Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132
Below is a list of PhD dissertations written by students at the Harvard Department of Mathematics. All scholars can order copies of most Harvard dissertations from 1982 to the present by contacting UMI/ProQuest at 1-800-521-3042. Permission of the author is usually required to copy theses within the last five years. Most PhD dissertations submitted from March 2012 forward are available online in DASH Harvard's central open-access repository. Harvard affiliates with IDs and PINs can access the full text of most Harvard PhD theses since 1990 from the database Dissertations and Theses Full Text. Back to the graduate pages of the Harvard Mathematics department.

Year Name Advisor Title
2018 Jonathan Zhu Minicozzi Geometric Variational Problems for Mean Curvature
2018 Boyu Zhang Taubes Several compactness results in gauge theory and low dimensional topology
2018 Chenglong Yu S-T Yau Picard-Fuchs systems arising from toric and flag varieties
2018 Peter Smillie S-T Yau Entire surfaces of prescribed curvature in Minkowski 3-space
2018 Koji Shimizu Kisin Geometric Properties of Families of Galois Representations
2018 Benjamin Landon H-T Yau Local statistics of Dyson Brownian motion
2018 Jeremy Hahn M. Hopkins Variations on a Nilpotence Theorem of Hopkins and Mahowald
2018 Meng Guo M.Hopkins Some calculations of cobordism groups and their applications in physics
2018 Eduard Duryev Curtis McMullen Teichmüller curves in genus two: square-tiled surfaces and modular curves
2018 Ziliang Che H.T. Yau Universality of random matrices with dependent entries
2018 Christopher Justin Campbell Dennis Gaitsgory Nearby cycles of Whittaker sheaves
2017 Yihang Zhu Mark Kisin The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties
2017 Rong Zhou Mark Kisin Mod-p isogeny classes on Shimura varieties with parahoric level structure
2017 Ananth Shankar Mark Kisin The p-curvature conjecture and monodromy about simple closed loops
2017 Krishanu Sankar Michael Hopkins Symmetric Powers and the Equivariant Dual Steenrod Algebra
2017 Akhil Mathew Jacob Lurie Nilpotence and descent in stable homotopy theory
2017 Thomas Lovering Mark Kisin Integral canonical models for G-bundles on Shimura varieties of abelian type
2017 Erick Phillip Knight Mark Kisin A p-adic Jacquet-Langlands Correspondence
2017 David Lukas Benjamin Brantner Jacob Lurie The Lubin-Tate Theory of Spectral Lie Algebras
2016 Adrian Ioan Zahariuc Joe Harris Degenerations, Log K3 Pairs and Low Genus Curves on Algebraic Varieties
2016 Yi Xie Peter Kronheimer On the Framed Singular Instanton Floer Homology from Higher Rank Bundles
2016 Philip Douglas Tynan Michael Hopkins Equivariant Weiss Calculus and Loop Spaces of Stiefel Manifolds
2016 Yunqing Tang Mark Kisin Algebraicity criteria and their applications
2016 Alexander Richard Perry Joe Harris Derived categories and birational geometry of Gushel-Mukai varieties
2016 Yong Suk Moon Mark Kisin Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case
2016 Konstantin Matveev Alexei Borodin (MIT) q-deformed Interacting Particle Systems, RSKs and Random Polymers
2016 Jessica Fintzen Benedict Gross On the Moy-Prasad filtration and stable vectors
2016 Francesco Cavazzani Joe Harris Complete Homogeneous Varieties via Representation Theory
2016 Jason Charles Bland Benedict Gross On the Arithmetic of Hyperelliptic Curves
2015 Cheng-Chiang Tsai Dick Gross A formula for some Shalika germs
2015 Ryosuke Takahashi Clifford Taubes The moduli space of S1-Type zero loci for Z/2 Harmonic spinors in dimension 3
2015 Charmaine Jia Min Sia Michael Hopkins Structures on Forms of K-Theory
2015 Simon Fabian Schieder Dennis Gaitsgory Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification
2015 Eric Riedl Joe Harris Rational Curves on Hypersurfaces
2015 Chao Li Dick Gross 2-Selmer groups and Heegner points on eliptic curves
2015 Jeffrey Kuan Alexei Borodin Several Theorems about Probabilistic limiting Expressions: The Gaussian free field, symmetric Pearcey process, and strong Szegö asymptotics
2015 Gijsbert Heuts Jacob Lurie Goodwillie approximations to higher categories
