Using the Differential Fay Identities for ribbon graph enumeration

Authors

Indalecio Soto Jr., University of Texas-Pan American

Date of Award

7-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Virgil Pierce

Second Advisor

Dr. Paul Bracken

Third Advisor

Dr. Timothy Huber

Abstract

In this paper we are exploiting connections between the Differential Fay Identities and the partition function of Gaussian Unitary Random Matrices. The partition function has a asymptotic expression whose terms give the generating function for the enumeration of ribbon graphs partitioned by genus. These ribbon graphs (k; j), of k vertices of degree j have an orientation in genus g where the edges are represented as ribbons. Furthermore, we will develop connections between the Differential Fay Identities and introduce several theorems between the hierarchies of the identities. Lastly, we will briefly explore the first Differential Fay Identity that contains the KP equation.

Comments

Copyright 2014 Indalecio Soto Jr. All Rights Reserved.

https://www.proquest.com/dissertations-theses/using-differential-fay-identities-ribbon-graph/docview/1572056283/se-2

Granting Institution

University of Texas-Pan American