# 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 (jcain2@math.harvard.edu) know if you have any questions not addressed in the document.

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 singularities |

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 Axioms |

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 Selection |

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 Problem |

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 Density |

2014 | Lee, Geoffrey | Jacob Lurie | The Classification of Topological Quantum Field Theories in Two Dimensions |

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 Neuroscience |

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 Components |

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 Catgories |

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 A _{n} |

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 identity |

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 Selection |

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 Punishment |

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 Memory |

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 Unirationality |

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 R ^{3} |

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 C^{n} |

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 Fields |

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 Distributions |

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 Group |

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 Conjectures |

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 them |

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 3-Manifolds |

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 |