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• 1.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Philosophy of mathematics in “La Science et l’Hypothèse”, from Henri Poincaré.2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 2.
Columbia Univ, Dept Math, New York, NY 10027 USA.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
On the immersion classes of nearby Lagrangians2016In: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 9, no 1, p. 232-244Article in journal (Refereed)

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.
Columbia Univ, Dept Math, Room 509,MC 4406 2990 Broadway, New York, NY 10027 USA.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Simple homotopy equivalence of nearby Lagrangians2018In: Acta Mathematica, ISSN 0001-5962, E-ISSN 1871-2509, Vol. 220, no 2, p. 207-237Article in journal (Refereed)

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.
Alfred Renyi Inst Math, 13-15 Realtanoda U, H-1053 Budapest, Hungary..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Dehn surgeries and rational homology2017In: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 17, no 1, p. 487-527Article in journal (Refereed)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
A zero-one law for l-colourable structures with a vectorspace pregeometry2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
• 6.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Homogenizable structures and model completeness2016In: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, no 7-8, p. 977-995Article in journal (Refereed)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Simple structures axiomatized by almost sure theories2016In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, no 5, p. 435-456Article in journal (Refereed)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
To infinity and back: Logical limit laws and almost sure theories2014Licentiate thesis, comprehensive summary (Other academic)
• 9.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Limit laws and automorphism groups of random nonrigid structures2015In: Journal of Logic and Analysis, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 7, no 2, p. 1-53, article id 1Article in journal (Refereed)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
On sets with rank one in simple homogeneous structures2015In: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, p. 223-250Article in journal (Refereed)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Classifying Categories: The Jordan-Hölder and Krull-Schmidt-Remak Theorems for Abelian Categories2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
• 12.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Limitless Analysis2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 13.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Equation Solving in Indian Mathematics2018Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 14.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
A Categorical Study of Composition Algebras via Group Actions and Triality2015Doctoral thesis, comprehensive summary (Other academic)

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

1. Morphisms in the Category of Finite-Dimensional Absolute Valued Algebras
Open this publication in new window or tab >>Morphisms in the Category of Finite-Dimensional Absolute Valued Algebras
2011 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 125, no 2, p. 147-174Article in journal (Refereed) 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.

##### Keywords
absolute valued algebra, division algebra, homomorphism, irreducibility, composition
Mathematics
##### Identifiers
urn:nbn:se:uu:diva-172251 (URN)10.4064/cm125-2-2 (DOI)000299619900002 ()
Available from: 2012-04-04 Created: 2012-04-03 Last updated: 2017-12-07
2. Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras
Open this publication in new window or tab >>Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras
2015 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 219, no 5, p. 1519-1547Article in journal (Refereed) 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.

Mathematics
##### Identifiers
urn:nbn:se:uu:diva-247368 (URN)10.1016/j.jpaa.2014.06.014 (DOI)000349427000009 ()
Available from: 2015-03-20 Created: 2015-03-18 Last updated: 2017-12-04
3. An Approach to Finite-Dimensional Real Division Composition Algebras through Reflections
Open this publication in new window or tab >>An Approach to Finite-Dimensional Real Division Composition Algebras through Reflections
2015 (English)In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 139, no 4, p. 357-399Article in journal (Refereed) 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 $G_{2}$ , on pairs of orthogonal maps. We describe these subcategories further in terms of subgroups of $\mathrm{Aut}(\mathbb{O})$ and their cosets, which we express geometrically. This extends the study of finite-dimensional real division composition algebras with a one-sided unity.

##### Keywords
Composition algebra, division algebra, absolute valued algebra, reflection, G2-subgroup, G2-set
Mathematics
Mathematics
##### Identifiers
urn:nbn:se:uu:diva-224094 (URN)10.1016/j.bulsci.2014.10.001 (DOI)000356200200001 ()
Available from: 2014-05-03 Created: 2014-05-03 Last updated: 2017-12-05Bibliographically approved
4. Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra
Open this publication in new window or tab >>Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra
2016 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 445, p. 35-77Article in journal (Other academic) 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.

##### Keywords
Composition algebras, division algebras, absolute valued algebras, derivation algebras, quasi-descriptions
Mathematics
Mathematics
##### Identifiers
urn:nbn:se:uu:diva-224093 (URN)10.1016/j.jalgebra.2015.07.025 (DOI)000365826900002 ()
Available from: 2014-05-03 Created: 2014-05-03 Last updated: 2017-12-05Bibliographically approved
5. Composition Algebras and Outer Automorphisms of Algebraic Groups
Open this publication in new window or tab >>Composition Algebras and Outer Automorphisms of Algebraic Groups
(English)Article in journal (Other academic) 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 $n$ over a field $k$of characteristic not two, and a category arising from anaction of the projective similarity group of $n$on certain pairs of automorphisms of the group scheme $\mathbf{PGO}^+(n)$ defined ove $k$. This extends results recently obtained in the same direction for symmetric composition algebras. We also derive known resultson composition algebras from our equivalence.

