Senior Thesis

This page is for Undergraduate Senior Theses.  For Ph.D. Theses, see here.

So that Math Department senior theses can more easily benefit other undergraduate, 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 Wes Cain ( know if you have any questions not addressed in the document.

Year Name Advisor Title
2021 Garret Brown Cliff Taubes Spinors and Twistors in Riemannian Geometry
2021 Leul Dadi Melanie Wood Error Correction Algorithms: Applications of Number Theory
2021 CJ Dowd Noam Elkies On parameterizations of cyclic N-isogenies and strict K-curves lying above rational points of Y + 0 (N)
2021 Joey Feffer Noam Elkies The Higman-Sims Group and Associated Combinatorial Structures
2021 Aidan Gibbons Francesca Dominici, Natash Pillai A Socio-demographic Analysis of Emissions from Industrial Facilities across the United States through Logistic Regressions
2021 Demi Guo Alexander Rush Towards More Efficient Natural Language Processing
2021 William Hartog Subhabrata Sen, Cliff Taubes Lost in Sparsity: Compressing Sensing and its Applications
2021 Mathhew Hase-Liu Dennis Gaitsgory The Weil conjectures: “‘-adic geometry” and point-counts of varieties
2021 Serina Hu Pavel Etinghof (MIT), Mike Hopkins An Introduction to Deligne Categories
2021 Bobae Johnson Ada Chan (York University), Cliff Taubes Laplacian State Transfer on Continuous-Time antum Walks
2021 Kenz Kallal Mark Kisin The Arthur-Selberg trace formula and some applications to arithmetic statistics
2021 Mark Kong Dennis Gaitsgory The Hodge Decomposition Theorem
2021 Vinh-Kha Le Mike Hopkins Towards an elementary proof of the Adams conjecture
2021 Matthew Lipman Elden Elmanto Prismatic Cohomology and Chromatic Redshift at Height
2021 Winnie Lu Wes Cain Nonlinear Dynamical Systems in Modeling Infectious Disease and Antibiotic Resistance
2021 Amal Mattoo Lauren Williams Saturation of the Newton Polytopes of Type A and D Cluster Variables
2021 Mikayel Mkrtchvan Dennis Gaitsgory Geometric Local Class F12021 ELD Theory, After L. Fargues
2021 Hanna Mularczyk Lauren Williams Laurent Expansion Size of Cluster Variables from Finite Cluster Algebras
2021 Richard Muratore Oliver Knill, Alexander Young (Statistics) Parameter Estimation for Stochastic Differential Equations
2021 Philip Nicol Wes Cain Modeling cancer evolution as an interacting particle system
2021 Tarik Rashada Joe Harris Geometry of Hilbert Schemes in P 3 and P 4
2021 Andrew Rao Eric Maskin, Jeff Behrends A Balancing Axiom for Social Choice Theory with Interpersonal Comparisons
2021 Alec Sun Noam Elkies A Sparse Set of Primes in Short Intervals
2021 Christina Tran Dusty Grundmeier, Cliff Taubes Cheeger’s Inequality and its Application to the Estimation of Network Congestion
2021 Lux Zhao Ann Blair, Hugh Woodin The History and Mathematics of the Axiom of Choice
2021 Fan Zhou Dennis Gaitstgory The Classical and the Functional BGG Resolutions


Year Name Advisor Title
2020 Asilis, Julian Mike Hopkins Probability Monads: A motivated treatment of monads and their algebras
2020 Biggs, Anna Peter Kronheimer An Introduction to Kähler Geometry and the Calabi Conjecture
2020 Carlstein, Anne Eric Maskin Exploring Weak Strategy-Proofness in Voting Theory
2020 Chen, Zihong Denis Auroux Special Lagrangians in the Landau-Ginzburg Mirror of CP2
2020 En, Christopher Cliff Taubes, David Parkes Introduction to Auction Theory
2020 Fernandez del Castillo, Juan Carlos Martin Nowak Mathematical Modeling for Tumor Progression on a Genetic Landscape: Understanding Cancer as a Continuous Time Branching Process
2020 Gopolan, Jay Hugh Woodin Much Ado about Infinity
2020 Ilarion Sytilidis, Filippos Peter Kronheimer On Kontsevich’s characteristic classes
2020 Jia, Emily David Parkes, Lauren Williams Explaining Explanations and Perturbing Perturbations
2020 Liu, Allen Dusty Grundmeier The Stars Above Us: Regular and Uniform Polytopes up to Four Dimensions
2020 McDonald, Vaughn Barry Mazur The Chabauty Method: old and new
2020 Melas-Kyriazi, Luke Arjun Manrai (Medical School) The Geometry of Semi-Supervised Learning
2020 Menon, Shreya Wes Cain Analysis of One- and Two-Delay Differential Equations
2020 Miller, Caleb Mike Hopkins The K-theoretic resolution of the Hopf invariant one and vector fields on spheres problems
2020 Suzgun, Mirac Stuart Shieber, Peter Kronheimer Formal Language Theory as a Framework for Understanding the Limitations of Recurrent Neural Networks
2020 Wang, Lucy Peter Koellner, Barry Mazur THROUGH THE ULTRAFILTER: Dictators and God


