, and the flat torus. A systematic study of integrability is prompted by advances in two-dimensional turbulence, bridging the long-time behaviour of 2D Euler equations with questions of point-vortex integrability. A gallery of solutions is given in the appendix.
23.	Nyagahakwa, Venuste, et al. (författare) Sets with the Baire property in topologies formed from a given topology and ideals of sets 2017 Ingår i: Questions and answers in General Topology. - Osaka : Symposium of General Topology / Iso Shinpojumu. - 0918-4732. ; 35:1, s. 59-76 Tidskriftsartikel (refereegranskat)abstract Let X be a set, τ1, τ2 topologies on X and Bp(X, τi) the family of all subsets of X possessing the Baire property in (X, τi), i = 1, 2. In this paper we study conditions on τ1 and τ2 that imply a relationship (for example, inclusion or equality) between the families Bp(X, τ1) and Bp(X, τ2). We are mostly interested in the case where the topology τ2 is formed with the help of a local function defined by the topology τ1 and an ideal of sets I on X. We also consider several applications of the local function defined by the usual topology on the reals and the ideal of all meager sets there, for proving some known facts.
24.	Rowlett, Julie, 1978, et al. (författare) How to hear the corners of a drum 2019 Ingår i: Matrix Annals. - Cham : Springer International Publishing. ; 2017, s. 243-278, s. 243-278 Konferensbidrag (refereegranskat)abstract We prove that the existence of corners in a class of planar domain, which includes all simply connected polygonal domains and all smoothly bounded domains, is a spectral invariant of the Laplacian with both Neumann and Robin boundary conditions. The main ingredient in the proof is a locality principle in the spirit of Kac’s “principle of not feeling the boundary,” but which holds uniformly up to the boundary. Albeit previously known for Dirichlet boundary condition, this appears to be new for Robin and Neumann boundary conditions, in the geometric generality presented here. For the case of curvilinear polygons, we describe how the same arguments using the locality principle are insufficient to obtain the analogous result. However, we describe how one may be able to harness powerful microlocal methods and combine these with the locality principles demonstrated here to show that corners are a spectral invariant; this is current work-in-progress (Nursultanov et al., Preprint).
25.	Samuelsson Kalm, Håkan, 1976 (författare) The dbar-equation, duality, and holomorphic forms on a reduced complex space 2021 Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 31:2, s. 1786-1820 Tidskriftsartikel (refereegranskat)abstract We solve the $\bar\partial$-equation for (p, q)-forms locally on any reduced pure-dimensional complex space and we prove an explicit version of Serre duality by introducing suitable concrete fine sheaves of certain (p, q)-currents. In particular this gives a condition for the partial derivative-equation to be globally solvable. Our results also give information about holomorphic p-forms on singular spaces.
26.	Caraiani, Ana, et al. (författare) Vanishing theorems for Shimura varieties at unipotent level 2023 Ingår i: Journal of the European Mathematical Society. - 1435-9863 .- 1435-9855. ; 25:3, s. 869-911 Tidskriftsartikel (refereegranskat)abstract We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite Γ1.p1/-level (defined with respect to a Borel subgroup) vanishes above the middle degree, under the assumption that the group of the Shimura datum splits at p. This generalizes and strengthens the vanishing result proved in [A. Caraiani et al., Compos. Math. 156 (2020)]. As an application of this vanishing theorem, we prove a result on the codimensions of ordinary completed homology for the same groups, analogous to conjectures of Calegari–Emerton for completed (Borel–Moore) homology.