##### Keywords
Composition algebras, algebraic groups, outer automorphisms, triality
Mathematics
##### Identifiers
urn:nbn:se:uu:diva-248499 (URN)
Available from: 2015-03-30 Created: 2015-03-30 Last updated: 2015-04-07
• 15.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
An Approach to Finite-Dimensional Real Division Composition Algebras through Reflections2015In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 139, no 4, p. 357-399Article in journal (Refereed)

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 $G_{2}$ , on pairs of orthogonal maps. We describe these subcategories further in terms of subgroups of $\mathrm{Aut}(\mathbb{O})$ and their cosets, which we express geometrically. This extends the study of finite-dimensional real division composition algebras with a one-sided unity.

• 16.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Classification of the Finite-Dimensional Real Division Composition Algebras having a Non-Abelian Derivation Algebra2016In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 445, p. 35-77Article in journal (Other academic)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Composition Algebras and Outer Automorphisms of Algebraic GroupsArticle in journal (Other academic)

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

• 18.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras2012Report (Other academic)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras2015In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 219, no 5, p. 1519-1547Article in journal (Refereed)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Generalisations of the Algebraic Theory of Connective Segmentation2010Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
• 21.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Morphisms in the Category of Finite Dimensional Absolute Valued Algebras2011Report (Other academic)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Morphisms in the Category of Finite-Dimensional Absolute Valued Algebras2011In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 125, no 2, p. 147-174Article in journal (Refereed)

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.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
On Finite-Dimensional Absolute Valued Algebras2012Licentiate thesis, comprehensive summary (Other academic)
• 24.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Knots, Reidemeister Moves and Knot Invariants2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 25.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Elliptiska kurvor och kryptografi2020Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 26. Andersen, Henning Haahr
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Category O for quantum groups2015In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 17, no 2, p. 405-431Article in journal (Refereed)

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.

• 27.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Random sampling of finite graphs with constraints2014Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
• 28.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Contact Homology of Legendrian Knots in Five-Dimensional Circle Bundles2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
• 29.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Linking and Morse Theory2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 30.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Extremal Hypergraphs2013Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 31. Baur, Karin
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras2012In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 372, p. 85-107Article in journal (Refereed)

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.

• 32.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Om talet Π2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 33. Berger, Josef
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
A predicative completion of a uniform space2012In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 163, no 8, p. 975-980Article in journal (Refereed)

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

• 34.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Arkimedes metod2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 35.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Cohomology of the toric arrangement associated with A(n)2019In: Journal of Fixed Point Theory and Applications, ISSN 1661-7738, E-ISSN 1661-7746, Vol. 21, no 1, article id 15Article in journal (Refereed)

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.

• 36.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Equivariant cohomology of moduli spaces of genus three curves with level two structure2019In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 202, no 1, p. 165-191Article in journal (Refereed)

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.

• 37.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
The Unprovability of the Continuum Hypothesis Using the Method of Forcing2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 38.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Flexible isotopy classification of flexible links2016In: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 25, no 8, article id 1650049Article in journal (Refereed)

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.

• 39.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Legendrian contact homology in the product of a punctured Riemann surface and the real line2016In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 94, no 3, p. 970-992Article in journal (Refereed)

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.

• 40.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
On percolation in one-dimensional stable Poisson graphs2015In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 20Article in journal (Refereed)

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..

• 41.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Undecidability of finite satisfiability and characterization of NP in finite model theory2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 42.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Miniräknarmania: eller hur att få ut så mycket som möjligt från en enkel reklamräknare2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 43.
Renyi Inst Math, Realtanoda 13-15, H-1053 Budapest, Hungary..
Univ Florence, Dept Math & Informat, Viale Morgagni 67-A, I-50134 Florence, Italy.. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Cuspidal curves and Heegaard Floer homology2016In: Proceedings of the London Mathematical Society, ISSN 0024-6115, E-ISSN 1460-244X, Vol. 112, no 3, p. 512-548Article in journal (Refereed)

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.

• 44.
Natl Inst Nucl Phys, Sez Firenze, Florence, Italy..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Natl Inst Nucl Phys, Sez Firenze, Florence, Italy..
A bi-Hamiltonian system on the Grassmannian2016In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 189, no 1, p. 1401-1410Article in journal (Refereed)

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.

• 45.
ULB.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Stanford University. MIT. Stanford University.
Effect of Legendrian Surgery2012In: Geometry and Topology, ISSN 1465-3060, E-ISSN 1364-0380, Vol. 16, no 1, p. 301-389Article in journal (Refereed)

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].

• 46.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Extremal Kahler Metrics on Projectivized Vector Bundles2015In: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 164, no 2, p. 195-233Article in journal (Refereed)

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).

• 47.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Konstruktionen av en regelbunden 17-hörning2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 48.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Localization of Multiscale Screened Poisson Equation2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 49.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Primtal och kryptografi2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 50.
Univ Nantes, F-44035 Nantes 1, France.
Univ Nantes, F-44035 Nantes 1, France. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Positive Legendrian Isotopies And Floer Theory2019In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 69, no 4, p. 1679-1737Article in journal (Refereed)

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.

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