Year Name Advisor Title
2019 Chang, William Yum Tong Siu The Pair Correlation Conjecture for the Zeros of the Riemann Zeta Function
2019 Golowich, Noah Madhu Sudan
Cliff Taubes
The Role of Interaction in Common Randomness and Secret Key Generation
2019 Guo, Patrick Michael Mitzen- macher Lower bounds for graph stream algorithms through the Boolean Hidden Matching problem
2019 Kim, Daniel Barry Mazur Explicit Local Class Field Theory
2019 Krulewski, Cameron Mike Hopkins The K-Theoretic Classification of Topological Materials
2019 Lazowski, Davis Arthur Jaffe ADE quivers and Lie theory
2019 Li, Shira David Parkes, Scott Kominers, Cliff Taubes Deep Learning for Two-Sided Matching Markets
2019 Narayanan, Shyam Barry Mazur Modular Forms and Modular Congruences of the Partition Functions
2019 Pekala, Russell Salil Vadhan Computational Entropy and Cryptographic Constructions
2019 Polatajko, Daniel Michael Mitenmacher , Lauren Williams Algebraic Constructions of Ramanujan Graphs and Applications to Error Correcting Codes
2019 Saunders, Emily Mike Hopkins The Smale-Hirsch Theorem
2019 Spataru, Stefan Jelani Nelson Suprema of Stochastic Processes A Survery in estimating frequency moments of streams
2019 Stoner, David Prof. Zhao (MIT) and Cliff Taubes Graph Homomorphisms and Related Inequalities
2019 Sundaram, Aditi Peter Koellner Three Consistencies, Three Theories; An Exploration of Standard, Tableau, and Slow consistency in each of S ½, EA and Supexp
2019 Tian, Peter Yum Tong Siu Nash- Moser Theory ad Its Applications
2019 Tienni, Michele Arthur Jaffe Two Topological quantum field theories defined from subfactors
2019 Wang, Jack Cliff Taubes Secretaries and Prophets: Problems in Decision-Making Under Uncertainty.


Year Name Advisor Title
2018 Davis, Shanelle Dusty Grundmeier Further Analysis of Infinite Series: From Divergent to Convergent
2018 Gonzalez, Xavier Noam Elkies Uniqueness of the Leech Lattice
2018 Gordon, Andrew Joe Harris Punctual Hilbert Schemes of the Plane
2018 Gowravaram, Nihal Boaz Barak, Cliff Taubes Zero Knowledge Proofs and Applications to Financial Regulation
2018 Han, Johnnie Mark Kisin, Hector Pasten Bost’s Slopes and Transcendence Theory
2018 Hopkins, Max Madhu Sudan Representation-Theoretic Techniques for Independence Bounds of Cayley Graphs
2018 Hotchkiss, James Joe Harris The Noether-Lefschetz Theorem
2018 Hu, Jennifer Martin Nowak The Mathematics of Meaning: A Bayesian Approach to Comparing the Pragmatics of English
and Chinese
2018 Jagadeesan, Ravi Mboyo Esole, S. T. Yau Crepant resolutions of Q-factorial threefolds with compound Du Val
2018 Jain, Saksham Martin Nowak From Triangles to Teamwork: A Mathematical Explanation for the Evolution of Cooperation
2018 Kwon, Yong Wook Prof. Blitzstein, Wilfried Schmid, Prof. Nelson From Erdos-Renyi to Achlioptas: The Birth of a Giant
2018 Mackey, Wyatt Joe Harris Polygons Inscribed in One Curve and Circumscribed by Another
2018 Otness, Karl Michael Bronstein Graph Convolutions and Machine Learning
2018 Park, Handong Cliff Taubes, Daniel Cristofaro-Gardinar Investigating the Symplectic Ellipsoid Embedding Function
2018 Prasad, Rohil Cliff Taubes The Seiberg-Witten Invariant of a Homology S1 x S3
2018 Slipper, Aaron Noam Elkies Modular Magic: The theory of modular forms and the sphere
packing problem in dimensions 8 and 24
2018 Sundar, Vikram Aspuru-Guzik, David Gelbwaser, Martin Nowak Bounds on Errors in Observables Computed from Molecular
Dynamics Simulations
2018 Tao, James Dennis Gaitsgory Formal Aspects of Bezrukavnikov’s Equivalence for Affine Hecke Algebras
2018 Wang, Brabeeba Mike Hopkins What Information Does One Need to Recover the Homotopy Type of a Space at a Prime p
2018 Young, Fiona Mark Kempton, Ana Balibanu Non-Backtracking Random Walks on Graphs
2018 Sinik, Demren Joe Harris A Classification of the Representation s of Complex Semi-Simple Lie Algebras


Year Name Advisor Title
2017 Atanas, Adam Martin Nowak Michael Mitzenmacher Evolutionary Graph Theory of Biased Sexual Reproduction
2017 Cavitt, Justin Hugh Woodin Set-theoretic Geology, the Ultimate Inner Model and New
2017 Gaebler, Hans Hugh Woodin Large Cardinals and Projective Determinacy
2017 Jiradilok, Pakawut Tristan Collins Construction of a Heat Kernel on Holomorphic Line Bundles over Compact Riemann Surfaces
2017 Larson, Hannah Joe Harris Normal Bundles of Lines on Hypersurfaces
2017 Ma, Ziyu Martin Nowak Evolutionary Games on Structured Population: When Will Cooperation be Favored under Weak
2017 McNamara, Jake Hiro Tanaka How to Draw a Derived Manifold
2017 Parker, Gregory Cliff Taubes Lefschetz Fibrations on 4-Manifolds
2017 Salazar, Julian Mboyo Esole, Noam Elkies Crepant resolutions of Weierstrass Models with Torsion
2017 Swaminathan, Ashvin Joe Harris Anand Patel Inflection Points in Families of Algebraic Curves
2017 Torres, George Mike Hopkins The Maslov Index and the Poincare Birkhoff Theorem in Planar Hamiltonian Dynamics
2017 Vasudevan Sahana S.T. Yau Pseudonorms on thePluricanonical Spaces of Riemann Surfaces
2017 Wang, Xie S.T. Yau Positive Ricci Curvature on Compact 3-manifolds
2017 Yan, Jeffrey Arthur Jaffe Discrete Quantum Gravity and Schrader’s Last Theorem
2017 Yang, Greg Madhu Sudan, S.T. Yau A Homological Theory of Functions
2017 Yang, Kevin H.T. Yau Bulk Universality of Biregular Bipartite Graphs and Dyson’s
Brownian Motion for Covariance Matrices
2017 Zhou, Kat Barry Mazur The Golod-Shafarevich Theorem and the Class Field Tower
2017 Carrick, Christian Mike Hopkins An Elementary Proof of Quillen’s Theormem for Complex Cobordism