27.	Holroyd, Alexander E., et al. (författare) Minimal matchings of point processes 2022 Ingår i: Probability Theory and Related Fields. - : Springer Science and Business Media LLC. - 0178-8051 .- 1432-2064. ; 184:1-2, s. 571-611 Tidskriftsartikel (refereegranskat)abstract Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in R-d. For a positive (respectively, negative) parameter gamma we consider red-blue matchings that locally minimize (respectively, maximize) the sum of gamma th powers of the edge lengths, subject to locally minimizing the number of unmatched points. The parameter can be viewed as a measure of fairness. The limit gamma -> -infinity is equivalent to Gale-Shapley stable matching. We also consider limits as gamma approaches 0, 1-, 1+ and infinity. We focus on dimension d = 1. We prove that almost surely no such matching has unmatched points. (This question is open for higher d). For each gamma < 1 we establish that there is almost surely a unique such matching, and that it can be expressed as a finitary factor of the points. Moreover, its typical edge length has finite rth moment if and only if r < 1 /2. In contrast, for gamma = 1 there are uncountably many matchings, while for gamma > 1 there are countably many, but it is impossible to choose one in a translation-invariant way. We obtain existence results in higher dimensions (covering many but not all cases). We address analogous questions for one-colour matchings also.
28.	Meisner, Patrick, et al. (författare) Low-lying zeros in families of elliptic curve L-functions over function fields 2022 Ingår i: Finite Fields and their Applications. - : Elsevier BV. - 1071-5797 .- 1090-2465. ; 84 Tidskriftsartikel (refereegranskat)abstract We investigate the low-lying zeros in families of L-functions attached to quadratic and cubic twists of elliptic curves defined over Fq(T). In particular, we present precise expressions for the expected values of traces of high powers of the Frobenius class in these families with a focus on the lower order behavior. As an application we obtain results on one-level densities and we verify that these elliptic curve families have orthogonal symmetry type. In the quadratic twist families our results refine previous work of Comeau-Lapointe. Moreover, in this case we find a lower order term in the one-level density reminiscent of the deviation term found by Rudnick in the hyperelliptic ensemble. On the other hand, our investigation is the first to treat these questions in families of cubic twists of elliptic curves and in this case it turns out to be more complicated to isolate lower order terms due to a larger degree of cancellation among lower order contributions.
29.	Gardella, Eusebio, et al. (författare) Strongly outer actions of amenable groups on Z-stable nuclear C-algebras 2022 Ingår i:* Journal des Mathématiques Pures et Appliquées. - : Elsevier BV. - 0021-7824. ; 162, s. 76-123 Tidskriftsartikel (refereegranskat)abstract Let A be a separable, unital, simple, Z-stable, nuclear C*-algebra, and let alpha: G -+ Aut(A) be an action of a discrete, countable, amenable group. Suppose that the orbits of the action of G on T(A) are finite and that their cardinality is bounded. We show that the following are equivalent: (1) alpha is strongly outer; (2) alpha (R) idZ has the weak tracial Rokhlin property. If G is moreover residually finite, the above conditions are also equivalent to (3) alpha (R) idZ has finite Rokhlin dimension (in fact, at most 2). If partial differential eT(A) is furthermore compact, has finite covering dimension, and the orbit space partial differential eT(A)/G is Hausdorff, we generalize results by Matui and Sato to show that alpha is cocycle conjugate to alpha (R) idZ, even if alpha is not strongly outer. In particular, in this case the equivalences above hold for alpha in place of alpha (R) idZ. In the course of the proof, we develop equivariant versions of complemented partitions of unity and uniform property Gamma as technical tools of independent interest. (c) 2022 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
30.	Goffeng, Magnus C H T, 1987, et al. (författare) Constructing KMS states from infinite-dimensional spectral triples 2019 Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 143, s. 107-149 Tidskriftsartikel (refereegranskat)abstract We construct KMS-states from Li1-summable semifinite spectral triples and show that in several important examples the construction coincides with well-known direct constructions of KMS-states for naturally defined flows. Under further summability assumptions the constructed KMS-state can be computed in terms of Dixmier traces. For closed manifolds, we recover the ordinary Lebesgue integral. For Cuntz–Pimsner algebras with their gauge flow, the construction produces KMS-states from traces on the coefficient algebra and recovers the Laca–Neshveyev correspondence. For a discrete group acting on its Stone–Čech boundary, we recover the Patterson–Sullivan measures on the Stone-Čech boundary for a flow defined from the Radon–Nikodym cocycle.
