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  • 1.
    Aboud, Mathilde
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Philosophy of mathematics in “La Science et l’Hypothèse”, from Henri Poincaré.2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 2.
    Abouzaid, Mohammed
    et al.
    Columbia Univ, Dept Math, New York, NY 10027 USA.
    Kragh, Thomas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On the immersion classes of nearby Lagrangians2016Inngår i: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 9, nr 1, s. 232-244Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that the transfer map on Floer homotopy types associated to an exact Lagrangian embedding is an equivalence. This provides an obstruction to representing isotopy classes of Lagrangian immersions by Lagrangian embeddings, which, unlike previous obstructions, is sensitive to information that cannot be detected by Floer cochains. We show this by providing a concrete computation in the case of spheres.

  • 3.
    Abouzaid, Mohammed
    et al.
    Columbia Univ, Dept Math, Room 509,MC 4406 2990 Broadway, New York, NY 10027 USA.
    Kragh, Thomas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Simple homotopy equivalence of nearby Lagrangians2018Inngår i: Acta Mathematica, ISSN 0001-5962, E-ISSN 1871-2509, Vol. 220, nr 2, s. 207-237Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Given a closed exact Lagrangian in the cotangent bundle of a closed smooth manifold, we prove that the projection to the base is a simple homotopy equivalence.

  • 4.
    Aceto, Paolo
    et al.
    Alfred Renyi Inst Math, 13-15 Realtanoda U, H-1053 Budapest, Hungary..
    Golla, Marco
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Dehn surgeries and rational homology2017Inngår i: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 17, nr 1, s. 487-527Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the question of which Dehn surgeries along a given knot bound rational homology balls. We use Ozsvath and Szabo's correction terms in Heegaard Floer homology to obtain general constraints on the surgery coefficients. We then turn our attention to the case of integral surgeries, with particular emphasis on positive torus knots. Finally, combining these results with a lattice-theoretic obstruction based on Donaldson's theorem, we classify which integral surgeries along torus knots of the form Tkq 1; q bound rational homology balls.

  • 5.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    A zero-one law for l-colourable structures with a vectorspace pregeometry2012Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 6.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Homogenizable structures and model completeness2016Inngår i: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, nr 7-8, s. 977-995Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A homogenizable structure M is a structure where we may add a finite amount of new relational symbols to represent some 0-definable relations in order to make the structure homogeneous. In this article we will divide the homogenizable structures into different classes which categorize many known examples and show what makes each class important. We will show that model completeness is vital for the relation between a structure and the amalgamation bases of its age and give a necessary and sufficient condition for an countably categorical model-complete structure to be homogenizable.

  • 7.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Simple structures axiomatized by almost sure theories2016Inngår i: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, nr 5, s. 435-456Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this article we give a classification of the binary, simple, ω-categorical structures with SU-rank 1 and trivial algebraic closure. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as ω-stability or strong minimality.

  • 8.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    To infinity and back: Logical limit laws and almost sure theories2014Licentiatavhandling, med artikler (Annet vitenskapelig)
  • 9.
    Ahlman, Ove
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Limit laws and automorphism groups of random nonrigid structures2015Inngår i: Journal of Logic and Analysis, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 7, nr 2, s. 1-53, artikkel-id 1Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of classes of finite structures with increasingly more complex automorphism groups. Such a hierarchy can be defined in more than one way. For example, the kth level of the hierarchy can consist of all structures having at least k elements which are moved by some automorphism. Or we can consider, for any finite group G, all finite structures M such that G is a subgroup of the group of automorphisms of M; in this case the "hierarchy" is a partial order. In both cases, as well as variants of them, each "level" satisfies a logical limit law, but not a zero-one law (unless k = 0 or G is trivial). Moreover, the number of (labelled or unlabelled) n-element structures in one place of the hierarchy divided by the number of n-element structures in another place always converges to a rational number or to infinity as n -> infinity. All instances of the respective result are proved by an essentially uniform argument.

  • 10.
    Ahlman, Ove
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On sets with rank one in simple homogeneous structures2015Inngår i: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, s. 223-250Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study definable sets D of SU-rank 1 in Meq, where M is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a 'canonically embedded structure', which inherits all relations on D which are definable in Meq, and has no other definable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, then there is a close relationship between triviality of dependence and D being a reduct of a binary random structure. Somewhat more precisely: (a) if for every n≥2, every n-type p(x1,...,xn) which is realized in D is determined by its sub-2-types q(xi,xj)⊆p, then the algebraic closure restricted to D is trivial; (b) if M has trivial dependence, then D is a reduct of a binary random structure.