Year Name Advisor Title
2016 Aida, Tara Daniel Cristofaro-Gardiner The Anand-Dumir-Gupta Conjectures and Generating Functions
2016 Al-Natsheh, Adam Mike Hopkins E infinity-Ring Spectra from Diagram Spaces and Their Topological Hochschild Homology
2016 Chen, Sitan Joe Harris, Joseph Landsbert (Texas AM), Leslie Valiant Geometry in Algorithms and Complexity: Holographic Algorithms
and Valiant’s Conjecture
2016 Ding, David Noam Elkies Ranks of Elliptic Curves via the Shioda-Tate Theorem
2016 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
2016 Dragoi, Octav Arul Shankar The Sarnak Conjecture: Orthogonality of the Mobius Function
on Bounded Depth Circuits
2016 Harris, Connor Roberto Martinez Complex Singularities and Twist Quantum Fields
2016 He, Xiaoyu Arul Shankar Primes of the Form p+ny
2016 Landesman, Aaron Joe Harris, Anand Patel Interpolation in Algebraic Geometry
2016 Li, Ben HT Yau, Samuel Kou Random Projection Ensembles and Extensions
2016 Lombardi, Alex Noam Elkies Ranks of Elliptic Curves over Q: Theory and Computation
2016 Menon, Priyanka Barry Mazur Ultrafilters in Social Choice Theory
2016 Roberts, David Clifford Taubes A Variational Approach to Topological Degeneracy in Superconductors
2016 Watters, Nicholas ST Yau Information Geometric Approaches for Neural Network Algorithms
2016 Ibeling, Duligur Cristofaro-Gardiner The Limit of the Abelian Sandpile: An Approach Using PDE
2016 Hitzig, Zoe Martin Nowak, Ned Hall The Evolutionary Dynamics of Distributive Justice
2016 Nat Mayer, Clifford Taubes Mostow rigidity and the proportionality principle for
simplicial volume


Year Name Advisor Title
2015 Dalal, Rahul H T Yau Edge Universality for Random Matrices through the Method of Steepest Descent
2015 Eur, Christopher Melody Chan An Introduction to Toric Varieties
2015 Gavin, Nicholas Neil Shephard, Sukhada Fadnavis Pricing Variance, Covariance and Correlation Swaps Using Time-Deformed Levy Processes
2015 Makelov, Aleksandar Salil Vadhan, Curt McMullen Expansion in Lifts of Graphs
2015 Mackereth, Stephen Peter Koellner Ramsey’s Theorem for Pairs is Incomparable with Weak Konig’s Lemma
2015 McKenzie, Theo Peter Csikvari, Sukhada Fadnavis Real Stable Polynomials: Description and Applications
2015 Monks, Keenan Harry Lewis The Linear Sampling Problem in 2 Dimensions
2015 Pfeffer, Joshua HT Yau Dyson Brownian Motion and Local Quantum Unique Ergodicity for the Generalized
Erdos-Renyi Ensemble
2015 Proulx, Michael Cliff Taubes An Introduction to Virtual Knot Topology and Khovanov Homology Theory
2015 Raskit, Arpon Jacob Lurie Characters in Global Equivariant Homotopy Theory
2015 Ryan Patrick Igor Rapinchuk The Grothendieck-Riemann-Roch Theorem.
2015 Tng, Barry Oliver Knill How big is that Cookie? The Integral Geometric Approach to
Geometrical Quantities
2015 Yuan, Allen Mike Hopkins The Burnside Category and Equivariant Stable Homotopy Theory
2015 ODorney, Evan Benedict Gross Rings of small rank over a Dedekind domain
2015 Seth Viren Neel Mahalanobis Matching and Equal Percent Bias Reduction


Year Name Advisor Title
2014 Alpoge, Levent Jacob Tsimerman The Average Elliptic Curve Has Few Integral Points
2014 Balasubramanian, Anirudha Curt McMullen Self Avoiding Walks: Counting and Criticality
2014 Cuipan, Andre Eric Maskin Efficient Auctions with Common Values
2014 Cooney, Daniel Cliff Taubes Rock -Paper-Scissors: An Application of Evolutionary Game Theory to Electoral Politics
2014 Dai, Irving Cliff Taubes An Introduction to Contact Topology: Foliation Theory and the Classification of
Overtwisted Contact Structures
2014 Goldberg, Gabriel Peter Koellner Reflection Properties of the Largest Large Cardinals
2014 Latta, Jack Sukhada Fadnavis Large Graphs and the Relationship Between Edge and Triangle
2014 Lee, Geoffrey Jacob Lurie The Classification of Topological Quantum Field Theories in Two
2014 Lehner, Marina Emily Riehl “All Concepts are Kan Extensions” Kan Extensions as the Most
Universal of the Universal Constructions
2014 Li, Changlin Nate Ackerman Noncomputable Isomorphism Types Computable Relative To All noncomputable Sets
2014 Mathew, Akhil Mike Hopkins The Galois Group of a Stable Homotopy Theory
2014 Postema, Jacob Dick Gross The Kronecker-Weber Theorem an Exploration of Algebraic Number Theory
2014 Ruescher, Joseph Nate Ackerman Zero-One Laws and Limiting Structures
2014 Stanton, Caitlin Dick Gross An Introduction to L functions and their Applications
2014 Stock, Chris Cliff Taubes Random Walk Processes and Stochastic Differential Equations with Applications in
2014 Vogt, Isabel Dick Gross The Lubin-Tate Deformation Space of Formal Groups
2014 Wong, Felix Cliff Taubes Quantum Ergodicity and the Analysis of Semiclassical
Pseudodifferential Operators
2014 Sheridan, John Joe Harris An Investigation of Schubert Calculus


