## 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.