  • 11.
    Ahlsén, Daniel
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Classifying Categories: The Jordan-Hölder and Krull-Schmidt-Remak Theorems for Abelian Categories2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 12.
    Ahlsén, Daniel
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Limitless Analysis2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 13.
    Al Homsi, Rania
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Equation Solving in Indian Mathematics2018Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 14.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    A Categorical Study of Composition Algebras via Group Actions and Triality2015Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    A composition algebra is a non-zero algebra endowed with a strictly non-degenerate, multiplicative quadratic form. Finite-dimensional composition algebras exist only in dimension 1, 2, 4 and 8 and are in general not associative or unital. Over the real numbers, such algebras are division algebras if and only if they are absolute valued, i.e. equipped with a multiplicative norm. The problem of classifying all absolute valued algebras and, more generally, all composition algebras of finite dimension remains unsolved. In dimension eight, this is related to the triality phenomenon. We approach this problem using a categorical language and tools from representation theory and the theory of algebraic groups.

    We begin by considering the category of absolute valued algebras of dimension at most four. In Paper I we determine the morphisms of this category completely, and describe their irreducibility and behaviour under the actions of the automorphism groups of the algebras.

    We then consider the category of eight-dimensional absolute valued algebras, for which we provide a description in Paper II in terms of a group action involving triality. Then we establish general criteria for subcategories of group action groupoids to be full, and applying this to the present setting, we obtain hitherto unstudied subcategories determined by reflections. The reflection approach is further systematized in Paper III, where we obtain a coproduct decomposition of the category of finite-dimensional absolute valued algebras into blocks, for several of which the classification problem does not involve triality. We study these in detail, reducing the problem to that of certain group actions, which we express geometrically.

    In Paper IV, we use representation theory of Lie algebras to completely classify all finite-dimensional absolute valued algebras having a non-abelian derivation algebra. Introducing the notion of quasi-descriptions, we reduce the problem to the study of actions of rotation groups on products of spheres.

    We conclude by considering composition algebras over arbitrary fields of characteristic not two in Paper V. We establish an equivalence of categories between the category of eight-dimensional composition algebras with a given quadratic form and a groupoid arising from a group action on certain pairs of outer automorphisms of affine group schemes

    Delarbeid
    1. Morphisms in the Category of Finite-Dimensional Absolute Valued Algebras
    Åpne denne publikasjonen i ny fane eller vindu >>Morphisms in the Category of Finite-Dimensional Absolute Valued Algebras
    2011 (engelsk)Inngår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 125, nr 2, s. 147-174Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms from two-dimensional algebras we describe the orbits under the actions of the automorphism groups involved. Parts of these descriptions rely on a suitable choice of a cross-section of four-dimensional absolute valued algebras, and we thus end by providing an explicit means of transferring these results to algebras outside this cross-section.

    Emneord
    absolute valued algebra, division algebra, homomorphism, irreducibility, composition
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-172251 (URN)10.4064/cm125-2-2 (DOI)000299619900002 ()
    Tilgjengelig fra: 2012-04-04 Laget: 2012-04-03 Sist oppdatert: 2017-12-07
    2. Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras
    Åpne denne publikasjonen i ny fane eller vindu >>Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras
    2015 (engelsk)Inngår i: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 219, nr 5, s. 1519-1547Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    We define and study the class of left reflection algebras, which is a subclass of eight-dimensional absolute valued algebras. We reduce its classification problem to the problem of finding a transversal for the action of a subgroup of O-7 on O-7 by conjugation. As a basis for this study, we give a general criterion for finding full subcategories of group action categories, which themselves arise from group actions.

