# Senior Theses

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