Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132
For PhD Thesis, see here. This page is about Senior thesis.

In order that senior thesis produced by Harvard math students are easier for other undergrads to benefit from, we would like to exhibit more senior theses online (while all theses are available through Harvard university archives, it would be more convenient to have them online). It is absolutely voluntary, but if you decide to give us your permission, please send an electronic version of your thesis to cindy@math. The format can be in order of preference: DVI, PS, PDF. In the case of submitting a DVI format, make sure to include all EPS figures. You can also submit Latex or MS word source files.

If you are looking for information and advice from students and faculty about writing a senior thesis, look at this document. It was compiled from comments of students and faculty in preparation for, and during, an information session. Let Rosalie Belanger-Rioux ( know if you have any questions not addressed in this advice document.
Lawrence Cabusora '04 Diophantine Sets, Primes, and the Resolution of Hilbert’s 10th Problem PDF
Kevin Chan '04 Uniformization of Riemann Surfaces PDF
Jayce Getz '04 Classical and p-adic modular forms arising from the Borcherds exponents of other modular forms PDF
Dimitar Jetchev '04 Visible Elements of the Shafarevich-Tate Group PDF
Seth Kleinerman '04 On The Torsion Points of Elliptic Curves & Modular Abelian Varieties PDF
Richard Rivero '04 States, Link Polynomials, and the Tait Conjectures PDF
Alexander Schwartz '04 Elliptic Curves, Group Schemes and Mazur's Theorem PDF
Jonathan Michael Bloom '04 The local structure of smooth maps on manifoldsPDF
Gabriel Carroll '05 Formal Properties of Categorial Grammars PDF
Adam Simon Levine '05 Quasiconvexity in Word-Hyperbolic Coxeter Groups PDF
Ian Le '05 Tangent Lines to Curves Arising from Automorphic Distributions PDF
Emily Riehl '06 Lubin-Tate Formal Groups and Local Class Field Theory PDF
Elena Yudovina '08 Ratner's Theorems and The Oppenheimer Conjecture PDF
Dustin Clausen '08 The Springer Correspondence PDF
Silas Richelson '08 Classifying Varieties with Many Lines PDF
Alex Waldron '08 Fano Varieties of low-degree smooth hypersurfaces and unirationality PDF
Alison Miller '08 Explicit class field theory in function fields: Gross-Stark units and Drinfeld modules PDF
Sam Lewallen '08 The Volume Conjecture PDF
Joseph Armao IV '09 Evolutionary Game Dynamics, Cooperation and Costly Punishment PDF
John Cobb '09 An Introduction to Reverse Mathematics PDF
Hilary Finucane '09 Worst-Case and Average-Case Floating Codes for Flash Memory PDF
Kelley Harris '09 >On the Dynamics of Prebiotic Evolution PDF
John Lesieutre '09 The Knot Concordance Group PDF
Yakir Reshef '09 On Resilient and Exposure-Resilient Functions PDF
Shrenik Shah '09 Framed Deformation and Modularity PDF
Jeremy Booher'10 The Spirit of Moonshine: Connections between the Mathieu Groups and Modular Forms PDF
Zhou Fan '10 Global and Local Limit Laws for Eigenvalues of the Gaussian Unitary Ensemble and the Wishart Ensemble PDF
Daniel Litt '10 Introduction to Hodge-type Structures PDF
Laura Starkston '10 Contact Structures and Classifications of Legendrian and Transverse Knots PDF
Michael Viscardi '10 Alternate Compactifications of the Moduli Space of Genus One Maps PDF
Nicholas Wage '10 Evolutionary Games on Structured Populations under Weak Selection PDF
Jonathan Wang '11 The Moduli Stack of G-Bundles PDF
Rebecca Resnick '11 Finding the best model for continuous computation PDF
Brent Ho '11 Some constructions of irreducible representations of generic Hecke algebras of type An PDF
Roxana Feier '12 Methods of proof in random matrix theory PDF
Benjamin Dozier '12 Classification and Structure of Periodic Fatou Components PDF
Alex Kunkel '12 Étale Fundamental Group: An Exposition PDF
Eva Belmont '12 Stable Homotopy and the J-Homomorphism PDF
Rachel Zax '12 Simplifying Complicated Simplicial Complexes: Discrete Morse Theory and its Applications PDF
Krishna Dasaratha '13 The Reducibility and Dimension of Hilbert Schemes of Complex Projective Curves PDF
Eric Larson '13 The Maximal Rank Conjecture for Sections of Curves PDF
Christian Anderson '13 Defining physics at imaginary time: reflection positivity for certain Riemannian manifolds PDF
Jack Latta '14 Large graphs and the relationship between edge and triangle density PDF
Geoffrey Lee '14 The Classification of Topological Quantum Field Theories in Two Dimensions PDF
Levent Alpoge '14 The Average Elliptic Curve Has Few Integral Points PDF
Akhil Mathew '14 The Galois Group of a Stable Homotopy Theory PDF
Felix Wong '14 Quantum Ergodicity and the Analysis of Semiclassical Pseudodifferential Operators PDF
Marina Lehner '14 Kan Extensions as the Most Universal of the Universal Constructions PDF
Ryan Patrick '15 The Grothendieck-Riemann-Roch Theorem . PDF
Barry Jia Hao Tng '15 How big is that cookie? The integral geometric approach to geometric quantities. PDF
Theo McKenzie '15 Real Stable Polynomials: Description and Applications PDF
Seth Viren Neel '15 Mahalanobis Matching and Equal Percent Bias Reduction PDF
Alexander Makelov '15 Expansion in lifts of graphs PDF
Arpon Rakit '15 Characters in global equivariant homotopy theory PDF
Evan O'Dorney '15 Rings of small rank over a Dedekind domain PDF
Connor Harris '16 Complex Singularities and Twist Quantum Fields PDF
Kate Donahue '16 All Together Now" Linking the Public Goods Game and Prisoner's Dilemma for Robustness Against Free-Riders PDF
Nat Mayer '16 Mostow rigidity and the proportionality principle for simplicial volume PDF
Octav Dragoi '16 The Sarnak Conjecture: Orthogonality of the Mobius Function on Bounded Depth Circuits PDF
Sitan Chen '16 Geometry in Algorithms and Complexity: Holographic Algorithms and Valiant's Conjecture PDF
Xiaoyu He '16 Primes of the Form p+ny PDF
Justin William Henry Cavitt '17 Set-theoretic Geology, the Ultimate Inner Model, and New Axioms PDF
Greg Parker '17 Lefschetz Fibrations on 4-Manifolds PDF
Julian Salazar '17 Crepant resolutions of Weierstrass models with torsion PDF
Ashvin Swaminathan '17 Inflection Points in Families of Algebraic Curves PDF
Kevin Yang '17 Bulk Universality of Biregular Bipartite Graphs and Dyson's Brownian Motion for Covariance Matrices PDF
Kathleen Zhou '17 The Golod-Shafarevich Theorem and the class field tower problem PDF

