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Numrering	Referens	Omslagsbild	Hitta
1.	Sorooshian, Shahryar, 1980, et al. (författare) Expedited analytical hierarchical process for multicriteria decision making 2022 Ingår i: ICIC Express Letters. - 1881-803X. ; 16:2, s. 145-151 Tidskriftsartikel (refereegranskat)abstract In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
2.	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.
3.	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.
4.	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.
5.	Proceedings of the 2010 Winter Simulation Conference 2010 Samlingsverk (redaktörskap) (refereegranskat)
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.	Casarino, V., et al. (författare) On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one 2024 Ingår i: Annali Di Matematica Pura Ed Applicata. - 0373-3114 .- 1618-1891. ; 203:1, s. 205-219 Tidskriftsartikel (refereegranskat)abstract Consider the variation seminorm of the Ornstein-Uhlenbeck semigroup Ht in dimension one, taken with respect to t. We show that this seminorm defines an operator of weak type (1, 1) for the relevant Gaussian measure. The analogous Lp estimates for 1 < p < 8 were already known.
11.	Lundengård, Karl, 1987- (författare) Generalized Vandermonde matrices and determinants in electromagnetic compatibility 2017 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.
12.	Arnlind, Joakim, et al. (författare) Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras 2011 Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 52:12, s. 123502- Tidskriftsartikel (refereegranskat)abstract As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]
13.	Balkanova, O., et al. (författare) NON-VANISHING OF MAASS FORM L-FUNCTIONS AT THE CENTRAL POINT 2021 Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 149:2, s. 509-523 Tidskriftsartikel (refereegranskat)abstract In this paper, we consider the family {L-j(s)}(j=1)(infinity) of L-functions associated to an orthonormal basis {u(j)}(j=1)(infinity) of even Hecke-Maass forms for the modular group SL(2, Z) with eigenvalues {lambda(j) = kappa(2)(j) + 1/4}(j=1)(infinity). We prove the following effective non-vanishing result: At least 50% of the central values L-j(1/2) with kappa(j) <= T do not vanish as T -> infinity. Furthermore, we establish effective non-vanishing results in short intervals.
14.	Mertens, M. H., et al. (författare) Modular forms of virtually real-arithmetic type I: Mixed mock modular forms yield vector-valued modular forms 2021 Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 28:2, s. 511-561 Tidskriftsartikel (refereegranskat)abstract The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals. Applications beyond number theory range from combinatorics, geometry, and representation theory to string theory and conformal field theory. We unify these relaxed notions in the framework of vector-valued modular forms by introducing a new class of SL2(Z)-representations: virtually real-arithmetic types. The key point of the paper is that virtually real-arithmetic types are in general not completely reducible. We obtain a rationality result for Fourier and Taylor coefficients of associated modular forms.
15.	Raum, Martin (författare) Relations among Ramanujan-type congruences I 2022 Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 409 Tidskriftsartikel (refereegranskat)abstract We prove that Ramanujan-type congruences for integral weight modular forms away from the level and the congruence prime are equivalent to specific congruences for Hecke eigenvalues. In particular, we show that Ramanujan-type congruences are preserved by the action of the shallow Hecke algebra. More generally, we show for weakly holomorphic modular forms of integral weight, that Ramanujan-type congruences naturally occur for shifts in the union of two square-classes as opposed to single square-classes that appear in the literature on the partition function. We also rule out the possibility of square-free periods, whose scarcity in the case of the partition function was investigated recently. We complement our obstructions on maximal Ramanujan-type congruences with several existence statements. Our results are based on a framework that leverages classical results on integral models of modular curves via modular representation theory, and applies to congruences of all weakly holomorphic modular forms. Steinberg representations govern all maximal Ramanujan-type congruences for integral weights. We discern the scope of our framework in the case of half-integral weights through example calculations.(c) 2022 The Author(s). Published by Elsevier Inc. This is an (http://creativecommons.org/licenses/by/4.0/).
16.	Westerholt-Raum, Martin, 1985, et al. (författare) All modular forms of weight 2 can be expressed by Eisenstein series 2020 Ingår i: Research in Number Theory. - : Springer Science and Business Media LLC. - 2522-0160 .- 2363-9555. ; 6:3 Tidskriftsartikel (refereegranskat)abstract We show that every elliptic modular form of integral weight greater than 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central L-values present in all previous work. For weights greater than 2, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice.