2015 Gabriel Tavares Bujokas Joe Harris Covers of an elliptic curve E and curves in E x P1
2015 George Andrew Boxer Richard Taylor Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
2015 Atanas Valeryev Atanasov Joe Harris Interpolation and vector bundles on curves
2015 Omar Antolin Camarena Jacob Lurie The mod 2 homology of free spectral Lie algebras
2014 Jie Zhou S.T Yau Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds
2014 Matthew Woolf Joe Harris Relative Jacobeans of Linear Systems
2014 Samuel David Raskin Dennis Gatisgory Chiral Principal Series Categories
2014 Nathan Pflueger Joe Harris Regeneration of Elliptic Chains with Exceptional Linear Series
2014 Bao Viet Le Hung RIchard Taylor Modularity of some elliptic curves over totally real fields
2014 Oleg Ivrii Curt McMullen The geometry of the Weil-Petersson metric in complex dynamics
2014 Hansheng Diao Marc Kisin The Eigencurve is Proper
2014 Aliakbar Daemi Peter Kronheimer Symmetric Spaces and Knot Invariants from Gauge Theory
2014 Stergios Antonakoudis Curtis McMullen The complex geometry of Teichmuller space
2013 Xiaoheng Wang Joe Harris Pencils of quadrics and Jacobians of hyperellipitc curves
2013 Carl William Wang Erickson Benedict Gross Moduli of Galois Representations
2013 Pei-Yu Tsai Benedict Gross On Newforms for Split Special Odd Orthogonal Groups
2013 Giulio Tiozzo Curt McMullen Entropy, dimension and combinatorial moduli for one-dimensional dynamical systems
2013 Yih Sung Yum-Tong Siu Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications
2013 Anand Pankaj Patel Joe Harris The Geometry of Hurwitz Space
2013 Yu-Shen Lin Shing-Tung Yau Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing
2013 Nathan Kaplan Noam Elkies Rational Point Counts for del Pezzo Surfaces over Finite Fields and Coding Theory
2012 Jack Thorne Richard Taylor The Arithmetic of Simple Singularities
2012 Ethan Street Peter Kronheimer Towards an Instanton Floer Homology for Tangles
2012 Aaron Silberstein Florian Pop Anabelian Intersection Theory
2012 Yi Li Shing-Tung Yau Analysis of some PDEs over manifolds
2012 Thomas Koberda Curtis McMullen Mapping class groups, homology and finite covers of surfaces
2012 Tatyana Khodorovskiy Peter Kronheimer Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls
2012 Jack Huizenga Joe Harris Restrictions of Steiner bundles and divisors on the Hilbert scheme of points in the plane
2012 Anand Deopurkar Joe Harris Alternate Compactifications of Hurwitz spaces
2012 Ana Caraiani Richard Taylor Local-Global Compatibility and the Action of Monodromy on Nearby Cycles
2012 Ivana Bozic Martin Nowak Mathematical Models of Cancer
2012 Jonathan Barlev Dennis Gaitsgory D-modules on Spaces of Rational Maps and on Other Generic Data
2011 Stewart Wilcox Pavel Etingof Representations of the rational Cherednik algebras
2011 Chung-Jun Tsai Clifford Taubes Asymptotic spectral flow for Dirac operators of disjoint Dehn twists
2011 Ruifang Song Shing-Tung Yau The Picard-Fuchs systems of Calabi-Yau complete intersections in homogeneous spaces
2011 David Roe Dick Gross The Local Langlands Correspondence for Tamely Ramified Groups
2011 Ryan Reich Dennis Gaitsgory Twisted geometric Satake equivalence via gerbes on the factorizable grassmannian
2011 Greta Panova Richard Stanley Combinatorial applications of symmetric function theory to certain classes of permutations and truncated tableaux
2011 Si Li Shing-Tung Yau Calabi-Yau Geometry and Higer Genus Mirror Symmetry
2011 Daniel Kane Barry Mazur On Elliptic Curves, the ABC Conjecture, and Polynomial Threshold Functions
2011 Wushi Goldring Richard Taylor The Picard-Fuchs systems of Calabi-Yau complete intersections in homogeneous spaces
2011 Ming-Tao Chuan Shing Tung Yau Existence of Hermitian-Yang-Mills Metrics under Conifold Transitions
2011 Po-Ning Chen Shing-Tung Yau Quasi-local energy in General Relativity
2010 Yevgeny Zaytman Noam Elkies K3 surfaces of high Picard number and arithmetic applications
2010 Jeechul Woo Noam Elkies Arithmetic of Elliptic Curves and Surface: Descents and Quadratic Sections
2010 Frederick van der Wyck Joseph Harris Moduli of singular curves and crimping