Thesis 2017

Atanas, Adam Martin Nowak Michael Mitzenmacher Evolutionary Graph Theory of Biased Sexual Reproduction
Cavitt, Justin Hugh Woodin Set-Theoretic Geology, the Ultimate Inner Model and New Axioms
Gaebler, Hans Hugh Woodin Large Cardinals and Projective Determinacy
Jiradilok, Pakawut Tristan Collins Construction of a Heat Kernel on Holomorphic Line Bundles over Compact Riemann Surfaces
Larson, Hannah Joe Harris Normal Bundles of Lines on Hypersurfaces
Ma, Ziyu Martin Nowak Evolutionary Games on Structured Population: When Will Cooperation be Favored under Weak Selection
McNamara, Jake Hiro Tanaka How to Draw a Derived Manifold
Parker, Gregory Cliff Taubes Lefschetz Fibrations on 4-manifolds
Salazar, Julian Mboyo Esole, Noam Elkies Crepant Resolutions of Weierstrass Models with Torsion
Swaminathan, Ashvin Joe Harris Anand Patel Inflection Points in Families of Algebraic Curves
Torres, George Mike Hopkins The Maslov Index and the Poincare Birkhoff Theorem in Planar Hamiltonian Dynamics
Vasudevan Sahana S.T. Yau Pseudonorms on thePluricanonical Spaces of Riemann Surfaces
Wang, Xie S.T. Yau Positive Ricci Curvature on Compact 3-manifolds
Yan, Jeffrey Arthur Jaffe Discrete Quantum Gravity and Schrader's Last Theorem
Yang, Greg Madhu Sudan, S.T. Yau A Homological Theory of Functions
Yang, Kevin H.T. Yau Bulk Universality of Biregular Bipartite Graphs and Dyson's Brownian Motion for Covariance Matrices
Zhou, Kat Barry Mazur Golod-Shafarevich Theorem and the Class Field Tower Problem
Carrick, Christian Mike Hopkins An Elementary Proof of Quillen's Theormem for Complex Cobordism

Thesis 2016

Aida, Tara Daniel Cristofaro-Gardiner The Anand-Dumir-Gupta Conjectures and Generating Functions
Al-Natsheh, Adam Mike Hopkins E infinity-Ring Spectra from Diagram Spaces and Their Topological Hochschild Homology
Chen, Sitan Joe Harris, Joseph Landsbert (Texas AM), Leslie Valiant Geometry in Algorithms and Complexity: Holographic Algorithms and Valiant's Conjecture
Ding, David Noam Elkies Ranks of Elliptic Curves via the Shioda-Tate Theorem
Donahue, Kate Christian Hilbe, Oliver Hauser, Martin Nowak, Cliff Taubes "All Together Now" Linking the Public Goods Game and Prisoner's Dilemma for Robustness Against Free-Riders
Dragoi, Octav Arul Shankar The Sarnak Conjecture: Orthogonality of the Mobius Function on Bounded Depth Circuits
Harris, Connor Roberto Martinez Complex Singularities and Twist Quantum Fields
He, Xiaoyu Arul Shankar Primes of the Form p+ny
Landesman, Aaron Joe Harris, Anand Patel Interpolation in Algebraic Geometry
Li, Ben HT Yau, Samuel Kou Random Projection Ensembles and Extensions
Lombardi, Alex Noam Elkies Ranks of Elliptic Curves over Q: Theory and Computation
Menon, Priyanka Barry Mazur Ultrafilters in Social Choice Theory
Roberts, David Clifford Taubes A Variational Approach to Topological Degeneracy in Superconductors
Watters, Nicholas ST Yau Information Geometric Approaches for Neural Network Algorithms
Ibeling, Duligur Cristofaro-Gardiner The Limit of the Abelian Sandpile: An Approach Using PDE
Hitzig, Zoe Martin Nowak, Ned Hall The Evolutionary Dynamics of Distributive Justice
Nat Mayer, Clifford Taubes Mostow rigidity and the proportionality principle for simplicial volume

