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  • 1.
    Aas, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Linusson, Svante
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Continuous multi-line queues and TASEP2018In: Annales de l'Institut Henri Poincare D: Combinatorics, Physics and their Interactions, ISSN 2308-5827, E-ISSN 2308-5835, Vol. 5, no 1, p. 127-152Article in journal (Refereed)
    Abstract [en]

    In this paper, we study a distribution Xi of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations and give conjectures for a larger class. We give a complete conjecture for the probability of two particles i, j being next to each other on the cycle, for which we prove some cases. We also find that two natural events associated to the process have exactly the same probability expressed as a Vandermonde determinant. It is unclear whether this is just a coincidence or a consequence of a deeper connection.

  • 2.
    Abathun, Addisalem
    Stockholm University, Faculty of Science, Department of Mathematics.
    Asymptotic distribution of zeros of a certain class of hypergeometric polynomials2014Licentiate thesis, monograph (Other academic)
    Abstract [en]

    The thesis consists of two papers, both treating hypergeometric polynomials, and a short introduction. The main results are as follows.In the first paper,we study the asymptotic zero distribution of a family of hypergeometric polynomials in one complex variable as their degree goes to infinity,using the associated differential equations that hypergeometric polynomials satisfy.   We describe in particular the curve complex on which the zeros cluster, as level curves associated to integrals on an algebraic curve derived from the equation.   The new result is first of all that we are able to formulate results on the location of zeros of generalized hypergeometric polynomials in greater generality than before (earlier results are mainly concerned with the Gauss hypergeometric case.) Secondly, we are able to formulate a precise conjucture giving the asymptotic behaviour of zeros in the generalized case of our polynomials, which covers previous results.In the second paper we partly prove one of the  conjectures in the first paper by using Euler integral representation of the Gauss hypergeometric functions together with the Saddle point method.

  • 3.
    Abdallah, Nancy
    University of Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, Franc.
    On Hodge Theory of Singular Plane Curves2016In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 59, no 3, p. 449-460Article in journal (Refereed)
    Abstract [en]

    The dimensions of the graded quotients of the cohomology of a plane curve complement U = P-2/C with respect to the Hodge filtration are described in terms of simple geometrical invariants. The case of curves with ordinary singularities is discussed in detail. We also give a precise numerical estimate for the difference between the Hodge filtration and the pole order filtration on H-2(U, C).

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  • 4.
    Abdallah, Nancy
    University of Nice.
    On Plane Curves with Double and Triple Points2016In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 119, no 1, p. 60-72Article in journal (Refereed)
  • 5.
    Abdallah, Nancy
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Emsalem, Jacques
    Paris, France.
    Iarrobino, Anthony
    Department of Mathematics, Northeastern University, Boston, MA, 02115, USA.
    Nets of conics and associated Artinian algebras of length 72023In: European Journal of Mathematics, ISSN 2199-675X, E-ISSN 2199-6768, Vol. 9, no 2, article id 22Article in journal (Refereed)
    Abstract [en]

    We classify the orbits of nets of conics under the action of the projective linear group and we determine the specializations of these orbits, using geometric and algebraic methods. We study related geometric questions, as the parametrization of planar cubics. We show that Artinian algebras of Hilbert function H=(1,3,3,0) determined by nets, can be smoothed—deformed to a direct sum of fields; and that algebras of Hilbert function H=(1,r,2,0), determined by pencils of quadrics, can also be smoothed. This portion is a translation and update of a 1977 version, a typescript by the second two authors that was distributed as a preprint of University of Paris VII. In a new Historical Appendix A we describe related work prior to 1977. In an Update Appendix B we survey some developments since 1977 concerning nets of conics, related geometry, and deformations of Artinian algebras of small length.

  • 6.
    Abdallah, Nancy
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics.
    Hansson, Mikael
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Hultman, Axel
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Topology of posets with special partial matchings2019In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 348, p. 255-276Article in journal (Refereed)
    Abstract [en]

    Special partial matchings (SPMs) are a generalisation of Brentis special matchings. Let a pircon be a poset in which every non-trivial principal order ideal is finite and admits an SPM. Thus pircons generalise Mariettis zircons. We prove that every open interval in a pircon is a PL ball or a PL sphere. It is then demonstrated that Bruhat orders on certain twisted identities and quasiparabolic W-sets constitute pircons. Together, these results extend a result of Can, Cherniaysky, and Twelbeck, prove a conjecture of Hultman, and confirm a claim of Rains and Vazirani.

  • 7.
    Abdallah, Nancy
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Hultman, Axel
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Combinatorial invariance of Kazhdan-Lusztig-Vogan polynomials for fixed point free involutions2018In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 47, no 4, p. 543-560Article in journal (Refereed)
    Abstract [en]

    When acts on the flag variety of , the orbits are in bijection with fixed point free involutions in the symmetric group . In this case, the associated Kazhdan-Lusztig-Vogan polynomials can be indexed by pairs of fixed point free involutions , where denotes the Bruhat order on . We prove that these polynomials are combinatorial invariants in the sense that if is a poset isomorphism of upper intervals in the Bruhat order on fixed point free involutions, then for all v amp;gt;= u.