Year Name Advisor Title
2013 Rediet Abebe Mike Hopkins, Richard Stanley Plethysm of Schur Functions and Irreducible Polynomial Representations of the Complex
General Linear Group
2013 Christian Anderson Arthur Jaffe Defining physics at imaginary time: reflection positivity
for certain Riemannian manifolds
2013 Ben Adlam H T Yau
2013 Baek, Gye Hyun Rachel Epstein The Online Bipartite Matching Problem
2013 Ashok Cutkosky Erez Lieberman Aiden Polymer Simulations and DNA T
2013 Krishna Dasartha Joe Harris The Reducibility and Dimension of Hilbert Schemes of
Complex Projective Curves
2013 Gurbir Dhillon Dennis Gaitsgory The Verdier Duality (for dummies)
2013 Tony Feng Mark Kisin Hodge-Tate Theory
2013 Amy (Qian) Huang Sukhada Fadnavis Chromatic Polynomials: An Exposition
2013 Michael Jemison Mike Hopkins Quantum Variants of 3- Manifolds
2013 Yacoub Kureh Vaibhav Gadre Perron-FrobeniusTheorem: Background, Proof and Applications
2013 Eric Larson Joe Harris The Maximal Rank Conjecture for Sections of Curves
2013 Lucia Mocz Mark Kisin Birch and Swinnerton-Dyer conjecture for Rank 0 and 1 Elliptic Curves over Q
2013 Elena-Madalina Persu Leslie Valiant Computational Learning Methods for Evolution
2013 Sarwar, Arush H T Yau Way of the Wavelet: Time-frequency Localization
2013 Sealfon, Adam Salil Vadhan Fault Tolerant Graph Spanners


Year Name Advisor Title
2012 Osber Bastani Barry Mazur Homomorphic Encryption Schemes
2012 Eva Belmont Michael Hopkins Stable Homotopy and the J-Homomorphism
2012 Utsav Bhat H. T. Yau Limiting Spectral Distributions of Large Random Covariance Matrices
2012 Tiffany Cai Joe Rabinoff Finite Group Schemes
2012 John Casale Cliff Taubes Classification of Compact, Connected Surfaces
2012 Benjamin Dozier Sarah Koch Classification and Structure of Periodic Fatou
2012 Roxana Feier Michael Brenner Methods of Proof in Random Matrix Theory
2012 Hallie Glickman-Hoch Kristen Wicklegren
2012 Jeffrey Kalmus H.T. Yau The Long-run Behavior of Sinai’s Random Walk in Random Environment
2012 Alexander Kunkel Kirsten Wicklegren Étale Fundamental Group: An Exposition
2012 Weiping Spencer Liang Michael Hopkins Spectral Sequences and the Stable Homotopy Group of Spheres
2012 Philip Mocz Andrew Cotton-Clay The Poincare-Birkhoff Fixed Point Theorem and Periodic Orbits in the Restricted
Three-body Problem
2012 Ellen Rice Martin Nowak & Cliff Taubes The Dynamics of Intermittent Latent Reservoir Stimulation as a Tool for Eradication of
Human Immunodeficiency Virus (HIV) Infection
2012 Paul VanKoughnett Michael Hopkins On Two Non-Quillen-Equivalent Stable Model Categories with Triangle-Equivalent Homotopy
2012 Zhuo Aubrey Yang Yum Tong Siu Primes in Arbitrarily Long Arithmetic Progression
2012 Rachel Zax Michael Hopkins Simplifying Complicated Simplicial Complexes: Discrete Morse
Theory and its Applications
2012 Lin Zhai Scott Sheffield MIT and H. T. Yau Internal Diffusion Limited Aggregation and the Divisible Sandpile
2012 Zhang, Yu Cliff Taubes From Penrose Tiles to Islamic Architecture, Aperiodic Tiling and Its Construction


Year Name Advisor Title
2011 Iurie Boreico Benedict Gross Relative Elliptic Curves
2011 Kevin Donoghue Cliff Taubes An Introduction to Morse Homology
2011 Sherry Gong Dennis Gaitsgory On Cyclic Homology
2011 Francois Greer Joe Harris Hurwitz Moduli
2011 Brent Ho Barry Mazur Some Constructions of Irreducible Representations of Generic
Hecke Algebras of Type An
2011 Yannik Pitcan Paul Bourgade Finite Markov Chain Mixing Time Analysis Using the Logarithmic Sobolev inequalities
2011 Rebecca Resnick Gerald Sacks Finding The Best Model For Continuous Computation
2011 Adrian Sanborn Sarah Koch Scaling Dimensions with Fractal Curves and applications to DNA folding
2011 Arnav Tripathy Joe Harris Rational Connectivity
2011 Dmitry Vaintrob Michael Hopkins Prime Isogenies of Elliptic Curves Over Arbitrary Number Fields
2011 Jonathan Wang Dennis Gaitsgory The Moduli Stack of G-Bundles


Year Name Advisor Title
2010 Zachary Abel Salil Vadhan Lattice Tensor Constructions in the Complexity of the Shortest Vector Problem
2010 Onur Alper Horng-Tzer Yau The Navier-Stokes Problem: An Introduction
2010 Jeremy Booher Benedict Gross The Spirit of Moonshine: Connections between the Mathieu
Groups and Modular Forms
2010 Jonathan Brito John Hall An Introduction to Geometric Invariant Theory
2010 Zhou Fan Horng-Tzer Yau Global and Local Limit Laws for Eigenvalues of the Gaussian
Unitary Ensemble and the Wishart Ensemble
2010 Ernest Fontes Michael Hopkins Hopkins A General descent approach for the Picard group of A(1)
2010 Jesse Geneson Warren Goldfarb Entscheidungsproblem: solvability of the extended Ackermann-Denton-Kostyrko class with
2010 Daniel Litt Wilfred Schmid Introduction to Hodge-type Structures
2010 Andrew Schlafly Gerald Sacks Partial Recursive Functions in Zermelo-Fraenkel Set Theory
2010 Laura Starkston Andrew Cotton-Clay Contact Structures and Classifications of Legendrian and
Transverse Knots
2010 Yi Sun Dennis Gaitsgory Frobenius Splitting for Schubert Varieties
2010 Ameya Velingker Joseph Harris Series Expansions Arising from Gelfand Pairs and their Spherical Functions
2010 Michael Viscardi Joseph Harris Alternate Compactifications of the Moduli Space of Genus
One Maps
2010 Nicholas Wage Martin Nowak Evolutionary Games on Structured Populations under Weak
2010 Olga Zverovich Salil Vadhan The Minimum Assignment Problem
2010 Harrison Pugh Sarah Koch Applications of Differential Chains to Complex Analysis and Dynamics