Thesis 2015

Dalal, Rahul H T Yau Edge Universality for Random Matrices through the Method of Steepest Descent
Eur, Christopher Melody Chan An Introduction to Toric Varieties
Gavin, Nicholas Neil Shephard, Sukhada Fadnavis Pricing Variance, Covariance and Correlation Swaps Using Time-Deformed Levy Processes
Makelov, Aleksandar Salil Vadhan, Curt McMullen Expansion in Lifts of Graphs
Mackereth, Stephen Peter Koellner Ramsey's Theorem for Pairs is Incomparable with Weak Konig's Lemma
McKenzie, Theo Peter Csikvari, Sukhada Fadnavis Real Stable Polynomials: Description and Application
Monks, Keenan Harry Lewis The Linear Sampling Problem in 2 Dimensions
Pfeffer, Joshua HT Yau Dyson Brownian Motion and Local Quantum Unique Ergodicity for the Generalized Erdos-Renyi Ensemble
Proulx, Michael Cliff Taubes An Introduction to Virtual Knot Topology and Khovanov Homology Theory
Raskit, Arpon Jacob Lurie Characters in Global Equivariant Homotopy Theory
Ryan Patrick Igor Rapinchuk The Grothendieck-Riemann-Roch Theorem
Tng, Barry Oliver Knill How big is that Cookie? The Integral Geometric Approach to Geometrical Quantities
Yuan, Allen Mike Hopkins The Burnside Category and Equivariant Stable Homotopy Theory
ODorney, Evan Benedict Gross Rings of small rank over a Dedekind domain

Thesis 2014

Alpoge, Levent Jacob Tsimerman The Average Elliptic Curve Has Few Integral Points
Balasubramanian, Anirudha Curt McMullen Self Avoiding Walks: Counting and Criticality
Cuipan, Andre Eric Maskin Efficient Auctions with Common Values
Cooney, Daniel Cliff Taubes Rock -Paper-Scissors: An Application of Evolutionary Game Theory to Electoral Politics
Dai, Irving Cliff Taubes An Introduction to Contact Topology: Foliation Theory and the Classification of Overtwisted Contact Structures
Goldberg, Gabriel Peter Koellner Reflection Properties of the Largest Large Cardinals
Latta, Jack Sukhada Fadnavis Large Graphs and the Relationship Between Edge and Triangle Density
Lee, Geoffrey Jacob Lurie The Classification of Topological Quantum Field Theories in Two Dimensions
Lehner, Marina Emily Riehl "All Concepts are Kan Extensions" Kan Extensions as the Most Universal of the Universal Constructions
Li, Changlin Nate Ackerman Noncomputable Isomorphism Types Computable Relative To All noncomputable Sets
Mathew, Akhil Mike Hopkins The Galois Group of a Stable Homotopy Theory
Postema, Jacob Dick Gross The Kronecker-Weber Theorem an Exploration of Algebraic Number Theory
Ruescher, Joseph Nate Ackerman Zero-One Laws and Limiting Structures
Stanton, Caitlin Dick Gross An Introduction to L functions and their Applications
Stock, Chris Cliff Taubes Random Walk Processes and Stochastic Differential Equations with Applications in Neuroscience
Vogt, Isabel Dick Gross The Lubin-Tate Deformation Space of Formal Groups
Wong, Felix Cliff Taubes Quantum Ergodicity and the Analysis of Semiclassical Pseudodifferential Operators
Sheridan, John Joe Harris An Investigation of Schubert Calculus

Thesis 2013

Rediet Abebe Mike Hopkins, Richard Stanley Plethysm of Schur Functions and Irreducible Polynomial Representations of the Complex General Linear Group
Christian Anderson Arthur Jaffe Defining physics at imaginary time: reflection positivity for certain Riemannian manifolds
Ben Adlam H T Yau
Baek, Gye Hyun Rachel Epstein The Online Bipartite Matching Problem
Ashok Cutkosky Erez Lieberman Aiden Polymer Simulations and DNA T
Krishna Dasartha Joe Harris The Reducibility and Dimension of Hilbert Schemes of Complex Projective Curves
Gurbir Dhillon Dennis Gaitsgory The Verdier Duality (for dummies)
Tony Feng Mark Kisin Hodge-Tate Theory
Amy (Qian) Huang Sukhada Fadnavis Chromatic Polynomials: An Exposition
Michael Jemison Mike Hopkins Quantum Variants of 3- Manifolds
Yacoub Kureh Vaibhav Gadre Perron-FrobeniusTheorem: Background, Proof and Applications
Eric Larson Joe Harris The Maximal Rank Conjecture for Sections of Curves
Lucia Mocz Mark Kisin Birch and Swinnerton-Dyer conjecture for Rank 0 and 1 Elliptic Curves over Q
Elena-Madalina Persu Leslie Valiant Computational Learning Methods for Evolution
Sarwar, Arush H T Yau Way of the Wavelet: Time-frequency Localization
Sealfon, Adam Salil Vadhan Fault Tolerant Graph Spanners

Thesis 2012

Osber Bastani Barry Mazur Homomorphic Encryption Schemes
Eva Belmont Michael Hopkins Stable Homotopy and the J-Homomorphism
Utsav Bhat H. T. Yau Limiting Spectral Distributions of Large Random Covariance Matrices
Tiffany Cai Joe Rabinoff Finite Group Schemes
John Casale Cliff Taubes Classification of Compact, Connected Surfaces
Benjamin Dozier Sarah Koch Classification and Structure of Periodic Fatou Components
Roxana Feier Michael Brenner Methods of Proof in Random Matrix Theory
Hallie Glickman-Hoch Kristen Wicklegren
Jeffrey Kalmus H.T. Yau The Long-run Behavior of Sinai's Random Walk in Random Environment
Alexander Kunkel Kirsten Wicklegren Etale Fundmental Group
Weiping Spencer Liang Michael Hopkins Spectral Sequences and the Stable Homotopy Group of Spheres
Philip Mocz Andrew Cotton-Clay The Poincare-Birkhoff Fixed Point Theorem and Periodic Orbits in the Restricted Three-body Problem
Ellen Rice Martin Nowak & Cliff Taubes The Dynamics of Intermittent Latent Reservoir Stimulation as a Tool for Eradication of Human Immunodeficiency Virus (HIV) Infection
Paul VanKoughnett Michael Hopkins On Two Non-Quillen-Equivalent Stable Model Categories with Triangle-Equivalent Homotopy Catgories
Zhuo Aubrey Yang Yum Tong Siu Primes in Arbitrarily Long Arithmetic Progression
Rachel Zax Michael Hopkins Simplifying Complicated Simplicial Complexes: Discrete Morse Theory and its Applications
Lin Zhai Scott Sheffield MIT and H. T. Yau Internal Diffusion Limited Aggregation and the Divisible Sandpile
Zhang, Yu Cliff Taubes From Penrose Tiles to Islamic Architecture, Aperiodic Tiling and Its Construction