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  • 8.
    Abouzaid, Mohammed
    et al.
    Columbia Univ, Dept Math, 2990 Broadway,MC 4406, New York, NY 10027 USA.;Stanford Univ, Dept Math, Bldg 380, Stanford, CA 94305 USA.
    Diogo, Luis
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Monotone Lagrangians in cotangent bundles of spheres2023In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 427, article id 109114Article in journal (Refereed)
    Abstract [en]

    We study the compact monotone Fukaya category of T*Sn, for n & GE; 2, and show that it is split-generated by two classes of objects: the zero-section Sn (equipped with suitable bounding cochains) and a 1-parameter family of monotone Lagrangian tori (S1 x Sn-1)& tau;, with monotonicity constants & tau; > 0 (equipped with rank 1 unitary local systems). As a consequence, any closed orientable spin monotone Lagrangian (possibly equipped with auxiliary data) with non-trivial Floer cohomology is non-displaceable from either Sn or one of the (S1 x Sn-1)& tau;. In the case of T*S3, the monotone Lagrangians (S1 x S2)& tau; can be replaced by a family of monotone tori T & tau;3.& COPY.

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  • 9.
    Abouzaid, Mohammed
    et al.
    Columbia Univ, Dept Math, New York, NY 10027 USA.
    Kragh, Thomas
    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)
    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.

  • 10.
    Abouzaid, Mohammed
    et al.
    Columbia Univ, Dept Math, Room 509,MC 4406 2990 Broadway, New York, NY 10027 USA.
    Kragh, Thomas
    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)
    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.

  • 11.
    Abou-Zeid, M.
    et al.
    Georg August Univ Gottingen, SUB, Pl Gottinger Sieben 1, D-37073 Gottingen, Germany.
    Hull, C. M.
    Imperial Coll London, Blackett Lab, Theory Grp, Prince Consort Rd, London SW7 2AZ, England.
    Lindström, Ulf
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Imperial Coll London, Blackett Lab, Theory Grp, Prince Consort Rd, London SW7 2AZ, England.
    Rocek, M.
    SUNY Stony Brook, CN Yang Inst Theoret Phys, Stony Brook, NY 11794 USA.
    T-duality in (2,1) superspace2019In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 6, article id 138Article in journal (Refereed)
    Abstract [en]

    We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The complexified duality transformations we find are equivalent to the usual Buscher duality transformations (including an important refinement) together with diffeomorphisms. We use the gauging of sigma-models in (2,1) superspace, which we review and develop, finding a manifestly real and geometric expression for the gauged action. We discuss the obstructions to gauging (2,1) sigma-models, and find that the obstructions to (2,1) T-duality are considerably weaker.

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  • 12. Abramov, V.
    et al.
    Paal, E.Tallinn University of Technology.Silvestrov, Sergei D.Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Stolin, A.Chalmers University of Techology.
    Proceedings of the 3rd Baltic-Nordic Workshop “Algebra, Geometry, and Mathematical Physics”2008Conference proceedings (editor) (Refereed)
  • 13. Aghajani, A.
    et al.
    Razani, Abdolrahman
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Department of Mathematics, Faculty of Science, Imam Khomeini International University, Iran .
    Some completeness theorems in the Menger probabilistic metric space2008In: Applied Sciences: APPS, E-ISSN 1454-5101, Vol. 10, p. 1-8Article in journal (Refereed)
    Abstract [en]

    In this article, some new completeness theorems in probabilistic normed space are proved. Moreover, the existence of a constrictive Monger probabilistic normed space is shown.

  • 14. Aguilar, Marcelo
    et al.
    Menegon, Aurelio
    Seade, José
    On the Boundary of the Milnor Fiber2021In: Singularities and Their Interaction with Geometry and Low Dimensional Topology, Birkhäuser Verlag, 2021, p. 313-332Chapter in book (Refereed)
  • 15.
    Aichholzer, Oswin
    et al.
    Graz University of Technology, Austria.
    Anna, Brötzner
    Malmö University, Faculty of Technology and Society (TS), Department of Computer Science and Media Technology (DVMT).
    Bicolored Order Types2024In: Computing in Geometry and Topology, ISSN 2750-7823, Vol. 3, no 2Article in journal (Refereed)
    Abstract [en]

    In their seminal work on Multidimensional Sorting, Goodman and Pollack introduced the so-called order type, which for each ordered triple of a point set in the plane gives its orientation, clockwise or counterclockwise. This information is sufficient to solve many problems from discrete geometry where properties of point sets do not depend on the exact coordinates of the points but only on their relative positions. Goodman and Pollack showed that an efficient way to store an order type in a matrix λ of quadratic size (w.r.t. the number of points) is to count for every oriented line spanned by two points of the set how many of the remaining points lie to the left of this line. We generalize the concept of order types to bicolored point sets (every point has one of two colors). The bicolored order type contains the orientation of each bicolored triple of points, while no information is stored for monochromatic triples. Similar to the uncolored case, we store the number of blue points that are to the left of an oriented line spanned by two red points or by one red and one blue point in λB. Analogously the number of red points is stored in λR. As a main result, we show that the equivalence of the information contained in the orientation of all bicolored point triples and the two matrices λB and λR also holds in the colored case. This is remarkable, as in general the bicolored order type does not even contain sufficient information to determine all extreme points (points on the boundary of the convex hull of the point set).We then show that the information of a bicolored order type is sufficient to determine whether the two color classes can be linearly separated and how one color class can be sorted around a point of the other color class. Moreover, knowing the bicolored order type of a point set suffices to find bicolored plane perfect matchings or to compute the number of crossings of the complete bipartite graph drawn on a bicolored point set in quadratic time.