Year Name Advisor Title
2009 Joseph Armao Martin Nowak Evolutionary Game Dynamics, Cooperation and Costly
2009 Kevin Carde Lauren Williams Symmetric Functions, Hook Expansions, and the Hook Formula
2009 John Cobb Warren Goldfarb (Phil) An Introduction to Reverse Mathematics
2009 Grant Dasher Greg Morrisett (CS) & Cliff Taubes The Effects of Dependency: Combining Dependent Types and Effectful Computation
2009 Alexander Dubbs M.Brenner(SEAS) Algorithms on Groups and Graph Isomorphism
2009 Hilary Finucane Michael Mitzenmacher Worst-Case and Average-Case Floating Codes for Flash
2009 Kelley Harris Irene Chen (Sys.Bio) and Cliff Taubes >On the Dynamics of Prebiotic Evolution
2009 Scott Kominers, Noam Elkies Weighted Generating Functions & Configuration Results for Type II Lattices and Codes
2009 John Lesieutre, Peter Kronheimer The Knot Concordance Group
2009 Samuel Lichtenstein, Dennis Gaitsgory Vanishing cycles for algebraic D-Modules,
2009 Shira Mitchell, Joe Blitzstein (Stat) Semiparametric Survival Models with Applications to HIV
2009 Gilbert Moss Toby Gee Chebotarev’s Theorem and Artin L-Functions
2009 Charles Nathanson Martin Nowak Evolution of Cooperation in Structured Pupulations under Weak Selection
2009 Yakir Reshef Salil Vadhan (EECS) On Resilient and Exposure-Resilient Functions
2009 Shrenik Shah Richard Taylor Framed Deformation and Modularity
2009 NIke Sun, Wilfried Schmid & Yum Tong Siu Conformally Invarinat Scaling Limits in Planar Critical Percolation
2009 Matthew Tai, Shlomo Sternberg The Topology of the Energy-Momentum Level Sets for the Lagrange Top
2009 Neal Wadhwa Martin Nowak Update Rules in Graph-Structures Populations


Year Name Advisor Title
2008 Bae Justin Peter Kronheimer The Classification, Construction, and Application of Symplectic Manifolds
2008 Candelori Luca Barry Mazur Samit Dasgupta Modular Curves and Mazur’s Theorem
2008 Chao Connie Cliff Taubes Attila Ambrus (Econ) Coalitional Reasoning in Normal Form Games
2008 Clausen Dustin Dennis Gaitsgory The Springer Correspondence
2008 Con Diaz Gerardo Cliff Taubes Kirby Diagrams
2008 Goodman Elizabeth Veronique Godin Essential Cohomology Operations
2008 Hendriks Kristen Veronique Godin Morse Theory and the Bott Periodicity Theorem
2008 Lewallen Sam Peter Kronheimer The Volume Conjecture
2008 Miller Alison Samit Dasgupta Explicit class field theory in function fields: Gross-Stark
units and Drinfeld modules
2008 Richelson Silas Joe Harris Classifying Varieties with Many Lines
2008 Tang Tina Martin Nowak Hidden Markov Models and Dynamic Programming Algorithms in Bioinformatics
2008 Waldron Alex Joe Harris Fano Varieties of Low-Degree Smooth Hypersurfaces and
2008 Walters Robin Thomas Lam Quantum Groups
2008 Wang Irena Benedict Gross Analogies between Elliptic Curves and Drinfeld Modules
2008 Yudovina Elena Daniela Damjanovic Ratner’s Theorems and The Oppenheimer Conjecture


Year Name Advisor Title
2007 Bass Jared Barry Mazur Asymptotic Behavior in Coding Theory
2007 Ellis Alexander Clifford Taubes Spin Geometry on Surfaces
2007 Fontes Lila Peter Koellner (Phil) Independence Results for Peano Arithmetic
2007 Gardiner Daniel Denis Gaitsgory Div Pic and Representability
2007 Goodman Danny Robert Strain A Survey of Some Partial Existence and Regularity Results for the Incompressible
Navier-Stokes Equations on R3
2007 Jackson-Hanen David Peter Kronheimer The Seiberg-Witten Equations and Four-Manifolds
2007 Jerison Daniel H.T. Yau Derivation of the Hartree energy functional for bosons with mean-field interaction
2007 Levin Alex Noam Elkies Modular Forms and Sums of Squares Formulas
2007 Lewis Joel Thomas Lam On Differential Posets
2007 Lipson Mark Clifford Taubes, Jeremy Gunawardena Differential and graphical approaches to multistability in chemical reaction networks
2007 Morgan Emily Rani Nelken Generalizing Synchronism to Linear Context-Free Rewriting Systems
2007 Nakhoul Hani Andreea Nicoara Subelliptic Estimates and Finite Type for the delta-Neumann Problem on Cn
2007 Nguyen Tien Anh John Dunacan Modular Invariance of Characters of Rational Vertex Operator Algebras
2007 Papaioannou Athanasios Michael Hopkins Iwasawa Theory and the Stable Homotopy Category
2007 Preygel Anatoly Joe Harris Degrees of Severi Varieties
2007 Rapinchuk Igor Barry Mazur Elliptic Curves with Complex Multiplication and Kronecker’s Jugendtraum
2007 Seshadri Goutham Martin Nowak Consanguinity on Weighted Digraphs
2007 Slavov Kaloyan Samit Dasgupta Gross-Stark Units for Totally Real Number Fields
2007 Todorova Sonia Veronique Godin The Alexander Polynomial for Knots
2007 Von Korff Michael Peter Kronheimer The Computational Complexity of the Jones Polynomial
2007 Zhang Yan Lauren Williams An Introduction to Cluster Algebras