Thesis 2011

Iurie Boreico Benedict Gross Relative Elliptic Curves
Kevin Donoghue Cliff Taubes An Introduction to Morse Homology
Sherry Gong Dennis Gaitsgory On Cyclic Homology
Francois Greer Joe Harris Hurwitz Moduli
Brent Ho Barry Mazur Some Constructions of Irreducible Representations of Generic Hecke Algebras of Type An
Yannik Pitcan Paul Bourgade Finite Markov Chain Mixing Time Analysis Using the Logarithmic Sobolev inequalities
Rebecca Resnick Gerald Sacks Finding The Best Model For Continuous Computation
Adrian Sanborn Sarah Koch Scaling Dimensions with Fractal Curves and applications to DNA folding
Arnav Tripathy Joe Harris Rational Connectivity
Dmitry Vaintrob Michael Hopkins Prime Isogenies of Elliptic Curves Over Arbitrary Number Fields
Jonathan Wang Dennis Gaitsgory The Moduli Stack of G-Bundles

Thesis 2010

Zachary Abel Salil Vadhan Lattice Tensor Constructions in the Complexity of the Shortest Vector Problem
Onur Alper Horng-Tzer Yau The Navier-Stokes Problem: An Introduction
Jeremy Booher Benedict Gross The Spirit of Moonshine: Connections between the Mathieu Groups and Modular Forms
Jonathan Brito John Hall An Introduction to Geometric Invariant Theory
Zhou Fan Horng-Tzer Yau Global and Local Limit Laws for Eigenvalues of the Gaussian Unitary Ensemble and the Wishart Ensemble
Ernest Fontes Michael Hopkins Hopkins A General descent approach for the Picard group of A(1)
Jesse Geneson Warren Goldfarb Entscheidungsproblem: solvability of the extended Ackermann-Denton-Kostyrko class with identity
Daniel Litt Wilfred Schmid Introduction to Hodge-type Structures
Andrew Schlafly Gerald Sacks Partial Recursive Functions in Zermelo-Fraenkel Set Theory
Laura Starkston Andrew Cotton-Clay Contact Structures and Classifications of Legendrian and Transverse Knots
Yi Sun Dennis Gaitsgory Frobenius Splitting for Schubert Varieties
Ameya Velingker Joseph Harris Series Expansions Arising from Gelfand Pairs and their Spherical Functions
Michael Viscardi Joseph Harris Alternate Compactifications of the Moduli Space of Genus One Maps
Nicholas Wage Martin Nowak Evolutionary Games on Structured Populations under Weak Selection
Olga Zverovich Salil Vadhan The Minimum Assignment Problem
Harrison Pugh Sarah Koch Applications of Differential Chains to Complex Analysis and Dynamics

Thesis 2009

Joseph Armao Martin Nowak Evolutionary Game Dynamics Cooperation, and Costly Punishment
Kevin Carde Lauren Williams Symmetric Functions, Hook Expansions, and the Hook Formula
John Cobb Warren Goldfarb (Phil) An Introduction to Reverse Mathematics
Grant Dasher Greg Morrisett (CS) & Cliff Taubes The Effects of Dependency: Combining Dependent Types and Effectful Computation
Alexander Dubbs M.Brenner(SEAS) Algorithms on Groups and Graph Isomorphism
Hilary Finucane Michael Mitzenmacher Worst-Case and Average-Case Floating Codes for Flash Memory
Kelley Harris Irene Chen (Sys.Bio) and Cliff Taubes On the Dynamics of Prebiotic Evolution
Scott Kominers, Noam Elkies Weighted Generating Functions & Configuration Results for Type II Lattices and Codes
John Lesieutre, Peter Kronheimer Slice Knots and the Concordance Group
Samuel Lichtenstein, Dennis Gaitsgory Vanishing cycles for algebraic D-Modules,
Shira Mitchell, Joe Blitzstein (Stat) Semiparametric Survival Models with Applications to HIV
Gilbert Moss Toby Gee Chebotarev's Theorem and Artin L-Functions
Charles Nathanson Martin Nowak Evolution of Cooperation in Structured Pupulations under Weak Selection
Yakir Reshef Salil Vadhan (EECS) On Resilient and Exposure-Resilient Functions
Shrenik Shah Richard Taylor Framed Deformation and Modularity
NIke Sun, Wilfried Schmid & Yum Tong Siu Conformally Invarinat Scaling Limits in Planar Critical Percolation
Matthew Tai, Shlomo Sternberg The Topology of the Energy-Momentum Level Sets for the Lagrange Top
Neal Wadhwa Martin Nowak Update Rules in Graph-Structures Populations