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  • 16.
    Aichholzer, Oswin
    et al.
    Graz University of Technology.
    Anna, Brötzner
    Malmö University, Faculty of Technology and Society (TS), Department of Computer Science and Media Technology (DVMT).
    Perz, Daniel
    Schnider, Patrick
    Department of Computer Science, ETH Zürich.
    Flips in Odd Matchings2024In: 40th European Workshop on Computational Geometry: Booklet of abstracts, 2024, Vol. 40, p. 447-452, article id 59Conference paper (Refereed)
    Abstract [en]

    Let P be a set of n = 2m + 1 points in the plane in general position. We define the graph GMP whose vertex set is the set of all plane matchings on P with exactly m edges. Two vertices in GMP are connected if the two corresponding matchings have m − 1 edges in common. In this work we show that GMP is connected.

  • 17.
    Alaee, Aghil
    et al.
    Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts; Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts.
    Cabrera Pacheco, Armando
    Department of Mathematics, Universität Tübingen, 72076 Tübingen, Germany.
    McCormick, Stephen
    Matematiska institutionen, Uppsala universitet, 751 06 Uppsala, Sweden.
    Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space2021In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 374, no 5, p. 3535-3555Article in journal (Refereed)
    Abstract [en]

    We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown–York quasi-local mass as it possesses positivity and rigidity properties, and therefore the stability of this rigidity statement can be studied. Specifically, we ask if the Brown–York mass of the boundary of some compact manifold is close to zero, must the manifold be close to a Euclidean domain in some sense?

    Here we consider a class of compact -manifolds with boundary that can be realized as graphs in , and establish the following. If the Brown–York mass of the boundary of such a compact manifold is small, then the manifold is close to a Euclidean hyperplane with respect to the Federer–Fleming flat distance.

  • 18.
    Alaee, Aghil
    et al.
    Clark Univ, Dept Math & Comp Sci, Worcester, MA 01610 USA.;Harvard Univ, Ctr Math Sci & Applicat, Cambridge, MA 02138 USA..
    Pacheco, Armando J. Cabrera
    Univ Tubingen, Dept Math, D-72076 Tubingen, Germany..
    McCormick, Stephen
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space2021In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 374, no 5, p. 3535-3555Article in journal (Refereed)
    Abstract [en]

    We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown-York quasi-local mass as it possesses positivity and rigidity properties, and therefore the stability of this rigidity statement can be studied. Specifically, we ask if the Brown-York mass of the boundary of some compact manifold is close to zero, must the manifold be close to a Euclidean domain in some sense? Here we consider a class of compact n-manifolds with boundary that can be realized as graphs in R-n(+1), and establish the following. If the Brown-York mass of the boundary of such a compact manifold is small, then the manifold is close to a Euclidean hyperplane with respect to the Federer-Fleming flat distance.

  • 19.
    Alegría, Carlos
    et al.
    Dipartimento di Ingegneria, Università Roma Tre, Italy.
    Anna, Brötzner
    Malmö University, Faculty of Technology and Society (TS), Department of Computer Science and Media Technology (DVMT).
    Nilsson, Bengt J.
    Malmö University, Faculty of Technology and Society (TS), Department of Computer Science and Media Technology (DVMT).
    Schmidt, Christiane
    Linköping University.
    Seara, Carlos
    Department of Mathematics, Universidad Politécnica de Catalunya, Spain.
    The Complexity of the Lower Envelope of Collections of Various Geometric Shapes2024In: 40th European Workshop on Computational Geometry: Booklet of abstracts, 2024, Vol. 40, p. 200-206, article id 25Conference paper (Refereed)
    Abstract [en]

    We study the problem of determining the complexity of the lower envelope of a collection of n geometric objects. For collections of rays; unit length line segments; and collections of unit squares to which we apply at most two transformations from translation, rotation, and scaling, we prove a complexity of Θ(n). If all three transformations are applied to unit squares, then we show the complexity becomes Θ(nα(n)), where α(n) is the slowly growing inverse of Ackermann’s function.

  • 20.
    Aleksanyan, Hayk
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Karakhanyan, Aram
    The University of Edinburgh.
    K-surfaces with free boundaries2017Manuscript (preprint) (Other academic)
  • 21.
    Alexandersson, Per
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Hopkins, Sam
    Zaimi, Gjergji
    Restricted Birkhoff Polytopes and Ehrhart Period Collapse2023In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444Article in journal (Refereed)
    Abstract [en]

    We show that the polytopes obtained from the Birkhoff polytope by imposing additional inequalities restricting the “longest increasing subsequence” have Ehrhart quasi-polynomials which are honest polynomials, even though they are just rational polytopes in general. We do this by defining a continuous, piecewise-linear bijection to a certain Gelfand–Tsetlin polytope. This bijection is not an integral equivalence but it respects lattice points in the appropriate way to imply that the two polytopes have the same Ehrhart (quasi-)polynomials. In fact, the bijection is essentially the Robinson–Schensted–Knuth correspondence.