Year Name Advisor Title
2006 Balakrishnan Jennifer Benedict Gross Samit Dasgupta CM Constructions for Elliptic Curves
2006 Catlin Michael Noam Elkies A Proof of the Mordell-Weil Theorem
2006 Corwin Ivan Wilfried Schmid Automorphic Distributions From Cocompact Fuchsian Groups
2006 Fithian William Dennis Gaitsgory The Riemann-Roch Theorem and Serre Duality for Algebraic Function Fields
2006 Ganatra Sheel Peter Kronheimer Einstein Metrics on 4-Manifolds and Seiberg-Witten Theory
2006 Gerasimov Timofei Jose Blanchet (Stat) Using Affine Processes to Price Defaultable bonds in an Intensity-Based Framework
2006 Hurder Stephanie Drew Fudenbereg (Econ) Interdependent Preferences and the Universal Type Space
2006 Le Jenna Barry Mazur The Structure of the Filtration of Ramification Groups for a Galois Extension of Local
2006 Liu Ricky Joseph Harris Specialization of Linear Systems of Plane Curves
2006 Tarnita Corina Joseph Harris The Fano Variety of Lines on a Hypersurface and the Debarre-De Jong Conjecture
2006 Patrikis Stefan Richard Taylor Lifting Symplectic Galois Representation
2006 Riehl Emily Francesco Calegari Lubin-Tate Formal Groups and Local Class Field Theory
2006 Rozenblyum Nikita Michael Hopkins Motivic Homotopy Theory and Power Operations in Motivic Cohomology
2006 Valiant Gregory Mike Mitzenmacher (Comp) The Inefficiency of Selfishness in Network Routing
2006 Zakharevich Inna Michael Hopkins Model Category Structures on sC


Year Name Advisor Title
2005 Daniel Almog Noam Elkies The Periodicity of the positions of a fixed Grundy value in certain poset games
2005 Benjamin Bakker Shing-Tung Yau Toric Varieties and Mirror Symmetry
2005 John Carlsson Todd Zickler A Mathematical Method for Musical Handwriting Recognition
2005 Gabriel Carroll Clifford Taubes Formal Properties of Categorial Grammars
2005 Andrew Chi Dylan Thurston A Topological Understanding of the AGM Iteration
2005 Michael Chiappa Paul Bamberg Probalistic Algorithms Hash Functions and Spell Checking
2005 Samuel Ganzfried Avi Pfeffer (CS) Computing Nash Equilibria in Two Player Strategic Form Games
2005 Jeff Hammerbacher Tomaso Poggio Concentration and Stability in Statistical Learning Theory
2005 Andrei Jorza William Stein The Birch and Swinnerton-Dyer Conjecture for Abelian Varieties over Number Fields
2005 Ian Le Wilfried Schmid Tangent Lines to Curves Arising from Automorphic
2005 Adam Levine Dylan Thurston Quasiconvexity in Word-Hyperbolic Coxeter Groups
2005 Danielle Li William Stein Proving Mordell-Weil: A Descent in Three Parts
2005 Arik Motskin L. Valiant Graph Planarity Kuratowski’s Theorem and Planarity-Testing Algorithms
2005 Ronen Mukamel Dylan Thurston Classifying Spaces for Riemann Structures on Smooth Surfaces
2005 Daniel Rosenbloom P.Koellner Borel Selections and Set-Theoretic Abstraction
2005 Jennifer Sinnott Frank Calegari On Stickelberger’s Theorem, Herbrands’s Theorem and Irregular Primes
2005 Tseno Tselkov Richard Taylor A Modular Proof of the Class Number One Problem
2005 Kartik Venkatram Tom Coates On the Number of Plane Conics through Five Points
2005 Stephen Walker A.Dempster On the Use of Fuzzy Logic in Cluster Analysis


Year Name Advisor Title
2004 Jonathan Bloom Peter Kronheimer The Local Structure of Smooth Maps of Manifolds
2004 Lawrence Cabusora Jessica Young Diophantine Sets, Primes, and the Resolution of Hilbert’s
10th Problem
2004 Dustin Cartwright Barry Mazur Higher K-Theory
2004 Kevin Chan Yum Tong Siu Uniformization of Riemann Surfaces
2004 Keziah Cook Dylan Thurston Stable and Unstable Laminations of Automorphisms of the 2-holed Torus
2004 Paul Fili Frank Calegari On the Elliptic Curve Method of Factorization
2004 John Francis Mike Hopkins On the Connective Real K-theory of K(Z4): an Application of Stable Homotopy to Integrals
on Spin Manifolds
2004 Jayce Getz William Stein Classical and p-adic Modular Forms Arising from
the Borcherds Exponents on Other Modular Forms
2004 Judah Jacobson Nathan Intrator (Brown) Lower Bounds on Estimator Error and the Threshold Effect
2004 Dimitar Jetchev William Stein Visible Elements of the Shafarevich-Tate
2004 Seth Kleinerman William Stein On The Torsion Points of Elliptic Curves
& Modular Abelian Varieties
2004 Kwun Kwai Yum Tong Siu The Bochner-Kodaira Techniques and Strong Rigidity of Compact K�hler Manifolds
2004 William Meyerson Derek Bruff Constructing the Daubechies Wavelet Basis
2004 C.Pasquali Gonzalez Laura Matusevich, Marcus Mobius(Econ) On the Derivation of the Kalman Filter and Stochastic Time Series Analysis
2004 Richard Rivero Dylan Thurston States, Link Polynomials, and the Tait
2004 Grant Schoenebeck Salil Vadhan The Computational Complexity of Finding Nash Equilibria in Succinctly Represented Games
2004 Alexander Schwartz Frank Calegari Torsion Points in Elliptic Curves over Arbitrary Fields
Elliptic Curves, Group Schemes and Mazur’s Theorem
2004 Eric Swartz Laurent Berger L-Invariants