Thesis 2008

Bae Justin Peter Kronheimer The Classification, Construction, and Application of Symplectic Manifolds
Candelori Luca Barry Mazur Samit Dasgupta Modular Curves and Mazur's Theorem
Chao Connie Cliff Taubes Attila Ambrus (Econ) Coalitional Reasoning in Normal Form Games
Clausen Dustin Dennis Gaitsgory The Springer Correspondence
Con Diaz Gerardo Cliff Taubes Kirby Diagrams
Goodman Elizabeth Veronique Godin Essential Cohomology Operations
Hendriks Kristen Veronique Godin Morse Theory and the Bott Periodicity Theorem
Lewallen Sam Peter Kronheimer The Volume Conjecture
Miller Alison Samit Dasgupta Explicit class field theory in function fields: Gross-Stark units and Drinfeld modules
Richelson Silas Joe Harris Classifying Varieties with Many Lines
Tang Tina Martin Nowak Hidden Markov Models and Dynamic Programming Algorithms in Bioinformatics
Waldron Alex Joe Harris Fano Varieties of Low-Degree Smooth Hypersurfaces and Unirationality
Walters Robin Thomas Lam Quantum Groups
Wang Irena Benedict Gross Analogies between Elliptic Curves and Drinfeld Modules
Yudovina Elena Daniela Damjanovic Ratner's Theorems and the Oppenheim Conjecture

Thesis 2007

Bass Jared Barry Mazur Asymptotic Behavior in Coding Theory
Ellis Alexander Clifford Taubes Spin Geometry on Surfaces
Fontes Lila Peter Koellner (Phil) Independence Results for Peano Arithmetic
Gardiner Daniel Denis Gaitsgory Div Pic and Representability
Goodman Danny Robert Strain A Survey of Some Partial Existence and Regularity Results for the Incompressible Navier-Stokes Equations on R3
Jackson-Hanen David Peter Kronheimer The Seiberg-Witten Equations and Four-Manifolds
Jerison Daniel H.T. Yau Derivation of the Hartree energy functional for bosons with mean-field interaction
Levin Alex Noam Elkies Modular Forms and Sums of Squares Formulas
Lewis Joel Thomas Lam On Differential Posets
Lipson Mark Clifford Taubes, Jeremy Gunawardena Differential and graphical approaches to multistability in chemical reaction networks
Morgan Emily Rani Nelken Generalizing Synchronism to Linear Context-Free Rewriting Systems
Nakhoul Hani Andreea Nicoara Subelliptic Estimates and Finite Type for the delta-Neumann Problem on Cn
Nguyen Tien Anh John Dunacan Modular Invariance of Characters of Rational Vertex Operator Algebras
Papaioannou Athanasios Michael Hopkins Iwasawa Theory and the Stable Homotopy Category
Preygel Anatoly Joe Harris Degrees of Severi Varieties
Rapinchuk Igor Barry Mazur Elliptic Curves with Complex Multiplication and Kronecker's Jugendtraum
Seshadri Goutham Martin Nowak Consanguinity on Weighted Digraphs
Slavov Kaloyan Samit Dasgupta Gross-Stark Units for Totally Real Number Fields
Todorova Sonia Veronique Godin The Alexander Polynomial for Knots
Von Korff Michael Peter Kronheimer The Computational Complexity of the Jones Polynomial
Zhang Yan Lauren Williams An Introduction to Cluster Algebras

Thesis 2006

Balakrishnan Jennifer Benedict Gross Samit Dasgupta CM Constructions for Elliptic Curves
Catlin Michael Noam Elkies A Proof of the Mordell-Weil Theorem
Corwin Ivan Wilfried Schmid Automorphic Distributions From Cocompact Fuchsian Groups
Fithian William Dennis Gaitsgory The Riemann-Roch Theorem and Serre Duality for Algebraic Function Fields
Ganatra Sheel Peter Kronheimer Einstein Metrics on 4-Manifolds and Seiberg-Witten Theory
Gerasimov Timofei Jose Blanchet (Stat) Using Affine Processes to Price Defaultable bonds in an Intensity-Based Framework
Hurder Stephanie Drew Fudenbereg (Econ) Interdependent Preferences and the Universal Type Space
Le Jenna Barry Mazur The Structure of the Filtration of Ramification Groups for a Galois Extension of Local Fields
Liu Ricky Joseph Harris Specialization of Linear Systems of Plane Curves
Tarnita Corina Joseph Harris The Fano Variety of Lines on a Hypersurface and the Debarre-De Jong Conjecture
Patrikis Stefan Richard Taylor Lifting Symplectic Galois Representation
Riehl Emily Francesco Calegari Lubin-Tate Formal Groups and Local Class Field Theory
Rozenblyum Nikita Michael Hopkins Motivic Homotopy Theory and Power Operations in Motivic Cohomology
Valiant Gregory Mike Mitzenmacher (Comp) The Inefficiency of Selfishness in Network Routing
Zakharevich Inna Michael Hopkins Model Category Structures on sC

Thesis 2005

Daniel Almog Noam Elkies The Periodicity of the positions of a fixed Grundy value in certain poset games
Benjamin Bakker Shing-Tung Yau Toric Varieties and Mirror Symmetry
John Carlsson Todd Zickler A Mathematical Method for Musical Handwriting Recognition
Gabriel Carroll Clifford Taubes Formal Properties of Categorial Grammars
Andrew Chi Dylan Thurston A Topological Understanding of the AGM Iteration
Michael Chiappa Paul Bamberg Probalistic Algorithms Hash Functions and Spell Checking
Samuel Ganzfried Avi Pfeffer (CS) Computing Nash Equilibria in Two Player Strategic Form Games
Jeff Hammerbacher Tomaso Poggio Concentration and Stability in Statistical Learning Theory
Andrei Jorza William Stein The Birch and Swinnerton-Dyer Conjecture for Abelian Varieties over Number Fields
Ian Le Wilfried Schmid Tangent Lines to Curves Arising from Automorphic Distributions
Adam Levine Dylan Thurston Quasiconvexity in Word-Hyperbolic Coxeter Groups
Danielle Li William Stein Proving Mordell-Weil: A Descent in Three Parts
Arik Motskin L. Valiant Graph Planarity Kuratowski's Theorem and Planarity-Testing Algorithms
Ronen Mukamel Dylan Thurston Classifying Spaces for Riemann Structures on Smooth Surfaces
Daniel Rosenbloom P.Koellner Borel Selections and Set-Theoretic Abstraction
Jennifer Sinnott Frank Calegari On Stickelberger's Theorem, Herbrands's Theorem and Irregular Primes
Tseno Tselkov Richard Taylor A Modular Proof of the Class Number One Problem
Kartik Venkatram Tom Coates On the Number of Plane Conics through Five Points
Stephen Walker A.Dempster On the Use of Fuzzy Logic in Cluster Analysis