    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-247368 (URN)10.1016/j.jpaa.2014.06.014 (DOI)000349427000009 ()
    Tilgjengelig fra: 2015-03-20 Laget: 2015-03-18 Sist oppdatert: 2017-12-04
    3. An Approach to Finite-Dimensional Real Division Composition Algebras through Reflections
    Åpne denne publikasjonen i ny fane eller vindu >>An Approach to Finite-Dimensional Real Division Composition Algebras through Reflections
    2015 (engelsk)Inngår i: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 139, nr 4, s. 357-399Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    We consider the category of all finite-dimensional real composition algebras which are division algebras. These are precisely the finite-dimensional absolute valued algebras, and exist only in dimension 1, 2, 4 and 8. We construct three decompositions of this category, each determined by the number of reflections composing left and right multiplication by idempotents. As a consequence, we obtain new full subcategories in dimension 8, in which all morphisms are automorphisms of the octonions. This reduces considerable parts of the still open classification problem in dimension 8 to the normal form problem of an action of the automorphism group of the octonions, which is a compact Lie group of type  , on pairs of orthogonal maps. We describe these subcategories further in terms of subgroups of  and their cosets, which we express geometrically. This extends the study of finite-dimensional real division composition algebras with a one-sided unity.

    Emneord
    Composition algebra, division algebra, absolute valued algebra, reflection, G2-subgroup, G2-set
    HSV kategori
    Forskningsprogram
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-224094 (URN)10.1016/j.bulsci.2014.10.001 (DOI)000356200200001 ()
    Tilgjengelig fra: 2014-05-03 Laget: 2014-05-03 Sist oppdatert: 2017-12-05bibliografisk kontrollert
    4. Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra
    Åpne denne publikasjonen i ny fane eller vindu >>Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra
    2016 (engelsk)Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 445, s. 35-77Artikkel i tidsskrift (Annet vitenskapelig) Published
    Abstract [en]

    We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a quasi-description of a category, and using it to express the problem in terms of normal form problems for certain group actions on products of 3-spheres.

    Emneord
    Composition algebras, division algebras, absolute valued algebras, derivation algebras, quasi-descriptions
    HSV kategori
    Forskningsprogram
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-224093 (URN)10.1016/j.jalgebra.2015.07.025 (DOI)000365826900002 ()
    Tilgjengelig fra: 2014-05-03 Laget: 2014-05-03 Sist oppdatert: 2017-12-05bibliografisk kontrollert
    5. Composition Algebras and Outer Automorphisms of Algebraic Groups
    Åpne denne publikasjonen i ny fane eller vindu >>Composition Algebras and Outer Automorphisms of Algebraic Groups
    (engelsk)Artikkel i tidsskrift (Annet vitenskapelig) Submitted
    Abstract [en]

    In this note, we establish an equivalence of categories between the category of all eight-dimensionalcomposition algebras with any given quadratic form  over a field of characteristic not two, and a category arising from anaction of the projective similarity group of on certain pairs of automorphisms of the group scheme  defined ove . This extends results recently obtained in the same direction for symmetric composition algebras. We also derive known resultson composition algebras from our equivalence.

    Emneord
    Composition algebras, algebraic groups, outer automorphisms, triality
    HSV kategori
    Identifikatorer
    urn:nbn:se:uu:diva-248499 (URN)
    Tilgjengelig fra: 2015-03-30 Laget: 2015-03-30 Sist oppdatert: 2015-04-07
  • 15.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    An Approach to Finite-Dimensional Real Division Composition Algebras through Reflections2015Inngår i: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 139, nr 4, s. 357-399Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the category of all finite-dimensional real composition algebras which are division algebras. These are precisely the finite-dimensional absolute valued algebras, and exist only in dimension 1, 2, 4 and 8. We construct three decompositions of this category, each determined by the number of reflections composing left and right multiplication by idempotents. As a consequence, we obtain new full subcategories in dimension 8, in which all morphisms are automorphisms of the octonions. This reduces considerable parts of the still open classification problem in dimension 8 to the normal form problem of an action of the automorphism group of the octonions, which is a compact Lie group of type  , on pairs of orthogonal maps. We describe these subcategories further in terms of subgroups of  and their cosets, which we express geometrically. This extends the study of finite-dimensional real division composition algebras with a one-sided unity.

  • 16.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra2016Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 445, s. 35-77Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a quasi-description of a category, and using it to express the problem in terms of normal form problems for certain group actions on products of 3-spheres.