17.	Aas, Erik, et al. (författare) Limiting directions for random walks in classical affine Weyl groups Annan publikation (övrigt vetenskapligt/konstnärligt)abstract Let be a finite Weyl group and the corresponding affine Weyl group. A random element of can be obtained as a reduced random walk on the alcoves of . By a theorem of Lam (Ann. Probab. 2015), such a walk almost surely approaches one of many directions. We compute these directions when is , and and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types and in the affirmative and for type in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the -TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.
18.	Hegarty, Peter, 1971, et al. (författare) Can connected commuting graphs of finite groups have arbitrarily large diameter ? 2015 Ingår i: Geometry, Structure and Randomness in Combinatorics, CRM Series, No. 18. - 9788876425257 ; , s. 141-144 Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract The whole paper is an extended abstract.
19.	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.
20.	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.
21.	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.
22.	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/).
23.	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.
24.	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
25.	Freij-Hollanti, Ragnar, et al. (författare) Cyclic Flats of Binary Matroids Annan publikation (övrigt vetenskapligt/konstnärligt)
26.	Freij-Hollanti, Ragnar, et al. (författare) Matroid Theory and StorageCodes: Bounds and Constructions 2018 Ingår i: Network Coding and Subspace Designs. - Cham : Springer. ; , s. 385-425 Bokkapitel (refereegranskat)
27.	Westerbäck, Thomas (författare) Parity check systems of nonlinear codes over finite commutative frobenius rings 2017 Ingår i: Advances in Mathematics of Communications. - : American Institute of Mathematical Sciences (AIMS). - 1930-5346 .- 1930-5338. ; 11:3, s. 409-427 Tidskriftsartikel (refereegranskat)
28.	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)
29.	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.
30.	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.
31.	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.
32.	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.
33.	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.
34.	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.
35.	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.
36.	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.
37.	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.
38.	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.
39.	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.
40.	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.
41.	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.
42.	Billig, Y., et al. (författare) Representations of the Lie algebra of vector fields on a sphere 2019 Ingår i: Journal of Pure and Applied Algebra. - : Elsevier BV. - 0022-4049. ; 223:8, s. 3581-3593 Tidskriftsartikel (refereegranskat)abstract For an affine algebraic variety X we study a category of modules that admit compatible actions of both the algebra A of functions on X and the Lie algebra of vector fields on X. In particular, for the case when X is the sphere S-2, we construct a set of simple modules that are finitely generated over A. In addition, we prove that the monoidal category that these modules generate is equivalent to the category of finite-dimensional rational GL(2)-modules. (C) 2018 Elsevier B.V. All rights reserved.
43.	Björklund, Michael, 1981, et al. (författare) Central limit theorems for generic lattice point counting 2023 Ingår i: Selecta Mathematica, New Series. - : Springer Science and Business Media LLC. - 1420-9020 .- 1022-1824. ; 29:1 Tidskriftsartikel (refereegranskat)abstract We consider the problem of counting lattice points contained in domains in Rd defined by products of linear forms. For d≥ 9 we show that the normalized discrepancies in these counting problems satisfy non-degenerate Central Limit Theorems with respect to the unique SL d(R) -invariant probability measure on the space of unimodular lattices in Rd. We also study more refined versions pertaining to “spiraling of approximations”. Our techniques are dynamical in nature and exploit effective exponential mixing of all orders for actions of diagonalizable subgroups on spaces of unimodular lattices.
44.	Björklund, Michael, 1981, et al. (författare) Central limit theorems for group actions which are exponentially mixing of all orders 2020 Ingår i: Journal dAnalyse Mathematique. - : Springer Science and Business Media LLC. - 0021-7670 .- 1565-8538. ; 141:2, s. 457-482 Tidskriftsartikel (refereegranskat)abstract In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie groups. Our proof uses a novel relativization of the classical method of cumulants, which should be of independent interest. As a sample application of our techniques, we show that the CLT holds along lacunary samples of the horocycle flow on finite-area hyperbolic surfaces applied to any smooth compactly supported function.