  • 22.
    Alm, Johan
    Stockholm University, Faculty of Science, Department of Mathematics.
    Universal algebraic structures on polyvector fields2014Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The theory of operads is a conceptual framework that has become a kind of universal language, relating branches of topology and algebra. This thesis uses the operadic framework to study the derived algebraic properties of polyvector fields on manifolds.The thesis is divided into eight chapters. The first is an introduction to the thesis and the research field to which it belongs, while the second chapter surveys the basic mathematical results of the field.The third chapter is devoted to a novel construction of differential graded operads, generalizing an earlier construction due to Thomas Willwacher. The construction highlights and explains several categorical properties of differential graded algebras (of some kind) that come equipped with an action by a differential graded Lie algebra. In particular, the construction clarifies the deformation theory of such algebras and explains how such algebras can be twisted by Maurer-Cartan elements.The fourth chapter constructs an explicit strong homotopy deformation of polynomial polyvector fields on affine space, regarded as a two-colored noncommutative Gerstenhaber algebra. It also constructs an explicit strong homotopy quasi-isomorphism from this deformation to the canonical two-colored noncommmutative Gerstenhaber algebra of polydifferential operators on the affine space. This explicit construction generalizes Maxim Kontsevich's formality morphism.The main result of the fifth chapter is that the deformation of polyvector fields constructed in the fourth chapter is (generically) nontrivial and, in a sense, the unique such deformation. The proof is based on some cohomology computations involving Kontsevich's graph complex and related complexes. The chapter ends with an application of the results to properties of a derived version of the Duflo isomorphism.The sixth chapter develops a general mathematical framework for how and when an algebraic structure on the germs at the origin of a sheaf on Cartesian space can be "globalized" to a corresponding algebraic structure on the global sections over an arbitrary smooth manifold. The results are applied to the construction of the fourth chapter, and it is shown that the construction globalizes to polyvector fields and polydifferential operators on an arbitrary smooth manifold.The seventh chapter combines the relations to graph complexes, explained in chapter five, and the globalization theory of chapter six, to uncover a representation of the Grothendieck-Teichmüller group in terms of A-infinity morphisms between Poisson cohomology cochain complexes on a manifold.Chapter eight gives a simplified version of a construction of a family of Drinfel'd associators due to Carlo Rossi and Thomas Willwacher. Our simplified construction makes the connections to multiple zeta values more transparent--in particular, one obtains a fairly explicit family of evaluations on the algebra of formal multiple zeta values, and the chapter proves certain basic properties of this family of evaluations.

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  • 23.
    Alyounes, Noraldeen
    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
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  • 24.
    Ameriani, Samaneh
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Geometri and Physics.
    Delaunay-ytor2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 25. Ammann, Bernd
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Humbert, Emmanuel
    Smooth yamabe invariant and surgery2013In: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 94, no 1, p. 1-58Article in journal (Refereed)
    Abstract [en]

    We prove a surgery formula for the smooth Yamabe invariant sigma(M) of a compact manifold M. Assume that N is obtained from M by surgery of codimension at least 3. We prove the existence of a positive constant Lambda(n), depending only on the dimension n of M, such that sigma(N) >= min{sigma(M), Lambda(n)}.

  • 26. Améndola, Carlos
    et al.
    Kohn, Kathlén
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Reichenbach, Philipp
    Seigal, Anna
    Toric invariant theory for maximum likelihood estimation in log-linear models2021In: Algebraic Statistics, ISSN 2693-2997, Vol. 12, p. 187-211Article in journal (Refereed)
  • 27.
    Andersson, Lars
    et al.
    KTH, Superseded Departments (pre-2005), Mathematics.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Howard, Ralph
    Boundary and lens rigidity of Lorentzian surfaces1996In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 348, p. 2307-2329Article in journal (Refereed)
    Abstract [en]

    Let g be a Lorentzian metric on the plane ℝ2 that agrees with the standard metric g0 = -dx2 + dy2 outside a compact set and so that there are no conjugate points along any time-like geodesic of (ℝ2, g). Then (ℝ2, g) and (ℝ2, g0) are isometric. Further, if (M*, g*) and (M*, p*) are two dimensional compact time oriented Lorentzian manifolds with space-like boundaries and so that all time-like geodesies of (M, g) maximize the distances between their points and (M, g) and (M*, g*) are "boundary isometric", then there is a conformal diffeomorphism between (M, g) and (M*, g*) and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

  • 28.
    Andreasson, Rolf
    et al.
    Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden.
    Hultgren, Jakob
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Solvability of Monge-Ampère equations and tropical affine structures on reflexive polytopesManuscript (preprint) (Other academic)
    Abstract [en]

    Given a reflexive polytope with a height function, we prove a necessary and sufficient condition for solvability of the associated Monge-Ampère equation. When the polytope is Delzant, solvability of this equation implies the metric SYZ conjecture for the corresponding family of Calabi-Yau hypersurfaces. We show how the location of the singularities in the tropical affine structure is determined by the PDE in the spirit of a free boundary problem and give positive and negative examples, demonstrating subtle issues with both solvability and properties of the singular set. We also improve on existing results regarding the SYZ conjecture for the Fermat family by showing regularity of the limiting potential.