Thesis 2004

Jonathan Bloom Peter Kronheimer The Local Structure of Smooth Maps of Manifolds
Lawrence Cabusora Jessica Young Diophantine Set Primes and the Resolution of Hilbert's 10th Problem
Dustin Cartwright Barry Mazur Higher K-Theory
Kevin Chan Yum Tong Siu Uniformization of Riemann Surfaces
Keziah Cook Dylan Thurston Stable and Unstable Laminations of Automorphisms of the 2-holed Torus
Paul Fili Frank Calegari On the Elliptic Curve Method of Factorization
John Francis Mike Hopkins On the Connective Real K-theory of K(Z4): an Application of Stable Homotopy to Integrals on Spin Manifolds
Jayce Getz William Stein Classical and p-adic Modular Forms Arising from the Borcherds Exponents on Other Modular Forms
Judah Jacobson Nathan Intrator (Brown) Lower Bounds on Estimator Error and the Threshold Effect
Dimitar Jetchev William Stein Visible Elements of the Shafarevich-Tate Group
Seth Kleinerman William Stein On the Torsion Points of Elliptic Curves & Modular Abelian Varieties
Kwun Kwai Yum Tong Siu The Bochner-Kodaira Techniques and Strong Rigidity of Compact Kähler Manifolds
William Meyerson Derek Bruff Constructing the Daubechies Wavelet Basis
C.Pasquali Gonzalez Laura Matusevich, Marcus Mobius(Econ) On the Derivation of the Kalman Filter and Stochastic Time Series Analysis
Richard Rivero Dylan Thurston States Link Polynomial and the Tait Conjectures
Grant Schoenebeck Salil Vadhan The Computational Complexity of Finding Nash Equilibria in Succinctly Represented Games
Alexander Schwartz Frank Calegari Torsion Points in Elliptic Curves over Arbitrary Fields
Eric Swartz Laurent Berger L-Invariants

Thesis 2003

Trevor Bass Richard Stanley Excluded Minor Theory and Its Algorithmic Byproducts
Dennis Clark Nathan Dunfield Heegaard Splittings and Efficient Algorithms for Fundamental Groups of 3-Manifolds
Andrew Cotton Peter Kronheimer Gromov's Nonsqueezing Theorem
Richard Cudney Shing-Tung Yau Jet Spaces of Schemes
James Fowler Nathan Dunfield Finding 0-Efficient Triangulations of 3-Manifolds
Michael Greene Peter Kronheimer Bordism and Cobordism of (B f) Manifolds
John Gregg (+COMP) William Stein On Factoring Integers and Evaluating Discrete Logarithms
Jonathan Guberman Steve Altschuler Lani Wu Mass Action Reaction Networks and The Deficiency Zero Theorem
Wei Ho Noam Elkies The Main Conjecture of Iwasawa Theory
Harpaul Kohli (+PHIL) Gerald Sacks Making it Harder: Parallels between Jumping to Greater Degrees of Unsolvability or Information Encoding and Jumping to More Difficult Classes of Solvabililty
Isidora Milin Nathan Dunfield Dehn Fillings of Hyperbolic Three-Manifolds
Andrew Obus Benedict Gross The Trace Formula for ?0(N)
Joseph Rabinoff Steven DeBacker The Bruhat-Tits building of a p-adic Chevalley group and an application to representation theory
Kenneth Shirley Carl Morris (Stat) Applications of Markov Theory to Baseball
Aaron Tievsky (+PHYS) Kalle Karu A Geometric Littlewood-Richardson Rule for Equivariant Schubert Calculus
Anthony Varilly Benedict Gross Singular and Supersingular Moduli
Kirsten Wickelgren Curt McMullen Billiards in Polygons
Lara Marie Buchak Ned Block (Phil) Conceptual Problems Within The Computational Theory of Mind
Elizabeth Ogburn Phil Consequentialism and the Person as an End-in-Itself

Thesis 2002

Bronfman Aaron No advisor Growth Function of the Positive Braid Monoid
Cais Bryden Noam Elkies Riemann Surfaces and Modular Function Field Extensions
Castillo Thomas Joseph Harris Conservation of Number and the Grassmannian Perspectives on Schubert's Principle
Dinkin Aaron Richard Stanley Perfect Graphs and the Perfect Graph Conjecture
Healy Alexander (MATH+COMP) Michael Rabin Lattice Basis Reduction and Public-Key Cryptography
Hill Michael Michael Hopkins Peter Kronheimer Vector Fields on Spheres and Applications to Homotopy Theory
Josephson William Michael Rabin Verifiable Secret Sharing
Kelner Jonathan Peter Kronheimer The Surgery Theoretic Classification of High-Dimensional Smooth and Piecewise Linear Simply Connected Manifolds
Levine Lionel Noam Elkies The Rotor-Router Model
Matchett Phil Stephen DeBacker Haar Measure and Representation of the Heisenberg Group
Mihelich Chris William Stein Arithmetic Properties of Restricted partition functions
Miyasaka Eiichi Noam Elkies The Classification of some Finite Simple Groups and the Exceptional Isomorphisms between them
Moss Sarah Daniel Goroff Arrow's Impossibility Theorem: Combinatorial and Topological Approaches
Musiker Gregg Richard Stanley Cluster Algebras Somos Sequences and Exchange Graphs
Schedler Travis Nathan Dunfield Troels Jorgensen's Once-Punctured Torus Theory
Snyder Noah Dick Gross Artin's L-functions: A Historical Approach
Speyer David William Stein The Eichler-Shimura Correspondence: Theoretical and Computational Aspects
Tenner Bridget Wilfried Schmid Paul Sally (Chicago)
Warshall Andrew Noam Elkies Principles of Combinatorial Game Theory
Weinstein Jared Dick Gross The L-series of Number Fields and of Abelian Varieties
Agarwal Neil (COMP+MATH) Gerald Sacks, Salil Vadhan Automorphisms of the lattice of computably enumerable sets

