Essays about: "branched coverings"

Found 2 essays containing the words branched coverings.

1. 1. Generating Functions : Powerful Tools for Recurrence Relations. Hermite Polynomials Generating Function

   University essay from Linköpings universitet/Algebra, geometri och diskret matematik; Linköpings universitet/Tekniska fakulteten

   Author : Christoffer Rydén; [2023]
   Keywords : Ordinary power series generating function; Exponential generating function; Moment generating function; Hermite polynomials;

   Abstract : In this report we will plunge down in the fascinating world of the generating functions. Generating functions showcase the "power of power series", giving more depth to the word "power" in power series. We start off small to get a good understanding of the generating function and what it does. READ MORE

3. 2. Algorithmic Construction of Fundamental Polygons for Certain Fuchsian Groups

   University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

   Author : David Larsson; [2015]
   Keywords : Compact Riemann surfaces and uniformization; Fuchsian groups and automorphic functions; Hyperbolic geometry; Topological groups; Permutation groups; Computational methods; Covering spaces; branched coverings; Generators; relations; and presentations;

   Abstract : The work of mathematical giants, such as Lobachevsky, Gauss, Riemann, Klein and Poincaré, to name a few, lies at the foundation of the study of the highly structured Riemann surfaces, which allow definition of holomorphic maps, corresponding to analytic maps in the theory of complex analysis. A topological result of Poincaré states that every path-connected Riemann surface can be realised by a construction of identifying congruent points in the complex plane, the Riemann sphere or the hyperbolic plane; just three simply connected surfaces that cover the underlying Riemann surface. READ MORE