Year Name Advisor Title
2003 Trevor Bass Richard Stanley Excluded Minor Theory and Its Algorithmic Byproducts
2003 Dennis Clark Nathan Dunfield Heegaard Splittings and Efficient Algorithms for Fundamental Groups of 3-Manifolds
2003 Andrew Cotton Peter Kronheimer Gromov’s Nonsqueezing Theorem
2003 Richard Cudney Shing-Tung Yau Jet Spaces of Schemes
2003 James Fowler Nathan Dunfield Finding 0-Efficient Triangulations of 3-Manifolds
2003 Michael Greene Peter Kronheimer Bordism and Cobordism of (B f) Manifolds
2003 John Gregg (+COMP) William Stein On Factoring Integers and Evaluating Discrete Logarithms
2003 Jonathan Guberman Steve Altschuler Lani Wu Mass Action Reaction Networks and The Deficiency Zero Theorem
2003 Wei Ho Noam Elkies The Main Conjecture of Iwasawa Theory
2003 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
2003 Isidora Milin Nathan Dunfield Dehn Fillings of Hyperbolic Three-Manifolds
2003 Andrew Obus Benedict Gross The Trace Formula for ?0(N)
2003 Joseph Rabinoff Steven DeBacker The Bruhat-Tits building of a p-adic Chevalley group and an application to
representation theory
2003 Kenneth Shirley Carl Morris (Stat) Applications of Markov Theory to Baseball
2003 Aaron Tievsky (+PHYS) Kalle Karu A Geometric Littlewood-Richardson Rule for Equivariant Schubert Calculus
2003 Anthony Varilly Benedict Gross Singular and Supersingular Moduli
2003 Kirsten Wickelgren Curt McMullen Billiards in Polygons
2003 Lara Marie Buchak Ned Block (Phil) Conceptual Problems Within The Computational Theory of Mind
2003 Elizabeth Ogburn Phil Consequentialism and the Person as an End-in-Itself


Year Name Advisor Title
2002 Bronfman Aaron No advisor Growth Function of the Positive Braid Monoid
2002 Cais Bryden Noam Elkies Riemann Surfaces and Modular Function Field Extensions
2002 Castillo Thomas Joseph Harris Conservation of Number and the Grassmannian Perspectives on Schubert’s Principle
2002 Dinkin Aaron Richard Stanley Perfect Graphs and the Perfect Graph Conjecture
2002 Healy Alexander (MATH+COMP) Michael Rabin Lattice Basis Reduction and Public-Key Cryptography
2002 Hill Michael Michael Hopkins Peter Kronheimer Vector Fields on Spheres and Applications to Homotopy Theory
2002 Josephson William Michael Rabin Verifiable Secret Sharing
2002 Kelner Jonathan Peter Kronheimer The Surgery Theoretic Classification of High-Dimensional Smooth and Piecewise Linear
Simply Connected Manifolds
2002 Levine Lionel Noam Elkies The Rotor-Router Model
2002 Matchett Phil Stephen DeBacker Haar Measure and Representation of the Heisenberg Group
2002 Mihelich Chris William Stein Arithmetic Properties of Restricted partition functions
2002 Miyasaka Eiichi Noam Elkies The Classification of some Finite Simple Groups and the Exceptional Isomorphisms between
2002 Moss Sarah Daniel Goroff Arrow’s Impossibility Theorem: Combinatorial and Topological Approaches
2002 Musiker Gregg Richard Stanley Cluster Algebras Somos Sequences and Exchange Graphs
2002 Schedler Travis Nathan Dunfield Troels Jorgensen’s Once-Punctured Torus Theory
2002 Snyder Noah Dick Gross Artin’s L-functions: A Historical Approach
2002 Speyer David William Stein The Eichler-Shimura Correspondence: Theoretical and Computational Aspects
2002 Tenner Bridget Wilfried Schmid Paul Sally (Chicago)
2002 Warshall Andrew Noam Elkies Principles of Combinatorial Game Theory
2002 Weinstein Jared Dick Gross The L-series of Number Fields and of Abelian Varieties
2002 Agarwal Neil (COMP+MATH) Gerald Sacks, Salil Vadhan Automorphisms of the lattice of computably enumerable sets


Year Name Advisor Title
2001 Pranav Anand Warren Goldfarb Indicators for Non-Standard Models of Arithmetic
2001 David Farris Raoul Bott Basic Morse Theory via Half Spaces and the Morse Complex
2001 Lukasz Fidkowski Raoul Bott Several Approaches to Chern Classes
2001 Elizabeth Foster Dick Gross Reciprocity
2001 Daniel Glaser Leslie Valiant A Theoretical Discussion of Boosting
2001 Paula Levy Leslie Valiant Algebraic Complexity: A Compendium of VNP-complete Problems
2001 Maryanthe Malliaris Gerald Sacks Asymptotic Methods for Finite Models
2001 Ciprian Manolescu Peter Kronheimer Finite Dimensional Approximation in Seiberg-Witten Theory
2001 Davesh Maulik Dick Gross Explicit Class Field Theory for Function Fields
2001 Petar Maymounkov M. Mitzenmacher Divergence-proving Techniques for Best Fit Bin Packing and Random Fit
2001 Anna Medvedovsky Matt Baker Chebotarev’s Density Theorem
2001 Joshua Nichols-Barrer Joe Harris, Sean Keel GIT with an Application to the Birational Geometry of M31 and M41
2001 Janak Ramakrishnan Barry Mazur Hilbert’s 10th Problem and the Role of the Pell Equation
2001 Nikolai Roussanov Ilia Binder The Mandelbrot’s Conjecture and Critical Exponents for Brownian Motion
2001 Bhatt Meghana Leslie Valiant “Aggregating Simple Functions into Powerful Predictors”