  • 17.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Composition Algebras and Outer Automorphisms of Algebraic GroupsArtikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    In this note, we establish an equivalence of categories between the category of all eight-dimensionalcomposition algebras with any given quadratic form  over a field of characteristic not two, and a category arising from anaction of the projective similarity group of on certain pairs of automorphisms of the group scheme  defined ove . This extends results recently obtained in the same direction for symmetric composition algebras. We also derive known resultson composition algebras from our equivalence.

  • 18.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras2012Rapport (Annet vitenskapelig)
    Abstract [en]

    A condition for when two eight-dimensional absolute valued algebras are isomorphic was given in [4]. We use this condition to deduce a description (in the sense of Dieterich, [9]) of the category of such algebras, and show how previous descriptions of some full subcategories fit in this description. Led by the structure of these examples, we aim at systematically constructing new subcategories whose classification is manageable. To this end we propose, in greater generality, the definition of sharp stabilizers for group actions, and use these to obtain conditions for when certain subcategories of groupoids are full. This we apply to the category of eight-dimensional absolute valued algebras and obtain a class of subcategories, for which we simplify, and partially solve, the classification problem.

  • 19.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras2015Inngår i: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 219, nr 5, s. 1519-1547Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We define and study the class of left reflection algebras, which is a subclass of eight-dimensional absolute valued algebras. We reduce its classification problem to the problem of finding a transversal for the action of a subgroup of O-7 on O-7 by conjugation. As a basis for this study, we give a general criterion for finding full subcategories of group action categories, which themselves arise from group actions.

  • 20.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Generalisations of the Algebraic Theory of Connective Segmentation2010Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 21.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Morphisms in the Category of Finite Dimensional Absolute Valued Algebras2011Rapport (Annet vitenskapelig)
    Abstract [en]

    This is a study of morphisms in the category of nite dimensional absolute valued algebras, whose codomains have dimension four. We begin by citing and transferring a classication of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms from two-dimensional algebras we describe the orbits under the actions of the automorphism groups involved. Parts of these descriptions rely on a suitable choice of a cross-section of four-dimensional absolute valued algebras, and we thus end by providing an explicit means of transferring these results to algebras outside this crosssection.

  • 22.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Morphisms in the Category of Finite-Dimensional Absolute Valued Algebras2011Inngår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 125, nr 2, s. 147-174Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms from two-dimensional algebras we describe the orbits under the actions of the automorphism groups involved. Parts of these descriptions rely on a suitable choice of a cross-section of four-dimensional absolute valued algebras, and we thus end by providing an explicit means of transferring these results to algebras outside this cross-section.

  • 23.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On Finite-Dimensional Absolute Valued Algebras2012Licentiatavhandling, med artikler (Annet vitenskapelig)
  • 24.
    Alsätra, Tova
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Knots, Reidemeister Moves and Knot Invariants2019Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 25. Andersen, Henning Haahr
    et al.
    Mazorchuk, Volodymyr
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Category O for quantum groups2015Inngår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 17, nr 2, s. 405-431Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the BGG-categories O-q associated to quantum groups. We prove that many properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for O and for finite-dimensional U-q-modules we are able to determine all irreducible characters as well as the characters of all indecomposable tilting modules in O-q. As a consequence, we also recover the known result that the generic quantum case behaves like the classical category O.

  • 26.
    Andersson, Evelina
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Random sampling of finite graphs with constraints2014Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
  • 27.
    Asplund, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Contact Homology of Legendrian Knots in Five-Dimensional Circle Bundles2016Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
  • 28.
    Asplund, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Linking and Morse Theory2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 29.
    Asplund, Teo
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Extremal Hypergraphs2013Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 30. Baur, Karin
    et al.
    Mazorchuk, Volodymyr
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras2012Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 372, s. 85-107Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study certain types of ideals in the standard Borel subalgebra of an untwisted affine Lie algebra. We classify these ideals in terms of the root combinatorics and give an explicit formula for the number of such ideals in type A. The formula involves various aspects of combinatorics of Dyck paths and leads to a new interesting integral sequence.

  • 31.
    Berg, Sandra
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Om talet Π2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 32. Berger, Josef
    et al.
    Ishihara, Hajime
    Palmgren, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Schuster, Peter
    A predicative completion of a uniform space2012Inngår i: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 163, nr 8, s. 975-980Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We give a predicative construction of a completion of a uniform space in the constructive Zermelo-Fraenkel set theory.

