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  1. 1. Topics in Computational Algebraic Geometry and Deformation Quantization

    Författare :Christine Jost; Sandra Di Rocco; Boris Shapiro; Gregory G. Smith; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Segre classes; Chern-Schwartz-MacPherson classes; topological Euler characteristic; computational algebraic geometry; numerical algebraic geometry; numerical homotopy methods; deformation quantization; polyvector fields; Fedosov quantization; Grothendieck-Teichmüller group; Mathematics; matematik;

    Sammanfattning : This thesis consists of two parts, a first part on computations in algebraic geometry, and a second part on deformation quantization. More specifically, it is a collection of four papers. In the papers I, II and III, we present algorithms and an implementation for the computation of degrees of characteristic classes in algebraic geometry. LÄS MER

  3. 2. Topological and geometrical methods in data analysis

    Författare :Oliver Gäfvert; Sandra di Rocco; Henry Schenck; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; multiparameter persistent homology; computational algebraic geometry; algorithms; complexity; Mathematics; Matematik;

    Sammanfattning : This thesis concerns two related data analysis pipelines, using topological and geometrical methods respectively, to extract relevant information. The first pipeline, referred to as the topological data analysis (TDA) pipeline, constructs a filtered simplicial complex on a given data set in order to describe its shape. LÄS MER

  4. 3. Theoretical and computational advances in small-angle x-ray scattering tensor tomography

    Författare :Leonard Nielsen; Chalmers tekniska högskola; []
    Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; tensor tomography; reciprocal space map; small-angle scattering;

    Sammanfattning : The relationships between microscopic and macroscopic structures is a central topic of materials physics. Small-angle x-ray scattering (SAXS) is a powerful experimental technique for probing and mapping variations in electron density, given by the reciprocal space map, down to the nanometer scale in two dimensions. LÄS MER

  5. 4. Admissible transformations and the group classification of Schrödinger equations

    Författare :Celestin Kurujyibwami; Peter Basarab-Horwath; Roman Popovych; Pontelis Damianou; Linköpings universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES;

    Sammanfattning : We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. LÄS MER

  7. 5. Vector-valued Eisenstein series of congruence types and their products

    Författare :Jiacheng Xia; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Hecke operator; Fourier expansion of modular forms; congruence type; products of Eisenstein series; vector-valued modular forms;

    Sammanfattning : Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. LÄS MER