  • 29.
    Anna, Brötzner
    et al.
    Malmö University, Faculty of Technology and Society (TS), Department of Computer Science and Media Technology (DVMT).
    Nilsson, Bengt J.
    Malmö University, Faculty of Technology and Society (TS), Department of Computer Science and Media Technology (DVMT).
    Schmidt, Christiane
    Linköping University.
    The k-Transmitter Watchman Route Problem is NP-Hard Even in Histograms and Star-Shaped Polygons2024In: 40th European Workshop on Computational Geometry: Booklet of abstracts, 2024, Vol. 40, p. 381-387, article id 50Conference paper (Refereed)
    Abstract [en]

    A k-transmitter g in a polygon P, with n vertices, k-sees a point pP if the line segment gp intersects P’s boundary at most k times. In the k-Transmitter Watchman Route Problem we aim to minimize the length of a k-transmitter watchman route along which every point in the polygon—or a discrete set of points in the interior of the polygon—is k-seen. We show that the k-Transmitter Watchman Route Problem for a discrete set of points is NP-hard for histograms, uni-monotone polygons, and star-shaped polygons given a fixed starting point. For histograms and uni-monotone polygons it is also NP-hard without a fixed starting point. Moreover, none of these versions can be approximated to within a factor c · log n, for any constant c > 0.

  • 30. Ardila, Federico
    et al.
    Supina, Mariel
    Vindas-Meléndez, Andrés R.
    The equivariant Ehrhart theory of the permutahedron2020In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 148, no 12, p. 5091-5107Article in journal (Refereed)
    Abstract [en]

    Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness Conjecture in this special case.

  • 31.
    Arnlind, Joakim
    Linköping University, Department of Mathematics, Algebra, Geometry and Discrete Mathematics. Linköping University, Faculty of Science & Engineering.
    Levi-Civita connections for a class of noncommutative minimal surfaces2021In: International Journal of Geometric Methods in Modern Physics (IJGMMP), ISSN 0219-8878, Vol. 18, no 12, article id 2150194Article in journal (Refereed)
    Abstract [en]

    In this paper, we study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e. finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus for such modules, and provide a characterization in terms of the existence of a pseudo-inverse of the matrix representing the hermitian form with respect to a set of generators. As a first illustration of the above concepts, we find metric connections on the fuzzy sphere. Finally, the framework is applied to a class of noncommutative minimal surfaces, for which there is a natural concept of torsion, and we prove that there exist metric and torsion free connections for every minimal surface in this class.

  • 32.
    Arnlind, Joakim
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Huisken, Gerhard
    Max Planck Institute for Gravitational Physics.
    Multi linear formulation of differential geometry and matrix regularizations2012In: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 91, no 1, p. 1-39Article in journal (Refereed)
    Abstract [en]

    We prove that many aspects of the differential geometry of em-bedded Riemannian manifolds can be formulated in terms of multilinear algebraic structures on the space of smooth functions. Inparticular, we find algebraic expressions for Weingarten’s formula,the Ricci curvature and the Codazzi-Mainardi equations.For matrix analogues of embedded surfaces we define discretecurvatures and Euler characteristics, and a non-commutative Gauss–Bonnet theorem is shown to follow. We derive simple expressionsfor the discrete Gauss curvature in terms of matrices representingthe embedding coordinates, and explicit examples are provided.Furthermore, we illustrate the fact that techniques from differen-tial geometry can carry over to matrix analogues by proving thata bound on the discrete Gauss curvature implies a bound on theeigenvalues of the discrete Laplace operator.

  • 33.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Landi, Giovanni
    Univ Trieste, Italy; Inst Geometry & Phys IGAP, Italy; Ist Nazl Fis Nucl, Italy.
    Projections, modules and connections for the noncommutative cylinder2020In: Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, E-ISSN 1095-0753, Vol. 24, no 3, p. 527-562Article in journal (Refereed)
    Abstract [en]

    We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one can develop several concepts in a close analogy with the latter. In particular, we exhibit a countable number of nontrivial projections in the algebra of the noncommutative cylinder itself, and show that they provide concrete representatives for each class in the corresponding K-0 group. We also construct a class of bimodules endowed with connections of constant curvature. Furthermore, with the noncommutative cylinder considered from the perspective of pseudo-Riemannian calculi, we derive an explicit expression for the Levi-Civita connection and compute the Gaussian curvature.

