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  • Enumeration Problems on Symmetries of Riemann Surfaces

    Creator:
    Camacho, Charles A.
    Abstract:
    We describe two combinatorial problems in the theory of automorphism groups of compact Riemann surfaces of genus two or greater: enumerate the topological actions of a finite group on surfaces and determine the set of genera of surfaces admitting such a group action, called the genus spectrum. We illustrate results...
    Resource Type:
    Dissertation
    Full Text:
    : Enumeration Problems on Symmetries of Riemann Surfaces. Abstract approved: Ren Guo We describe two

  • On the Topologies of Moduli Spaces of Polygons: A Taxonomic Approach

    Creator:
    Krughoff, Stephen A.
    Abstract:
    Consider a polygon lying in the Euclidean plane with labeled edge lengths. The moduli space of polygons is the space of all polygons with the same labeled edge lengths, modulo orientation preserving isometries. It is well known that this space is generically a smooth manifold. For certain combinations of edge...
    Resource Type:
    Dissertation
    Full Text:
    Topologies of Moduli Spaces of Polygons: A Taxonomic Approach Abstract approved: Ren Guo Consider a polygon

  • Computable Randomness, and Coding the Orbits of the Collatz Map

    Creator:
    Robson, Charlie
    Abstract:
    In this thesis I will look at a definition of computable randomness from Algorithmic Information Theory as defined by Andre Nies through the lens of Computable Analaysis asdefined by Klaus Weihrauch. I will show that despite the fact that these two paradigmsgenerate distinct classes of computable supermartingales, the class of...
    Resource Type:
    Dissertation
    Full Text:
    , and Coding the Orbits of the Collatz Map Abstract approved: Ren Guo In this thesis I will look at a