Thesis 2001

Pranav Anand Warren Goldfarb Indicators for Non-Standard Models of Arithmetic
David Farris Raoul Bott Basic Morse Theory via Half Spaces and the Morse Complex
Lukasz Fidkowski Raoul Bott Several Approaches to Chern Classes
Elizabeth Foster Dick Gross Reciprocity
Daniel Glaser Leslie Valiant A Theoretical Discussion of Boosting
Paula Levy Leslie Valiant Algebraic Complexity: A Compendium of VNP-complete Problems
Maryanthe Malliaris Gerald Sacks Asymptotic Methods for Finite Models
Ciprian Manolescu Peter Kronheimer Finite Dimensional Approximation in Seiberg-Witten Theory
Davesh Maulik Dick Gross Explicit Class Field Theory for Function Fields
Petar Maymounkov M. Mitzenmacher Divergence-proving Techniques for Best Fit Bin Packing and Random Fit
Anna Medvedovsky Matt Baker Chebotarev's Density Theorem
Joshua Nichols-Barrer Joe Harris, Sean Keel GIT with an Application to the Birational Geometry of M31 and M41
Janak Ramakrishnan Barry Mazur Hilbert's 10th Problem and the Role of the Pell Equation
Nikolai Roussanov Ilia Binder The Mandelbrot's Conjecture and Critical Exponents for Brownian Motion
Bhatt Meghana Leslie Valiant "Aggregating Simple Functions into Powerful Predictors"

Thesis 2000

Ackerman Nate Gerald Sacks "Effective Descriptive Set Theory"
Acquista Karen Richard Taylor "Constructing the p-Adic L-Functions"
Barth Nils Joseph Harris "Pluricanonical Maps and Models of Algebraic Surfaces"
Bhat Harish Daniel Goroff "Aubry-Mather Sets and a Problem of Three-Bodies"
Gilchrist Pete Benedict Gross "An Exploration of Algebraic Number Theory: Algorithmic Development and Inplementation"
Jensen Meredith Warren Goldfarb "Establishing a Hierarchy for First-Order Quantifier Prefixes"
Kirkup George Barry Mazur "K2 of Number Fields"
Lee Dan Peter Kronheimer "Dirac Spinors and the Positive Energy Theorem"
Lee Alex Joseph Harris "The Hilbert Schemes of Curves in P3"
Lieblich Max Brian Conrad "Galois Representations Arising from p-Divisible Groups"
Lurie Jacob Benedict Gross "Simply Laced Lie Algebras and their Minuscule Representations"
McMillen Chris Daniel Goroff "Stochastic Calculus with Local Martingale Integrators"
Oprea Dragos Peter Kronheimer "Seiberg-Witten Invariants and Applications"
Proudfoot Nick Peter Kronheimer "Brieskorn's construction of Exotic Spheres"
Riesenfeld Samantha Michael Rabin "Computing the Irreducible Representations of a Finite Group over Finite Fields: The Non-Modular Case"
Sagalovskiy Dmitry David Kazhdan "Wavelets as Bases for LP Spaces"
Wichs David David Kazhdan "Morse Theory and its Applications"
Williams Lauren Eric Sommers "A q-analog of Weight Multiplicity"
Yasufuku Yu Richard Taylor "Deformation Theory of Formal Modules"
Harris David Gerald Sacks "Transcendence Degree in the General Setting"

Thesis 1999

Caramanis Constantine Cliff Taubes The Invariance of the Index of Elliptic Operators
Dasgupta Samit Brian Conrad Stark's Conjectures
Emanuel Michel Peter Kronheimer Classical Linear Groups over Finite Fileds
Friedman Marnie Michael Nakamaye and D Kleitman Lights Camera Optimal Actions: A Study of Strategies and Equilibria in Stochastic Games
Gnepp Andrei Clifford Taubes Smoothing of Topological Manifolds
Helm David Richard Taylor Barry Mazur The Euler System of Cyclotomic Units
Krieger Joachim Wilfried Schmid Geometric Methods in the Representation Theory of noncompact Liegroups
Lebow Eli Peter Kronheimer Gauge Theory and the ADHM Construction
Liu Ju Kuan Curt McMullen Integrating Quadratic Polynomials on the Real Line
Luber Harold Dan Strook The Central Limit Theorem: Proofs and Applications
Lyo Grace Cliff Taubes The Heegaard Decomposition Theorem A Morse-Theoretic Introduction
Marian Alina Wilfried Schmid On the Real Moment Map
Menon Sanjay Richard Taylor Barry Mazur Chebotarev's Density Theorem
Nichols Ann Michael Nakamaye, Jill Mesirov and James Ireland MIT A Bin Packing Algorithm Applied to a Genetic Reseqencing Assay
Ordway Damian S.-T. Yau The Topology of Manifolds with Positive Scalar Curvature
Oreskovich Anne Clifford Taubes On constructions Surgeries and Unique Decomposition Theorems of Knots Links and 3-Manifolds
Osserman Brian Richard Taylor Barry Mazur Heegner's Work and Its Applications
Plotkin Joshua Peter Kronheimer Cobordism and Exotic Spheres
Purdy David Noam Elkies Searching for High Rank Elliptic Curves
Sen Arun Richard Taylor Barry Mazur
Stephens Ben S.-T. Yau Compact Riemannian 7-Manifolds with Holonomy G2
Tenny Daniel Tom Braden Linear Programming and Karmarkar's Algorithm
Roshak Natalka (minor) PHIL+ Robert Nozick Warren Goldfarb - H.T. Number as an Internalized Regularity
Chang Yu-Han (minor) ECON+ Chris Foote - H.T. Exogenous Uncertainty in Computable General Equilibria Models: A Study on the Effects of Tax Policy on Economics Growth
Fernholz Dan Noam Elkies Quantum Error-Correcting Codes