  • 34.
    Arnlind, Joakim
    et al.
    Albert Einstein Institute, Golm, Germany..
    Silvestrov, Sergei
    Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden .
    Affine transformation crossed product type algebras and noncommutative surfaces2009In: Operator structures and dynamical systems :: July 21-25 2008, Lorentz Center, Leiden, the Netherlands, satellite conference of the fifth European Congress of Mathematics, American Mathematical Society (AMS), 2009, 503, p. 1-25Chapter in book (Refereed)
    Abstract [en]

    Several classes of *-algebras associated to teh action of an affine transformation are considered, and an investigation of the interplay between the different classes is initiated. Connections are established that relate representations of *-algebras, geometry of algebraic surfaces, dynamics of affine transformations, graphs and algebras coming from a quantization procedure of Poisson structures. In particular, algebras related to surgaced being inverse images of fourth order polynomials (in ) are studied in detail, and a close link between representation theory and geometric properties is established for compact as well as non-compact surfaces.

  • 35.
    Arnlind, Joakim
    et al.
    Albert Einstein Institute, Golm, Germany.
    Silvestrov, Sergei
    Lund University.
    Affine transformation crossed product type algebras and noncommutative surfaces2009In: Operator structures and dynamical systems: July 21-25 2008, Lorentz Center, Leiden, The Netherlands, satellite conference of the fifth European Congress of Mathematics, Amer. Math. Soc. , 2009, Vol. 503, p. 1-25Chapter in book (Refereed)
  • 36.
    Aryapoor, Masood
    Inst Res Fundamental Sci IPM, POB 19395-5746, Tehran, Iran.
    The Penrose transform in split signature2012In: Differential geometry and its applications (Print), ISSN 0926-2245, E-ISSN 1872-6984, Vol. 30, no 4, p. 334-346Article in journal (Refereed)
    Abstract [en]

    A version of the Penrose transform is introduced in split signature. It relates cohomological data on CP3 \ RP3 and the kernel of differential operators on M, the (real) Grassmannian of 2-planes in R-4. As an example we derive the following cohomological interpretation of the so-called X-ray transform

    H-c(1)(CP3\RP3, O(-2)) ->congruent to ker(rectangle(2.2) : Gamma(omega) (M, (epsilon|-1|) over tilde) -> Gamma(omega) (M, (epsilon|-3|) over tilde))

    where Gamma(omega) (M, (epsilon|-1|) over tilde) and Gamma(omega) (M, (epsilon|-3|) over tilde) are real analytic sections of certain (homogeneous) line bundles on M, c stands for cohomology with compact support and rectangle(2.2) is the ultrahyperbolic operator. Furthermore, this gives a cohomological realization of the so-called "minimal" representation of SL(4, R). We also present the split Penrose transform in split instanton backgrounds.

  • 37.
    Asekritova, Irina
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Carro, Maria J.
    Univ Barcelona, Spain.
    Kruglyak, Natan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Soria, Javier
    Univ Barcelona, Spain.
    Rearrangement estimates for A(infinity) weights2019In: Revista Matemática Complutense, ISSN 1139-1138, E-ISSN 1988-2807, Vol. 32, no 3, p. 731-743Article in journal (Refereed)
    Abstract [en]

    We find a new characterizations of an A(infinity) weight omega, in terms of the decreasing rearrangement of the restriction of omega to cubes Q.

  • 38.
    Asekritova, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Cerdá, Joan
    Barcelona University, Spain.
    Kruglyak, Natan
    Linköping University.
    The Riesz-Herz equivalence for capacitary maximal functions2012In: Revista Matemática Complutense, ISSN 1139-1138, Vol. 25, no 1, p. 43-59Article in journal (Refereed)
    Abstract [en]

    We prove a Riesz-Herz estimate for the maximal function associated toa capacity ConRn,MCf(x)=supQxC(Q)−1Q|f|, which extends the equivalence (Mf )∗(t)f∗∗(t) for the usual Hardy-Littlewood maximal function Mf. The proof is based on an extension of the Wiener-Stein estimates for the distribution function of the maximal function, obtained using a convenient family of dyadiccubes. As a byproduct we obtain a description of the norm of the interpolationspace (L1,L1,C)1/p,p,  where L1,C denotes the Morrey space based on a capacity.

  • 39.
    Asekritova, Irina
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Cobos, Fernando
    Complutense University of Madrid.
    Kruglyak, Natan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Interpolation of Closed Subspaces and Invertibility of Operators2015In: Journal of Analysis and its Applications, ISSN 0232-2064, Vol. 34, no 2015, p. 1-15Article in journal (Refereed)
    Abstract [en]

    Let (Y0,Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj, (j = 0,1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (θ, q) such that the real interpolation space (X0,X1)θ,q is a closed subspace of (Y0,Y1)θ,q. In particular, we establish conditions which are necessary and sufficient for the equality (X0,X1)θ,q = (Y0,Y1)θ,q, with the proof based on a previous result by Asekritova and Kruglyak on invertibility of operators. We also generalize the theorem by Ivanov and Kalton where this problem was solved under several rather restrictive conditions, such as that X1 = Y1 and X0 is a subspace of codimension one in Y0. 

