Mathematics Commons^™

Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis

Theses and Dissertations

This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.

Lattices And Their Applications To Rational Elliptic Surfaces, Gretchen Rimmasch

Theses and Dissertations

This thesis discusses some of the invariants of rational elliptic surfaces, namely the Mordell-Weil Group, Mordell-Weil Lattice, and another lattice which will be called the Shioda Lattice. It will begin with a brief overview of rational elliptic surfaces, followed by a discussion of lattices, root systems and Dynkin diagrams. Known results of several authors will then be applied to determine the groups and lattices associated with a given rational elliptic surface, along with a discussion of the uses of these groups and lattices in classifying surfaces.

Aspects Of Conformal Field Theory From Calabi-Yau Arithmetic, Rolf Schimmrigk

Faculty and Research Publications

This paper describes a framework in which techniques from arithmetic algebraic geometry are used to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and aspects of the underlying conformal field theory. As an application the algebraic number field determined by the fusion rules of the conformal field theory is derived from the number theoretic structure of the cohomological Hasse-Weil L-function determined by Artin's congruent zeta function of the algebraic variety. In this context a natural number theoretic characterization arises for the quantum dimensions in this geometrically determined algebraic number field.

Codes Over Rings From Curves Of Higher Genus, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

We construct certain error-correcting codes over finite rings and estimate their parameters. These codes are constructed using plane curves and the estimates for their parameters rely on constructing “lifts” of these curves and then estimating the size of certain exponential sums.

THE purpose of this paper is to construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools; notably, an estimate for the dimension of trace codes over rings (generalizing work of van der Vlugt over fields and some results on lifts of affin curves from field of characteristic p …

Dupin Submanifolds In Lie Sphere Geometry, Thomas E. Cecil, Shiing-Shen Chern

Mathematics Department Faculty Scholarship

No abstract provided.

Riemann Surfaces: Distribution Of Weierstrass Points On Nodal Curves Of Genus 2, Kathryn A. Furio '88

Fenwick Scholar Program

No abstract provided.