31.	Heinrich, Katharina, et al. (författare) The space of twisted cubics 2021 Ingår i: Epijournal de Geometrie Algebrique. - : Centre pour la Communication Scientifique Directe (CCSD). - 2491-6765. ; 5, s. 1-22 Tidskriftsartikel (refereegranskat)abstract We consider the Cohen-Macaulay compactification of the space of twisted cubics in Pn. This compactification is the fine moduli scheme representing the functor of CM-curves with Hilbert polynomial 3t + 1. We show that the moduli scheme of CM-curves in P3 is isomorphic to the twisted cubic component of the Hilbert scheme. We also describe the compactification for twisted cubics in Pn
32.	Pejlare, Johanna, 1976, et al. (författare) On the relations between geometry and algebra in Gestrinius' edition of Euclid's Elements 2016 Ingår i: Radford, L., Furinghetti, F., & Hausberger, T. (Eds.) (2016). Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics. Montpellier, France: IREM de Montpellier.. - 2909916510 ; , s. 513-523 Konferensbidrag (refereegranskat)abstract In 1637 the Swedish mathematician Martinus Erici Gestrinius contributed with a commented edition of Euclid’s Elements. In this article we analyse the relationship between geometry and algebra in Gestrinius’ Elements, as presented in Book II. Of particular interest are Propositions 4, 5, and 6, dealing with straight lines cut into equal and unequal parts, and the three kinds of quadratic equations Gestrinius associates with them. We argue that Gestrinius followed Clavius translation of the Elements, but was influenced by Ramus to include algebra.
33.	Pejlare, Johanna, 1976 (författare) On the relationships between the geometric and the algebraic ideas in Duhre’s textbooks of mathematics, as reflected via Book II of Euclid’s Elements 2017 Ingår i: “DIG WHERE YOU STAND” 4. Proceedings of the Fourth International Conference on the History of Mathematics Education. 23-26 September, 2015. Torino, Italy. - Roma : Edizioni Nuova Cultura. - 9788868128647 Konferensbidrag (refereegranskat)abstract The present article explores the relationships between the geometric and algebraic ideas presented in Anders Gabriel Duhre’s mathematics textbooks. Of particular interest is Book II of Euclid’s Elements as presented by Duhre in his textbook on geometry from 1721. We consider in detail Duhre’s two versions of Proposition II.5, dealing with straight lines cut into equal and unequal parts, as well as the two proofs of the propositions that he presents. Duhre’s formulations are slightly different from traditional geometric formulations, as he moved away from a purely geometrical context towards an algebraic one. Duhre established Proposition II.5 using algebra in Descartes’ notation as well as in the notation of Wallis and Oughtred. Duhre ́s reason for introducing algebra in Book II of Euclid’s Elements was to obtain convenience in calculations, as well as the possibility to generalize results to different kinds of quantities.
34.	Alaghmandan, Mahmood, 1983, et al. (författare) Completely bounded maps and invariant subspaces 2020 Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 294:1-2, s. 471-489 Tidskriftsartikel (refereegranskat)
35.	Albin, Patrik, 1960 (författare) ON EXTREME VALUE THEORY FOR GROUP STATIONARY GAUSSIAN PROCESSES 2018 Ingår i: Esaim-Probability and Statistics. - : EDP Sciences. - 1292-8100 .- 1262-3318. ; 22, s. 1-18 Tidskriftsartikel (refereegranskat)abstract We study extreme value theory of right stationary Gaussian processes with parameters in open subsets with compact closure of (not necessarily Abelian) locally compact topological groups. Even when specialized to Euclidian space our result extend results on extremes of stationary Gaussian processes and fields in the literature by means of requiring weaker technical conditions as well as by means of the fact that group stationary processes need not be stationary in the usual sense (that is, with respect to addition as group operation).
