# Senior Theses

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Available in PDF format (linked below) and in hard copy from the Mathematics Library (through 2010, more recent ones available soon). For more information, see Senior Thesis Guidelines.

## May 2015

Timothy Steven Murray, Spectral Asymptotics of the Laplacian on Surfaces of Constant Curvature

Thesis Advisor: Robert Strichartz, Mathematics

## January 2015

Matthew Stuart Farrell, The Halting Program for Chip-Firing on Finite Directed Graphs

Thesis Advisor: Lionel Levine, Mathematics

## May 2014

Walter Cai, Extremal 1-Cycle Lifespan Behavior under the Vietoris-Rips Complex

Thesis Advisor: Robert Strichartz, Mathematics

Sy yeu Chou, Numerical Simulations of N Point Vortices on Bounded Domains

Thesis Advisor: Robert Strichartz, Mathematics

Eric Primozic, Homogeneous Groups and Covers

Thesis Advisor: R. Keith Dennis, Mathematics

## May 2013

Thomas Brooks, Generating Sets of Mathieu Groups

Thesis Advisor: R. Keith Dennis, Mathematics

Weilin Li, Boundary Value Problems on a Half Sierpinski Gasket

Thesis Advisor: Robert Strichartz, Mathematics

Yiran Li, Hodge deRham Theory of Carpet Type Fractals

Thesis Advisor: Robert Strichartz, Mathematics

Min Lin, Strongly Flat p-Groups

Thesis Advisor: R. Keith Dennis, Mathematics

Diwakar Raisingh, Toward an Axiomatic Characterization of the Smash Sum

Thesis Advisor: Lionel Levine, Mathematics

Robert Ravier, Average Values of Functions on the Sierpinski Gasket

Thesis Advisor: Robert Strichartz, Mathematics

Yipu Wang, Maximal Unbalanced Families

Thesis Advisors: Louis Billera, Mathematics; Justin Moore, Mathematics

## May 2012

Sudesh Kalyanswamy, Inverse Galois Problem for Totally Real Number Fields

Thesis Advisor: Ravi Ramakrishna, Mathematics

Derek Lougee, Percolation on the Non-P.C.F. Sierpinski Gasket and Hexacarpet

Thesis Advisor: Benjamin Steinhurst, Mathematics

Benjamin Nachman, Generating Sequences of the Two Dimensional Special Projective Linear Group over Fields of Prime Order, PSL(2,p)

Thesis Advisor: R. Keith Dennis, Mathematics

Thomas Rudelius, A Geometric Understanding of Ricci Curvature in the Context of Pseudo-Riemannian Manifolds

Thesis Advisor: John Hubbard, Mathematics

Liang Ze Wong, Irredundant Generating Sets of Finite Nilpotent Groups

Thesis Advisor: R. Keith Dennis, Mathematics

## May 2011

Tarun Chitra, Generalized Complex Geometry, Sasakian Manifolds and ADS/CFT

Thesis Advisors: Leonard Gross, Mathematics; Liam McAllister, Physics

Matthew Guay, Infinity-Harmonic Functions on SG

Thesis Advisor: Robert Strichartz and Alexander Vladimirsky, Mathematics

Richard Gustavson, Some New Results on the Combinatorial Laplacian

Thesis Advisor: Edward Swartz, Mathematics

Zheng Kang Tham, Square-Free Matroids

Thesis Advisor: Edward Swartz, Mathematics

## May 2010

Divya Kirti, An Exploration of Transmission on Random Graphs

Thesis Advisor: Richard Durrett, Mathematics

## January 2010

Daniel Jack Collins, Generating Sequences of Finite Groups

Thesis Advisor: R. Keith Dennis, Mathematics

## May 2009

Kai Fong Ernest Chong, The Weak Order of Coxeter Systems and Combinatorial Properties of Descent Sets

Thesis Advisor: Edward Swartz, Mathematics

Steven Heilman, Homotopies of Eigenfunctions and the Spectrum of the Laplacian on the Sierpinski Carpet

Thesis Advisor: Robert Strichartz, Mathematics

Wei Quan Julius Poh, Properties of Posets in Non-crossing Pairings on Bitstrings

Thesis Advisor: Edward Swartz, Mathematics

## May 2008

Jessica Lucille DeGrado, Computing the Gradient of Laplacian Eigenfunctions on the Sierpinski Gasket

(This thesis consists of a joint paper produced with Professor Strichartz and Luke Rogers following Jessica's participation in the department's 2006 REU program.)

Thesis Advisor: Robert Strichartz, Mathematics

Hyun Kyu Kim, Representation Theoretic Existence Proof for Fischer Group Fi_23

Thesis Advisor: Gerhard O. Michler, Mathematics

Rami Mohieddine, Chaos in the Hodgkin-Huxley Equations: The Takens-Bodganov Cusp Bifurcation

Thesis Advisor: John Guckenheimer, Mathematics

## May 2007

Yu Tung Cheng, Continued Fractions

Thesis Advisor: Peter Kahn, Mathematics

Timothy David Cramer with Farkhod Eshmatov, Heat Kernel Coefficients for Periodic Schrödinger Operators

Thesis Advisor: Yuri Berest, Mathematics

Rafael Mariano Frongillo, Topological Entropy Bounds for Hyperbolic Dynamical Systems

Thesis Advisor: John Smillie, Mathematics

Yan Yancy Lo, Mathematical Models for Salmonella Transmission Dynamics

Thesis Advisor: Yrjo Grohn, Cornell Vet School; John Guckenheimer, Mathematics

Evan Jayson Marshak, A Survey of Results Regarding a Computational Approach to the Zeros of Dedekind Zeta Functions

Thesis Advisor: Ravi Ramakrishna, Mathematics

Jeremy Kenneth Miller, Finite Groups Acting on Surfaces as Rigid Motions of Euclidean Space

Thesis Advisor: Allen Hatcher, Mathematics

## May 2006

Thomas Franklin Church, The Magnus Representation of the Torelli Group I_{g,1}

Thesis Advisor: Karen Vogtmann, Mathematics

Wai Wai Liu, The Logarithmic Sobolev Constant of Some Finite Markov Chains

Thesis Advisor: Laurent Saloff-Coste, Mathematics

Philip Daniel Owrutsky, Orthogonal Polynomials with Respect to Self-Similar Measures

Thesis Advisor: Robert Strichartz, Mathematics

## May 2005

Saúl A. Blanco Rodríguez, Some Results on Combinatorial Game Theory

Thesis Advisor: Michael Morley, Mathematics

Vorrapan Chandee with Tian Tian Qiu, Counting Kneading Sequences

Thesis Advisor: Rodrigo Pérez, Mathematics

Timothy D. DeVries, The Weak Order and Flag h-Vector Inequalities

Thesis Advisor: Edward Swartz, Mathematics

Shawn Drenning, Fractal Analysis: Extending the Domain

Thesis Advisor: Robert Strichartz, Mathematics

## May 2004

Tian Tian Qiu with Vorrapan Chandee, Counting Kneading Sequences

Thesis Advisor: Rodrigo Pérez, Mathematics

Matthew J. Hirn, The Refinability of Step Functions

Thesis Advisor: Robert Strichartz, Mathematics

Elizabeth Rach, Power Law Distributions of Gene Family Sizes

Thesis Advisor: Richard Durrett, Mathematics