  • 40.
    Asekritova, Irina
    et al.
    Linköping University, Department of Mathematics, Analysis and Mathematics Education. Linköping University, Faculty of Science & Engineering.
    Kruglyak, Natan
    Linköping University, Department of Mathematics, Analysis and Mathematics Education. Linköping University, Faculty of Science & Engineering.
    Mastylo, M.
    Adam Mickiewicz Univ, Poland.
    Stability of the inverses of interpolated operators with application to the Stokes system2023In: Revista Matemática Complutense, ISSN 1139-1138, E-ISSN 1988-2807, Vol. 36, p. 163-206Article in journal (Refereed)
    Abstract [en]

    We study the stability of isomorphisms between interpolation scales of Banach spaces, including scales generated by well-known interpolation methods. We develop a general framework for compatibility theorems, and our methods apply to general cases. As a by-product we prove that the interpolated isomorphisms satisfy uniqueness-of-inverses. We use the obtained results to prove the stability of lattice isomorphisms on interpolation scales of Banach function lattices and demonstrate their application to the Calderon product spaces as well as to the real method scales. We also apply our results to prove solvability of the Neumann problem for the Stokes system of linear hydrostatics on an arbitrary bounded Lipschitz domain with a connected boundary in , with data in some Lorentz spaces over the set ∂Ω equipped with a boundary surface measure.

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  • 41.
    Asplund, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Chekanov-Eliashberg dg-algebras and partially wrapped Floer cohomology2021Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of an introduction and two research papers in the fields of symplectic and contact geometry. The focus of the thesis is on Floer theory and symplectic field theory.

    In Paper I we show that the partially wrapped Floer cohomology of a cotangent fiber stopped by the unit conormal of a submanifold, is equivalent to chains of based loops on the complement of the submanifold in the base. For codimension two knots in the n-sphere we show that there is a relationship between the wrapped Floer cohomology algebra of the fiber and the Alexander invariant of the knot. This allows us to exhibit codimension two knots with infinite cyclic knot group such that the union of the unit conormal of the knot and the boundary of a cotangent fiber is not Legendrian isotopic to the union of the unit conormal of the unknot union the boundary and the same cotangent fiber.

    In Paper II we study the Chekanov-Eliashberg dg-algebra which is a holomorphic curve invariant associated to a smooth Legendrian submanifold. We extend this definition to singular Legendrians. Using the new definition we formulate and prove a surgery formula relating the wrapped Floer cohomology algebra of the co-core disk of a stop with the Chekanov-Eliashberg dg-algebra of its attaching locus interpreted as the Weinstein neighborhood of a singular Legendrian. A special case of this surgery formula, when the Legendrian is non-singular, establishes a proof of a conjecture by Ekholm-Lekili and independently by Sylvan. We furthermore provide an alternative geometric proof of the pushout diagrams for partially wrapped Floer cohomology and the stop removal formulas of Ganatra-Pardon-Shende.

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  • 42.
    Asplund, Johan
    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
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  • 43.
    Asplund, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Fiber Floer cohomology and conormal stops2020Licentiate thesis, monograph (Other academic)
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  • 44.
    Asplund, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Geometri and Physics.
    Fiber Floer cohomology and conormal stops2021In: The Journal of Symplectic Geometry, ISSN 1527-5256, E-ISSN 1540-2347, Vol. 19, no 4, p. 777-864Article in journal (Refereed)
    Abstract [en]

    Let S be a closed orientable spin manifold. Let K ⊂ S be a submanifold and denote its complement by MK. In this paper we prove that there exists an isomorphism between partially wrapped Floer cochains of a cotangent fiber stopped by the unit conormal ΛK and chains of a Morse theoretic model of the based loop space of MK, which intertwines the A-structure with the Pontryagin product. As an application, we restrict to codimension 2 spheres K ⊂ Sn where n = 5 or n ≥ 7. Then we show that there is a family of knots K so that the partially wrapped Floer cohomology of a cotangent fiber is related to the Alexander invariant of K. A consequence of this relation is that the link ΛK ∪ Λx is not Legendrian isotopic to Λunknot ∪ Λx where x ∈ MK.

  • 45.
    Asplund, Johan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Geometri and Physics.
    Ekholm, Tobias
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Geometri and Physics.
    Chekanov-Eliashberg dg-algebras for singular Legendrians2022In: The Journal of Symplectic Geometry, ISSN 1527-5256, E-ISSN 1540-2347, Vol. 20, no 3, p. 509-559Article in journal (Refereed)
    Abstract [en]

    The Chekanov–Eliashberg dg-algebra is a holomorphic curve invariant associated to Legendrian submanifolds of a contact manifold. We extend the definition to Legendrian embeddings of skeleta of Weinstein manifolds. Via Legendrian surgery, the new definition gives direct proofs of wrapped Floer cohomology push-out diagrams [22]. It also leads to a proof of a conjectured isomorphism [17, 25] between partially wrapped Floer cohomology and Chekanov–Eliashberg dg-algebras with coefficients in chains on the based loop space.

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  • 46.
    Athreya, Jayadev
    et al.
    Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA..
    Konstantoulas, Ioannis
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Lattice deformations in the Heisenberg group2020In: Groups, Geometry, and Dynamics, ISSN 1661-7207, E-ISSN 1661-7215, Vol. 14, no 3, p. 1007-1022Article in journal (Refereed)
    Abstract [en]

    The space of deformations of the integer Heisenberg group under the action of Aut(H(R)) is a homogeneous space for a non-reductive group. We analyze its structure as a measurable dynamical system and obtain mean and variance estimates for Heisenberg lattice point counting in measurable subsets of R-3; in particular, we obtain a random Minkowski-type theorem. Unlike the Euclidean case, we show there are necessary geometric conditions on the sets that satisfy effective variance bounds.