36.	Aldana, C. L., et al. (författare) A Polyakov Formula for Sectors 2018 Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 28:2, s. 1773-1839 Tidskriftsartikel (refereegranskat)abstract We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using Carslaw-Sommerfeld's heat kernel. We also compute the zeta-regularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.
37.	Andersson, Mats, 1957 (författare) A global Briançon-Skoda-Huneke-Sznajdman theorem 2018 Ingår i: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 1903-1807 .- 0025-5521. ; 122:1, s. 31-52 Tidskriftsartikel (refereegranskat)abstract We prove a global effective membership result for polynomials on a non-reduced algebraic sub variety of C-N. It can be seen as a global version of a recent local result of Sznajdman. generalizine the Briancon-Skoda-Huneke theorem for the local ring of holomorphic functions at a point on a reduced analytic space.
38.	Andersson, Mats, 1957, et al. (författare) Global representation of Segre numbers by Monge–Ampère products 2021 Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 380:1-2, s. 349-391 Tidskriftsartikel (refereegranskat)abstract On a reduced analytic space X we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient B(X) that we think of as an analogue of the Chow group and a refinement of de Rham cohomology. This group allows us to study both global and local intersection theoretic properties. We provide many B-analogues of classical intersection theoretic constructions: For an analytic subspace V⊂ X we define a B-Segre class, which is an element of B(X) with support in V. It satisfies a global King formula and, in particular, its multiplicities at each point coincide with the Segre numbers of V. When V is cut out by a section of a vector bundle we interpret this class as a Monge–Ampère-type product. For regular embeddings we construct a B-analogue of the Gysin morphism.
39.	Andersson, Mats, 1957, et al. (författare) Non-pluripolar energy and the complex Monge-Ampere operator 2022 Ingår i: Journal Fur Die Reine Und Angewandte Mathematik. - : Walter de Gruyter GmbH. - 0075-4102 .- 1435-5345. ; 2022:792, s. 145-188 Tidskriftsartikel (refereegranskat)abstract Given a domain Omega subset of C-n we introduce a class of plurisubharmonic (psh) functions G(Omega) and Monge-Ampere operators u -> [dd(c)u](p), p <= n, on G(Omega) that extend the Bedford-Taylor-Demailly Monge-Ampere operators. Here [dd(c)u](p) is a closed positive current of bidegree (p, p) that dominates the non-pluripolar Monge-Ampere current < dd(c)u >(p). We prove that [dd(c)u](p) is the limit of Monge-Ampere currents of certain natural regularizations of u. On a compact Kahler manifold (X, omega) we introduce a notion of non-pluripolar energy and a corresponding finite energy class G(X, omega) subset of PSH(X, omega) that is a global version of the class G(Omega). From the local construction we get global Monge-Ampere currents [dd(c)phi + omega](p) for phi is an element of G(X, omega) that only depend on the current dd(c)phi + omega. The limits of Monge-Ampere currents of certain natural regularizations of phi can be expressed in terms of [dd(c)phi + omega](j) for j <= p. We get a mass formula involving the currents [dd(c)phi + omega](p) that describes the loss of mass of the non-pluripolar Monge-Ampere measure < dd(c)phi + omega >(n). The class G(X, omega) includes omega-psh functions with analytic singularities and the class E(X, omega) of omega-psh functions of finite energy and certain other convex energy classes, although it is not convex itself.
40.	Andersson, Mats, 1957, et al. (författare) Nonproper intersection products and generalized cycles 2021 Ingår i: European Journal of Mathematics. - : Springer Science and Business Media LLC. - 2199-675X .- 2199-6768. ; 7:4, s. 1337-1381 Tidskriftsartikel (refereegranskat)abstract We develop intersection theory in terms of the B-group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct images of Chern forms and it contains all usual cycles. However, contrary to Chow classes, the B-classes have well-defined multiplicities at each point. We focus on a B-analogue of the intersection theory based on the Stuckrad-Vogel procedure and the join construction in projective space. Our approach provides global B-classes which satisfy a Bezout theorem and have the expected local intersection numbers. We also introduce B-analogues of more classical constructions of intersections using the Gysin map of the diagonal. These constructions are connected via a B-variant of van Gastel's formulas. Furthermore, we prove that our intersections coincide with the classical ones on cohomology level.