45.	Boucksom, Sebastien, et al. (författare) Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry 2021 Ingår i: Advances in Mathematics. - : Elsevier BV. - 1090-2082 .- 0001-8708. ; 378 Tidskriftsartikel (refereegranskat)abstract Let L be an ample line bundle on a (geometrically reduced) projective variety X over any complete valued field. Our main result describes the leading asymptotics of the determinant of cohomology of large powers of L, with respect to the supnorm of a continuous metric on the Berkovich analytification of L. As a consequence, we establish in this setting the existence of transfinite diameters and equidistribution of Fekete points, following a strategy going back to Berman, Witt Nystrom and the first author for complex manifolds. In the non-Archimedean case, our approach relies on a version of the Knudsen-Mumford expansion for the determinant of cohomology on models over the (possibly non-No etherian) valuation ring, as a replacement for the asymptotic expansion of Bergman kernels in the complex case, and on the reduced fiber theorem, as a replacement for the Bernstein-Markov inequalities. Along the way, a systematic study of spaces of norms and the associated Fubini-Study type metrics is undertaken.
46.	Brandes, Julia, 1986, et al. (författare) Rational lines on cubic hypersurfaces 2021 Ingår i: Mathematical Proceedings of the Cambridge Philosophical Society. - 0305-0041 .- 1469-8064. ; 171:1, s. 99-112 Tidskriftsartikel (refereegranskat)abstract We show that any smooth projective cubic hypersurface of dimension at least 29 over the rationals contains a rational line. A variation of our methods provides a similar result over p-adic fields. In both cases, we improve on previous results due to the second author and Wooley.We include an appendix in which we highlight some slight modifications to a recent result of Papanikolopoulos and Siksek. It follows that the set of rational points on smooth projective cubic hypersurfaces of dimension at least 29 is generated via secant and tangent constructions from just a single point.
47.	Bringmann, K., et al. (författare) Almost holomorphic Poincaré series corresponding to products of harmonic Siegel-Maass forms 2016 Ingår i: Research in the Mathematical Sciences. - : Springer Science and Business Media LLC. - 2197-9847 .- 2522-0144. ; 3 Tidskriftsartikel (refereegranskat)abstract We investigate Poincare series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincare series are almost holomorphic as well. In general, this is not the case. The main point of this paper is the study of Siegel-Poincare series of degree 2 attached to products of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms. We establish conditions on the convergence and nonvanishing of such Siegel-Poincare series. We surprisingly discover that these Poincare series are almost holomorphic Siegel modular forms, although the product of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms (in contrast to the elliptic case) is not almost holomorphic. Our proof employs tools from representation theory. In particular, we determine some constituents of the tensor product of Harish-Chandra modules with walls.
48.	Casarino, V., et al. (författare) On the maximal operator of a general Ornstein-Uhlenbeck semigroup 2022 Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 301, s. 2393-2413 Tidskriftsartikel (refereegranskat)abstract If Q is a real, symmetric and positive definite n x n matrix, and B a real n x n matrix whose eigenvalues have negative real parts, we consider the Ornstein-Uhlenbeck semigroup on R-n with covariance Q and drift matrix B. Our main result says that the associated maximal operator is of weak type (1, 1) with respect to the invariant measure. The proof has a geometric gist and hinges on the "forbidden zones method" previously introduced by the third author.
49.	Casarino, V., et al. (författare) On the orthogonality of generalized eigenspaces for the Ornstein-Uhlenbeck operator 2021 Ingår i: Archiv der Mathematik. - : Springer Science and Business Media LLC. - 0003-889X .- 1420-8938. ; 117, s. 547-556 Tidskriftsartikel (refereegranskat)abstract We study the orthogonality of the generalized eigenspaces of an Ornstein-Uhlenbeck operator L in R-N, with drift given by a real matrix B whose eigenvalues have negative real parts. If B has only one eigenvalue, we prove that any two distinct generalized eigenspaces of L are orthogonal with respect to the invariant Gaussian measure. Then we show by means of two examples that if B admits distinct eigenvalues, the generalized eigenspaces of L may or may not be orthogonal.
50.	Deeley, Robin J., et al. (författare) Relative geometric assembly and mapping cones, part I: the geometric model and applications 2018 Ingår i: Journal of Topology. - : Wiley. - 1753-8416 .- 1753-8424. ; 11:4, s. 966-1000 Tidskriftsartikel (refereegranskat)abstract Inspired by an analytic construction of Chang, Weinberger and Yu, we define an assembly map in relative geometric K-homology. The properties of the geometric assembly map are studied using a variety of index theoretic tools (for example, the localized index and higher Atiyah–Patodi–Singer index theory). As an application we obtain a vanishing result in the context of manifolds with boundary and positive scalar curvature; this result is also inspired and connected to the work of Chang, Weinberger and Yu. Furthermore, we use results of Wahl to show that rational injectivity of the relative assembly map implies homotopy invariance of the relative higher signatures of a manifold with boundary.

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