  • 47.
    Avdek, Russell
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Combinatorial Reeb dynamics on punctured contact 3-manifolds2023In: Geometry and Topology, ISSN 1465-3060, E-ISSN 1364-0380, Vol. 27, no 3, p. 953-1082Article in journal (Refereed)
    Abstract [en]

    Let Lambda(+/-) = Lambda(+) boolean OR Lambda(-) subset of (R-3, xi(std)) be a contact surgery diagram determining a closed, connected contact 3-manifold (S-Lambda +/-(3), xi(Lambda +/-)) and an open contact manifold (R-Lambda +/-(3), xi(Lambda +/-)). Following work of Bourgeois, Ekholm and Eliashberg, we demonstrate how Lambda(+/-) determines a family alpha(epsilon) of contact forms for (R-Lambda +/-(3), xi(Lambda +/-)) whose closed Reeb orbits are in one-to-one correspondence with cyclic words of composable Reeb chords on Lambda(+/-). We compute the homology classes and integral Conley-Zehnder indices of these orbits diagrammatically and develop algebraic tools for studying holomorphic curves in surgery cobordisms between the (R-Lambda +/-(3), xi(Lambda +/-)). These new techniques are used to describe the first known examples of closed, tight contact manifolds with vanishing contact homology: they are contact 1/k surgeries along the right-handed, tb = 1 trefoil for k > 0, which are known to have nonzero Heegaard Floer contact classes by work of Lisca and Stipsicz.

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  • 48.
    Avdek, Russell
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Geometri and Physics.
    Liouville hypersurfaces and connect sum cobordisms2021In: The Journal of Symplectic Geometry, ISSN 1527-5256, E-ISSN 1540-2347, Vol. 19, no 4, p. 865-957Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is to introduce Liouville hypersurfaces in contact manifolds, which generalize ribbons of Legendrian graphs and pages of supporting open books. Liouville hypersurfaces are used to define a gluing operation for contact manifolds called the Liouville connect sum. Performing this operation on a contact manifold (M,ξ) gives an exact—and in many cases, Weinstein—cobordism whose concave boundary is (M,ξ)

    and whose convex boundary is the surgered manifold. These cobordisms are used to establish the existence of “fillability” and “non-vanishing contact homology” monoids in symplectomorphism groups of Liouville domains, study the symplectic fillability of a family of contact manifolds which fiber over the circle, associate cobordisms to certain branched coverings of contact manifolds, and construct exact symplectic cobordisms that do not admit Weinstein structures.

    The Liouville connect sum generalizes the Weinstein handle attachment and is used to extend the definition of contact (1/k)

    -surgery along Legendrian knots in contact 3-manifolds to contact (1/k)-surgery along Legendrian spheres in contact manifolds of arbitrary dimension. We use contact surgery to construct exotic contact structures on 5- and 13-dimensional spheres after establishing that S2 and S6 are the only spheres along which generalized Dehn twists smoothly square to the identity mapping. The exoticity of these contact structures implies that Dehn twists along S2 and S6 do not symplectically square to the identity, generalizing a theorem of Seidel. A similar argument shows that the (2n+1)-dimensional contact manifold determined by an open book whose page is (TSn,−λcan) and whose monodromy is any negative power of a symplectic Dehn twist is not exactly fillable.

  • 49.
    Avdek, Russell
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Univ Paris Saclay, Lab Math Orsay, Orsay, France..
    Simplified SFT moduli spaces for Legendrian links2023In: The Journal of Symplectic Geometry, ISSN 1527-5256, E-ISSN 1540-2347, Vol. 21, no 2, p. 265-329Article in journal (Refereed)
    Abstract [en]

    We study moduli spaces M of holomorphic maps U to R-4 with boundaries on the Lagrangian cylinder over a Legendrian link Lambda subset of (R-3, xi std). We allow our domains, sigma, to have non-trivial topology in which case M is the zero locus of an obstruction function O, sending a moduli space of holomorphic maps in C to H-1(sigma). In general, O-1(0) is not combinatorially computable. However after a Legendrian isotopy Lambda can be made left-right-simple, implying that any U1) of index 1 is a disk with one or two positive punctures for which 7rC o U is an embedding.2) of index 2 is either a disk or an annulus with 7rC o U simply covered and without interior critical points. Therefore any SFT invariant of Lambda is combinatorially computable using only disks with <= 2 positive punctures.

  • 50. Avdonina, Elena D.
    et al.
    Ibragimov, Nail H.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Heat conduction in anisotropic media: Nonlinear self-adjointness and conservation laws2012In: Discontinuity, Nonlinearity and Complexity, ISSN 2164-6376, Vol. 1, no 3, p. 237-251Article in journal (Refereed)
    Abstract [en]

    Nonlinear self-adjointness of the anisotropic nonlinear heat equation is investigated. Mathematical models of heat conduction in anisotropic media with a source are considered and a class of self-adjoint models is identified. Conservation laws corresponding to the symmetries of the equations in question are computed.

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