  • 33.
    Berglund, Björn
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Arkimedes metod2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 34.
    Bergvall, Olof
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Cohomology of the toric arrangement associated with A(n)2019Inngår i: Journal of Fixed Point Theory and Applications, ISSN 1661-7738, E-ISSN 1661-7746, Vol. 21, nr 1, artikkel-id 15Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We compute the total cohomology of the complement of the toric arrangement associated with the root system An as a representation of the corresponding Weyl group via fixed point theory of a twisted action of the group. We also provide several proofs of an explicit formula for the Poincare polynomial of the complement of the toric arrangement associated with An.

  • 35.
    Bergvall, Olof
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Equivariant cohomology of moduli spaces of genus three curves with level two structure2019Inngår i: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 202, nr 1, s. 165-191Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the cohomology of the moduli space of genus three curves with level two structure and some related spaces. In particular, we determine the cohomology groups of the moduli space of plane quartics with level two structure as representations of the symplectic group on a six dimensional vector space over the field of two elements. We also make the analogous computations for some related spaces such as moduli spaces of genus three curves with a marked point and strata of the moduli space of Abelian differentials of genus three.

  • 36.
    Bjerkeng van Keppel, Alvar
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    The Unprovability of the Continuum Hypothesis Using the Method of Forcing2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 37.
    Björklund, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Flexible isotopy classification of flexible links2016Inngår i: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 25, nr 8, artikkel-id 1650049Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we define and study flexible links and flexible isotopy in RP3 subset of CP3. Flexible links are meant to capture the topological properties of real algebraic links. We classify all flexible links up to flexible isotopy using Ekholm's interpretation of Viro's encomplexed writhe.

  • 38.
    Björklund, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Legendrian contact homology in the product of a punctured Riemann surface and the real line2016Inngår i: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 94, nr 3, s. 970-992Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We give a combinatorial description of the Legendrian differential graded algebra associated to a Legendrian knot in PxR, where P is a punctured Riemann surface. As an application we show that for any integer k and any homology class h in H_1(PxR) there are k Legendrian knots all representing h which are pairwise smoothly isotopic through a formal Legendrian isotopy but which lie in mutually distinct Legendrian isotopy classes.

  • 39.
    Björklund, Johan
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Falgas-Ravry, Victor
    Holmgren, Cecilia
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    On percolation in one-dimensional stable Poisson graphs2015Inngår i: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 20Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Equip each point x of a homogeneous Poisson point process P on R with D-x edge stubs, where the D-x are i.i.d. positive integer-valued random variables with distribution given by mu. Following the stable multi-matching scheme introduced by Deijfen, Haggstrom and Holroyd [1], we pair off edge stubs in a series of rounds to form the edge set of a graph G on the vertex set P. In this note, we answer questions of Deijfen, Holroyd and Peres [2] and Deijfen, Haggstrom and Holroyd [1] on percolation (the existence of an infinite connected component) in G. We prove that percolation may occur a.s. even if mu has support over odd integers. Furthermore, we show that for any epsilon > 0, there exists a distribution mu such that mu ({1}) > 1 - epsilon, but percolation still occurs a.s..

  • 40.
    Block, Max
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Undecidability of finite satisfiability and characterization of NP in finite model theory2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 41.
    Blomqvist, Christer
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Miniräknarmania: eller hur att få ut så mycket som möjligt från en enkel reklamräknare2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 42.
    Bodnar, Jozsef
    et al.
    Renyi Inst Math, Realtanoda 13-15, H-1053 Budapest, Hungary..
    Celoria, Daniele
    Univ Florence, Dept Math & Informat, Viale Morgagni 67-A, I-50134 Florence, Italy..
    Golla, Marco
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Cuspidal curves and Heegaard Floer homology2016Inngår i: Proceedings of the London Mathematical Society, ISSN 0024-6115, E-ISSN 1460-244X, Vol. 112, nr 3, s. 512-548Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We give bounds on the gap functions of the singularities of a cuspidal plane curve of arbitrary genus, generalising recent work of Borodzik and Livingston. We apply these inequalities to unicuspidal curves whose singularity has one Puiseux pair: we prove two identities tying the parameters of the singularity, the genus and the degree of the curve; we improve on some degree-multiplicity asymptotic inequalities; finally, we prove some finiteness results, we construct infinite families of examples, and, in some cases, we give an almost complete classification.