41.	Andersson, Mats, 1957, et al. (författare) On a Monge-Ampere Operator for Plurisubharmonic Functions with Analytic Singularities 2019 Ingår i: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518. ; 68:4, s. 1217-1231 Tidskriftsartikel (refereegranskat)abstract We study continuity properties of generalized Monge-Ampere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a formula for the total mass of the Monge-Ampere measure of such a function on a compact Kahler manifold.
42.	Atai, F., et al. (författare) Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation 2021 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 388:1, s. 435-468 Tidskriftsartikel (refereegranskat)abstract The super-Macdonald polynomials, introduced by Sergeev andVeselov (Commun Math Phys 288: 653-675, 2009), generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed Macdonald-Ruijsenaars operators introduced by the same authors in Sergeev and Veselov (CommunMath Phys 245: 249-278, 2004). We introduce a Hermitian form on the algebra spanned by the super-Macdonald polynomials, prove their orthogonality, compute their (quadratic) norms explicitly, and establish a corresponding Hilbert space interpretation of the super-Macdonald polynomials and deformed MacdonaldRuijsenaars operators. This allows for a quantum mechanical interpretation of the models defined by the deformedMacdonald-Ruijsenaars operators. Motivated by recent results in the nonrelativistic (q -> 1) case, we propose that these models describe the particles and anti-particles of an underlying relativistic quantum field theory, thus providing a natural generalisation of the trigonometric Ruijsenaars model.
43.	Balkanova, Olga, 1988, et al. (författare) Prime geodesic theorem for the Picard manifold 2020 Ingår i: Advances in Mathematics. - : Elsevier BV. - 1090-2082 .- 0001-8708. ; 375 Tidskriftsartikel (refereegranskat)abstract Let Γ=PSL(2,Z[i]) be the Picard group and H3 be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient Γ∖H3, called the Picard manifold, obtaining an error term of size O(X3/2+θ/2+ϵ), where θ denotes a subconvexity exponent for quadratic Dirichlet L-functions defined over Gaussian integers.
44.	Beckwith, Olivia, et al. (författare) Congruences of Hurwitz class numbers on square classes 2022 Ingår i: Advances in Mathematics. - : Elsevier BV. - 1090-2082 .- 0001-8708. ; 409 Tidskriftsartikel (refereegranskat)abstract We extend a holomorphic projection argument of our earlier work to prove a novel divisibility result for non-holomorphic congruences of Hurwitz class numbers. This result allows us to establish Ramanujan-type congruences for Hurwitz class numbers on square classes, where the holomorphic case parallels previous work by Radu on partition congruences. We offer two applications. The first application demonstrates common divisibility features of Ramanujan-type congruences for Hurwitz class numbers. The second application provides a dichotomy between congruences for class numbers of imaginary quadratic fields and Ramanujan-type congruences for Hurwitz class numbers.
45.	Berman, Robert, 1976, et al. (författare) Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs 2014 Ingår i: Geometric and Functional Analysis. - : Springer Science and Business Media LLC. - 1016-443X .- 1420-8970. ; 24:6, s. 1683-1730 Tidskriftsartikel (refereegranskat)abstract Let X be a canonically polarized variety, i.e. a complex projective variety such that its canonical class KXdefines an ample (Formula presented.)-line bundle, and satisfying the conditions G1and S2. Our main result says that X admits a Kähler–Einstein metric iff X has semi-log canonical singularities i.e. iff X is a stable variety in the sense of Kollár–Shepherd-Barron and Alexeev (whose moduli spaces are known to be compact). By definition a Kähler–Einstein metric in this singular context simply means a Kähler–Einstein on the regular locus of X with volume equal to the algebraic volume of KX, i.e. the top intersection number of KX. We also show that such a metric is uniquely determined and extends to define a canonical positive current in c1(KX). Combined with recent results of Odaka our main result shows that X admits a Kähler–Einstein metric iff X is K-stable, which thus confirms the Yau–Tian–Donaldson conjecture in this general setting of (possibly singular) canonically polarized varieties. More generally, our results are shown to hold in the setting of log minimal varieties and they also generalize some prior results concerning Kähler–Einstein metrics on quasi-projective varieties.
