Calculating the Conformal Modulus of Complex Tori and an Application to Graph Theory

Author

Jason Howard, University of Tennessee - Knoxville

Date of Award

12-2002

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Kenneth Stephenson

Committee Members

Charles Collins, Morwen Thistlethwaite

Abstract

In 1985 William Thurston conjectured that conformal mappings could be approximated using infintessimal circles. With this, the area of mathematics called Cirle Packing was born. The advantage of this technique is that it gives a computational method of understanding manifolds. In particular, we attempt to gain some insight of complex tori via Circle Packing. In practice, it is difficult to imagine what these tori look like. Computational techniques of Circle Packing will help us visualise these tori as points in moduli space by beginning with an initial triangulation of the torus. We then experiment with triangulations on a set number of vertices.

Recommended Citation

Howard, Jason, "Calculating the Conformal Modulus of Complex Tori and an Application to Graph Theory. " Master's Thesis, University of Tennessee, 2002.
https://trace.tennessee.edu/utk_gradthes/2066