Year Name Advisor Title
2000 Ackerman Nate Gerald Sacks “Effective Descriptive Set Theory”
2000 Acquista Karen Richard Taylor “Constructing the p-Adic L-Functions”
2000 Barth Nils Joseph Harris “Pluricanonical Maps and Models of Algebraic Surfaces”
2000 Bhat Harish Daniel Goroff “Aubry-Mather Sets and a Problem of Three-Bodies”
2000 Gilchrist Pete Benedict Gross “An Exploration of Algebraic Number Theory: Algorithmic Development and Inplementation”
2000 Jensen Meredith Warren Goldfarb “Establishing a Hierarchy for First-Order Quantifier Prefixes”
2000 Kirkup George Barry Mazur “K2 of Number Fields”
2000 Lee Dan Peter Kronheimer “Dirac Spinors and the Positive Energy Theorem”
2000 Lee Alex Joseph Harris “The Hilbert Schemes of Curves in P3”
2000 Lieblich Max Brian Conrad “Galois Representations Arising from p-Divisible Groups”
2000 Lurie Jacob Benedict Gross “Simply Laced Lie Algebras and their Minuscule Representations”
2000 McMillen Chris Daniel Goroff “Stochastic Calculus with Local Martingale Integrators”
2000 Oprea Dragos Peter Kronheimer “Seiberg-Witten Invariants and Applications”
2000 Proudfoot Nick Peter Kronheimer “Brieskorn’s construction of Exotic Spheres”
2000 Riesenfeld Samantha Michael Rabin “Computing the Irreducible Representations of a Finite Group over Finite Fields: The
Non-Modular Case”
2000 Sagalovskiy Dmitry David Kazhdan “Wavelets as Bases for LP Spaces”
2000 Wichs David David Kazhdan “Morse Theory and its Applications”
2000 Williams Lauren Eric Sommers “A q-analog of Weight Multiplicity”
2000 Yasufuku Yu Richard Taylor “Deformation Theory of Formal Modules”
2000 Harris David Gerald Sacks “Transcendence Degree in the General Setting”


Year Name Advisor Title
1999 Caramanis Constantine Cliff Taubes The Invariance of the Index of Elliptic Operators
1999 Dasgupta Samit Brian Conrad Stark’s Conjectures
1999 Emanuel Michel Peter Kronheimer Classical Linear Groups over Finite Fileds
1999 Friedman Marnie Michael Nakamaye and D Kleitman Lights Camera Optimal Actions: A Study of Strategies and Equilibria in Stochastic Games
1999 Gnepp Andrei Clifford Taubes Smoothing of Topological Manifolds
1999 Helm David Richard Taylor Barry Mazur The Euler System of Cyclotomic Units
1999 Krieger Joachim Wilfried Schmid Geometric Methods in the Representation Theory of noncompact Liegroups
1999 Lebow Eli Peter Kronheimer Gauge Theory and the ADHM Construction
1999 Liu Ju Kuan Curt McMullen Integrating Quadratic Polynomials on the Real Line
1999 Luber Harold Dan Strook The Central Limit Theorem: Proofs and Applications
1999 Lyo Grace Cliff Taubes The Heegaard Decomposition Theorem A Morse-Theoretic Introduction
1999 Marian Alina Wilfried Schmid On the Real Moment Map
1999 Menon Sanjay Richard Taylor Barry Mazur Chebotarev’s Density Theorem
1999 Nichols Ann Michael Nakamaye, Jill Mesirov and James Ireland MIT A Bin Packing Algorithm Applied to a Genetic Reseqencing Assay
1999 Ordway Damian S.-T. Yau The Topology of Manifolds with Positive Scalar Curvature
1999 Oreskovich Anne Clifford Taubes On constructions Surgeries and Unique Decomposition Theorems of Knots Links and
1999 Osserman Brian Richard Taylor Barry Mazur Heegner’s Work and Its Applications
1999 Plotkin Joshua Peter Kronheimer Cobordism and Exotic Spheres
1999 Purdy David Noam Elkies Searching for High Rank Elliptic Curves
1999 Sen Arun Richard Taylor Barry Mazur
1999 Stephens Ben S.-T. Yau Compact Riemannian 7-Manifolds with Holonomy G2
1999 Tenny Daniel Tom Braden Linear Programming and Karmarkar’s Algorithm
1999 Roshak Natalka (minor) PHIL+ Robert Nozick Warren Goldfarb – H.T. Number as an Internalized Regularity
1999 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
1999 Fernholz Dan Noam Elkies Quantum Error-Correcting Codes


Year Name Advisor Title
1998 David Agraz Kamal Khuri-Makdisi Artin L-functions: Applications and Calculations
1998 Joshua Barback Gerald Sacks Some results related to retraceable sets and Ramsey’s Theorem
1998 Daniel Biss Raoul Bott & Michael Hopkins Homotopy Theory with a view toward Stable Computation
1998 Andrew Blumberg David Kazhdan The Merkurjev-Suslin Theorem
1998 Patrick Corn Richard Taylor Modular Forms and Galois Representations
1998 Moon Duchin Persi Diaconis Combinatorial Methods and Constructive Notions for the Colin de Verdiere Graph Parameter
1998 Samuel Grushevsky Yum Tong Siu Fenchel-Nielsen boundary of Teichm�ller Space
1998 Jesse Hahnel Dick Gross Additive Number Theory Modular Forms and the partition Function
1998 Christopher Jerdonek Curt McMullen Hyperbolic Geometry in the Study of Three-Manifolds
1998 Benjamin Lee David Kazhdan Geometric Quillen-Suslin
1998 Florin Spinu Wilfried Schmid The Eisenstein Series of SL(2R)
1998 Julianna Tymoczko Joe Harris The p-components of the stable homotopy groups of spheres
1998 Stephen Wang Dick Gross The Uniqueness of Two Remarkable Lattices
1998 Jonathan Weinstein Kenneth Fan Length Functions on Finite Reflection Groups
1998 Eric Yeh Michael Nakamaye The Theory of Divisors in Krull Domains