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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. Asymptotic distribution of zeros of a certain class of hypergeometric polynomials

   Författare :Addisalem Abathun; Rikard Bögvad; Maurice Duits; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Hypergeometric polynomials; Potential theory; Mathematics; matematik;

   Sammanfattning : The thesis consists of two papers, both treating hypergeometric polynomials, and a short introduction. The main results are as follows. LÄS MER

4. 3. 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

5. 4. 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

7. 5. Dualities, affine vertex operator algebras, and geometry of complex polynomials

   Författare :Julius Borcea; Matematik (naturvetenskapliga fakulteten); []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Sendov s conjecture; annihilating fields; relative vertex operators; twisted modules; vertex operator algebras; Affine Lie algebras; standard modules; geometry of polynomials.; Mathematics; Matematik;

   Sammanfattning : This thesis consists of two parts which deal with different subjects. In the first part we study certain aspects of the representation theory of affine Kac-Moody Lie algebras and related structures. LÄS MER