46.	Berndtsson, Bo, 1950, et al. (författare) ALGEBRAIC FIBER SPACES and CURVATURE of HIGHER DIRECT IMAGES 2022 Ingår i: Journal of the Institute of Mathematics of Jussieu. - 1474-7480 .- 1475-3030. ; 21:3, s. 973-1028 Tidskriftsartikel (refereegranskat)abstract Let p : X → Y be an algebraic fiber space, and let L be a line bundle on. In this article, we obtain a curvature formula for the higher direct images of ΩiX/Y ⊗ L restricted to a suitable Zariski open subset of X. Our results are particularly meaningful if L is semi-negatively curved on X and strictly negative or trivial on smooth fibers of p. Several applications are obtained, including a new proof of a result by Viehweg-Zuo in the context of a canonically polarized family of maximal variation and its version for Calabi-Yau families. The main feature of our approach is that the general curvature formulas we obtain allow us to bypass the use of ramified covers - and the complications that are induced by them.
47.	Berndtsson, Bo, 1950 (författare) Bergman kernels for Paley-Wiener spaces and Nazarov’s proof of the Bourgain-Milman theorem 2022 Ingår i: Pure and Applied Mathematics Quarterly. - 1558-8599 .- 1558-8602. ; 18:2, s. 395-409 Tidskriftsartikel (refereegranskat)abstract We give a general inequality for Bergman kernels of Bergman spaces defined by certain convex weights in Cn. We also discuss how this can be used in Nazarov’s proof of the BourgainMilman theorem, as a substitute for Hörmander’s estimates for the ¯∂-equation.
48.	Berndtsson, Bo, 1950, et al. (författare) COMPLEX LEGENDRE DUALITY 2020 Ingår i: American Journal of Mathematics. - : Project Muse. - 0002-9327 .- 1080-6377. ; 142:1, s. 323-339 Tidskriftsartikel (refereegranskat)abstract We introduce complex generalizations of the classical Legendre transform, operating on Kahler metrics on a compact complex manifold. These Legendre transforms give explicit local isometric symmetries for the Mabuchi metric on the space of Kaler metrics around any real analytic Kahler metric, answering a question originating in Semmes' work.
49.	Berndtsson, Bo, 1950 (författare) Plurisubharmonic functions and real submanifolds of ℂ n 2023 Ingår i: Indagationes Mathematicae. - : Elsevier BV. - 0019-3577. ; 34:2, s. 357-366 Tidskriftsartikel (refereegranskat)abstract We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold M. Applications are given to the Hausdorff measure of the intersection of the variety with M and the exponential integrability of plurisubharmonic functions on M.
50.	Bershtein, O., et al. (författare) Maximum modulus principle for "holomorphic functions" on the quantum matrix ball 2019 Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 276:5, s. 1479-1509 Tidskriftsartikel (refereegranskat)abstract We describe the Shilov boundary ideal for a q-analog of the algebra of holomorphic functions on the unit ball in the space of n x n matrices and show that its C-envelope is isomorphic to the C-algebra of continuous functions on the quantum unitary group U-q(n). (C) 2018 Elsevier Inc. All rights reserved.

Skapa referenser, mejla, bekava och länka

Länka till träfflistan

Träfflista för sökning "hsv:(NATURVETENSKAP) hsv:(Matematik) hsv:(Geometri) "

Avgränsa träffmängd

År