Thesis 1998

David Agraz Kamal Khuri-Makdisi Artin L-functions: Applications and Calculations
Joshua Barback Gerald Sacks Some results related to retraceable sets and Ramsey's Theorem
Daniel Biss Raoul Bott & Michael Hopkins Homotopy Theory with a view toward Stable Computation
Andrew Blumberg David Kazhdan The Merkurjev-Suslin Theorem
Patrick Corn Richard Taylor Modular Forms and Galois Representations
Moon Duchin Persi Diaconis Combinatorial Methods and Constructive Notions for the Colin de Verdiere Graph Parameter
Samuel Grushevsky Yum Tong Siu Fenchel-Nielsen boundary of Teichmüller Space
Jesse Hahnel Dick Gross Additive Number Theory Modular Forms and the partition Function
Christopher Jerdonek Curt McMullen Hyperbolic Geometry in the Study of Three-Manifolds
Benjamin Lee David Kazhdan Geometric Quillen-Suslin
Florin Spinu Wilfried Schmid The Eisenstein Series of SL(2R)
Julianna Tymoczko Joe Harris The p-components of the stable homotopy groups of spheres
Stephen Wang Dick Gross The Uniqueness of Two Remarkable Lattices
Jonathan Weinstein Kenneth Fan Length Functions on Finite Reflection Groups
Eric Yeh Michael Nakamaye The Theory of Divisors in Krull Domains

Ph.D. Theses

Past Harvard Ph.D. thesis may be obtained directly from the address given to the right. The request must be sent in writing. They may reply with e-mail if you include your address, and will state the cost. Upon receipt of the requested dollar amount, they will send you a copy.
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Widener 90
Widener Library
Harvard University
Cambridge, MA 02138
(617) 295-2129

Since 2001, the titles of dissertations are listed online:

2001: 2001 Source:

Klenke, Tomas Antonius   Modular Varieties and Visibility   2001 June   14376
Mann, William Russell   Local Level-Raising for GLn   2001 June   14376
Pollack, Robert Jordan   On the p -adic L -function of a Modular Form at Supersingular Prime   2001 June   14376
Savitt, David Lawrence   Modularity of Some Potentially Barsotti-Tate Galois Representations   2001 June   14376
Vologodsky, Vadim   Hodge Structure on the Fundamental Group and Its Application to p-adic Integration   2001 June   14376
Warrington, Gregory Saunders   Kazhdan-Lusztig Polynomials, Pattern Avoidance and Singular Loci of Schubert Varieties   2001 June   14376
Williams, Samuel Rufus   Mod p L -functions and Analytic Kolyvagin Systems    2001 June   14376
2002: 2002 Source

Arinkin, Dmitro Olexandrovich    Fourier Transform for Quantized Completely Integrable Systems   2002 June   14593
DeMarco, Laura Grace   Holomorphic Families of Rational Maps: Dynamics, Geometry, and Potential Theory   2002 June   14593
Grushevsky, Samuel   Effective Schottky Problem   2002 June   14593
LiBine, Matvei   A Localization Argument for Characters of Reductive Lie Groups   2002 June   14593
Liu, Chiu-Chu Melissa   Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions   2002 June   14593
Mantovan, Elena   On Certain Unitary Group Shimura Varieties   2002 June   14593
Scott, Ralph H. III   Closed Self-Dual Two-Forms on Four-Dimensional Handlebodies   2002 November   14716
Trifkovic, Mak   On Mu-Invariants of Elliptic Curves over Q   2002 June   14593
Yang, Huan   Hecke Algebra Action on Siegel Modular Forms    2002 June    14593
2003: 2003 Source

Chen, Jiun-Cheng    Flops and Equivalences of Derived Categories for Threefolds with only Terminal Gorenstein Singularities   2003 June   14883
Cheng, Hsiao-Bing   Li-Yau-Hamilton Estimate For the Ricci Flow   2003 June   14883
Clark, Pete L.   Rational Points on Atkin-Lehner Quotients of Shimura Curves   2003 June   14883
Jao, David Yen   Supersingular Primes for Rational Points on Modular Curves   2003 June   14883
Karigiannis, Spiros   Deformations of G2 and Spin(7) Structures on Manifolds   2003 June   14883
Liu, Yu-Ru   Generalizations of the Turán and the Erds-Kac Theorems   2003 June   14883
Lucianovic, Mark William   Quaternion Rings, Ternary Quadratic Forms, and Fourier Coefficients of Modular Forms on PGSp(6)   2003 June   14883
Pop-Eleches, Cristian   Central Values of Rankin L-series Over Real Quadratic Fields   2003 June   14883
Rasmussen, Jacob Andrew   Floer Homology and Knot Complements   2003 June   14883
Weissman, Martin Hillel    The Fourier-Jacobi Map and Small Representations   2003 June   14883
2004: 2004 Source

Rauch, Daniel   Perturbations of the D-Bar Operator.   2004 March