  • 43.
    Bonechi, F.
    et al.
    Natl Inst Nucl Phys, Sez Firenze, Florence, Italy..
    Qiu, Jian
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Tarlini, M.
    Natl Inst Nucl Phys, Sez Firenze, Florence, Italy..
    A bi-Hamiltonian system on the Grassmannian2016Inngår i: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 189, nr 1, s. 1401-1410Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Considering the recent result that the Poisson-Nijenhuis geometry corresponds to the quantization of the symplectic groupoid integrating a Poisson manifold, we discuss the Poisson-Nijenhuis structure on the Grassmannian defined by the compatible Kirillov-Kostant-Souriau and Bruhat-Poisson structures. The eigenvalues of the Nijenhuis tensor are Gelfand-Tsetlin variables, which, as was proved, are also in involution with respect to the Bruhat-Poisson structure. Moreover, we show that the Stiefel bundle on the Grassmannian admits a bi-Hamiltonian structure.

  • 44.
    Bourgeois, Frederic
    et al.
    ULB.
    Ekholm, Tobias
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Eliashberg, Yakov
    Stanford University.
    Ganatra, Sheel
    MIT.
    Maydanskiy, Maksim
    Stanford University.
    Effect of Legendrian Surgery2012Inngår i: Geometry and Topology, ISSN 1465-3060, E-ISSN 1364-0380, Vol. 16, nr 1, s. 301-389Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The paper is a summary of the results of the authors concerning computations of symplectic invariants of Weinstein manifolds and contains some examples and applications. Proofs are sketched. The detailed proofs will appear in a forthcoming paper.

    In the Appendix written by S Ganatra and M Maydanskiy it is shown that the results of this paper imply P Seidel’s conjecture from [Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 415–434].

  • 45.
    Brönnle, Till
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Extremal Kahler Metrics on Projectivized Vector Bundles2015Inngår i: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 164, nr 2, s. 195-233Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove the existence of extremal, nonconstant-scalar curvature, Kahler metrics on certain unstable projectivized vector bundles P(E) -> M over a compact constant scalar curvature Kahler manifold M with discrete holomorphic automorphism group, in certain adiabatic Kahler classes. In particular, the vector bundles E -> M are assumed to split as a direct sum of stable subbundles E = El circle plus ... circle plus E-s all having different Mumford-Takemoto slope, for example, mu(E-1) > ... > mu(E-s).

  • 46.
    Bucht, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Konstruktionen av en regelbunden 17-hörning2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 47.
    Bäck, Viktor
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Localization of Multiscale Screened Poisson Equation2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 48.
    Carlbaum, Wilhelm
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Primtal och kryptografi2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 49.
    Chantraine, Baptiste
    et al.
    Univ Nantes, F-44035 Nantes 1, France.
    Colin, Vincent
    Univ Nantes, F-44035 Nantes 1, France.
    Dimitroglou Rizell, Georgios
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Positive Legendrian Isotopies And Floer Theory2019Inngår i: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 69, nr 4, s. 1679-1737Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Positive loops of Legendrian embeddings are examined from the point of view of Floer homology of Lagrangian cobordisms. This leads to new obstructions to the existence of a positive loop containing a given Legendrian, expressed in terms of the Legendrian contact homology of the Legendrian submanifold. As applications, old and new examples of orderable contact manifolds are obtained and discussed. We also show that contact manifolds filled by a Liouville domain with non-zero symplectic homology are strongly orderable in the sense of Liu.

  • 50.
    Chen, Chih-Whi
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri. Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China.
    Lam, Ngau
    Natl Cheng Kung Univ, Dept Math, Tainan 70101, Taiwan.
    Projective modules over classical Lie algebras of infinite rank in the parabolic category2020Inngår i: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 224, nr 1, s. 125-148Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the truncation functors and show the existence of projective cover with a finite Verma flag of each irreducible module in parabolic BGG category O over infinite rank Lie algebra of types a, b, c, d. Moreover, O is a Koszul category. As a consequence, the corresponding parabolic BGG category (O) over bar over infinite rank Lie superalgebra of types a, b, c, d through the super duality is also a Koszul category. 

123456 1 - 50 of 290
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