Honors College Senior Thesis Presentations
Numerical Investigation to Produce a Fundamental Polyhedron
Academic Level at Time of Presentation
Senior
Major
Mathematics
Minor
Biology/Chemistry
List all Project Mentors & Advisor(s)
Dr. Dubravko Ivansic
Presentation Format
Oral Presentation
Abstract/Description
Among the infinitely many basic types of surfaces (compact 2-dimensional manifolds) all but three can be given a hyperbolic geometry structure. The hyperbolic structure corresponds to an action on the hyperbolic plane of a discontinuous group of hyperbolic isometries. The connection between the resulting manifold and the group can be understood through the fundamental polyhedron of the group, a hyperbolic polygon whose images by the isometries properly cover the hyperbolic plane. Several general ways of constructing a fundamental polyhedron are known. The purpose of the project is to numerically investigate another method in order to gain insight into whether it will produce a fundamental polyhedron.
Spring Scholars Week 2024 Event
Honors College Senior Thesis Presentations
Numerical Investigation to Produce a Fundamental Polyhedron
Among the infinitely many basic types of surfaces (compact 2-dimensional manifolds) all but three can be given a hyperbolic geometry structure. The hyperbolic structure corresponds to an action on the hyperbolic plane of a discontinuous group of hyperbolic isometries. The connection between the resulting manifold and the group can be understood through the fundamental polyhedron of the group, a hyperbolic polygon whose images by the isometries properly cover the hyperbolic plane. Several general ways of constructing a fundamental polyhedron are known. The purpose of the project is to numerically investigate another method in order to gain insight into whether it will produce a fundamental polyhedron.