Sökning: "geometry of numbers"

Visar resultat 1 - 5 av 54 avhandlingar innehållade orden geometry of numbers.

  1. 1. Waring-type problems for polynomials : Algebra meets Geometry

    Författare :Alessandro Oneto; Boris Shapiro; Brian Harbourne; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; polynomials; Waring problems; Hilbert series; fat points; power ideals; secant varieties; Mathematics; matematik;

    Sammanfattning : In the present thesis we analyze different types of additive decompositions of homogeneous polynomials. These problems are usually called Waring-type problems and their story go back to the mid-19th century and, recently, they received the attention of a large community of mathematicians and engineers due to several applications. LÄS MER

  3. 2. Bounds on Hilbert Functions and Betti Numbers of Veronese Modules

    Författare :Ornella Greco; Mats Boij; Maria Evelina Rossi; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Hilbert function; Betti numbers; Veronese modules; Pinched veronese; h-vectors; Mathematics; Matematik;

    Sammanfattning : The thesis is a collection of four papers dealing with Hilbert functions and Betti numbers.In the first paper, we study the h-vectors of reduced zero-dimensional schemes in  . In particular we deal with the problem of findingthe possible h-vectors for the union of two sets of points of given h-vectors. LÄS MER

  4. 3. The density of rational points and invariants of genus one curves

    Författare :Manh Hung Tran; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; genus one; discriminant; modular form; Elliptic curve; height; descent; determinantal representation; invariant; rational point; theta function.; determinant method;

    Sammanfattning : The present thesis contains three papers dealing with two arithmetic problems on curves of genus one, which are closely related to elliptic curves. The first problem is to study the density of rational points presented in Papers I and II. LÄS MER

  5. 4. Geometry of numbers, class group statistics and free path lengths

    Författare :Samuel Holmin; Pär Kurlberg; Yiannis Petridis; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; geometry of numbers; lattices; class numbers; class groups; free path lengths; Mathematics; Matematik;

    Sammanfattning : This thesis contains four papers, where the first two are in the area of geometry of numbers, the third is about class group statistics and the fourth is about free path lengths. A general theme throughout the thesis is lattice points and convex bodies. LÄS MER

  7. 5. Convexity, Currents, and Lelong numbers

    Författare :Aron Lagerberg; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; complex analysis; convex analysis; currents; Lelong numbers; tropical geometry; L^2-estaimtes; Legendre transform; intersection theory; real Monge-Ampere operators; plurisubharmonic functions; integrability index; L^2-estaimtes;

    Sammanfattning : This thesis treats different aspects of convexity, both real and complex. On the real side, we study convexity in relation with certain currents. On the complex side, we study the singularities of plurisubharmonic functions. LÄS MER