2010 Aleksandar Subotic Denis Auroux (MIT) A monoidal structure for the Fukaya category
2010 Ji Oon Lee Horng-Tzer Yau Lower Bound for Ground State Energy of Dilute Bose Gas
2010 Vinh Le Anh Noam Elkies Some combinatorial problems in vector spaces over finite fields
2010 David Geraghty Richard Taylor Modularity Lifting Theorems for Ordinary Galois Representations
2009 Valentino Tosatti Shing-Tung Yau Geometry of complex Monge-Ampère equations
2009 Corina Tarnita Martin Nowak Evolutionary Dynamics in Structured Populations
2009 Cammie Smith Barnes Richard Stanley Enumeration of the Distinct Shuffles of Permutations
2009 Sarah Rasmussen Cliff Taubes A Number Theoretic Result for Berge's Conjecture
2009 Jesse Kass Joe Harris Good Completions of Neron Models
2009 Samuel Isaacson Michael Hopkins Cubical Homotopy Theory and Monoidal Model Categories
2009 Stefan Hornet Michael Hopkins A generalization of a theorem of Ravenel and Wilson
2009 Andrew Dittmer Barry Mazur Filament Geometry
2009 Suh-Hyun Choi Richard Taylor Local Universal Deformation Lifting Spaces Of Mod L Galois Representations
2009 Chen-Yu Chi Shing-Tung Yau Pseudonorms and Theorems of Torelli Type for Birational Equivalence
2009 Evan Bullock Joe Harris Subcanonical Points on Algebraic
2009 Samik Basu Michael Hopkins A Structures on Thom Spectra
2009 Thomas Barnet-Lamb Richard Taylor On Potential Automorphy and other topics in Number Theory
2008 David Smyth Joe Harris Compact Moduli of Singular Curves: A Case Study in Genus One
2008 Jonathan Pottharst Barry Mazur Selmer Growth and a Triangulordinary Local Condition
2008 Kai-Wen Lan Richard Taylor Arithmetic Compactifications of PEL-type Shimura Varieties
2008 David Harvey Barry Mazur Algorithms for p-adic Cohomology and p-adic Heights
2008 Cameron Freer Gerald Sacks Models with High Scott Rank
2008 Maksym Fedorchuk Joe Harris Severi Varieties and the Moduli Space of Curves
2008 Dawei Chen Joe Harris Covers of Elliptic Curves and Slopes of Effective Divisors on the Moduli Space of Curves
2008 Irena Anno Roman Bezrukavnikov (MIT) Weak Representation of Tangle Categories in Algebraic Geometry
2008 Amanda Alvine Cliff Taubes Investigation of J-holomorphic curves in M3 x S1
2007 Sug-Woo Shin Richard Taylor Counting points on Igusa varieties
2007 Katherine Paur Martin Nowak Modeling the Effects of Population Structure and Vaccination Strategy on Infectious Diseases
2007 Chung-Pang Mok Barry Mazur The Exceptional Zero Conjecture For Hilbert Modular Form
2007 Andrew Lobb Peter Kronheimer A slice genus lower bound from sl(n) Khovanov-Rozansky homology
2007 Sonal Jain Noam Elkies Minimal Heights and Regulators for Elliptic Surfaces
2007 Ethan Cotterill Joe Harris Enumerative Geometry of Curves with Exceptional Secant Planes
2006 Jeng-Daw Yu Shing-Tung Yau On Ordinary K3 surfaces over Fp
2006 Teruyoshi Yoshida Richard Taylor Weight Spectral Sequence and Hecke Correspondence on Shimura Varieties
2006 Chun-Chun Wu Shing-Tung Yau On the Geometry of Superstring with Torsion
2006 Rosa Sena-Dias Peter Kronheimer Estimated Transversality And Rational Maps
2006 Michael Schein Richard Taylor Weights Of Galois Representations Associated To Hilbert Modular Forms
2006 Ivan Petrakiev Joe Harris On Zero-Dimensional Schemes with Special Hilbert Functions
2006 Erick Matsen Martin Nowak Analysis of Probabilistic Models of Evolution
2006 Abhinav Kumar Noam Elkies K3 surfaces of high rank
2006 Florian Herzig Richard Taylor The Weight in Serre Type Conjecture for Tame n-Dimensional Galois Representations
2006 Jy-Ying Janet Chen Wilfried Schmid The Degree 4 L-Function of an Automorphic Form of Full Level on the Rank 2 Real Symplectic Group
2006 Sabin Cautis Joe Harris Extending Families of Curves: Monodromy and Applications
2006 Matthew Bainbridge Curtis McMullen Euler Characteristics of Teichm?ller Curves in Genus Two
2005 Vivek Mohta Cliff Taubes Applications of Chiral Perturbation Theory
2005 Jerrel Mast Cliff Taubes Pseudoholomorphic Punctured Spheres in the Symplectization of a Quotient
2005 Edward Lee Shing-Tung Yau A Modular Non-Rigid Calabi-Yau Threefold
2005 Deepee Khosla Joe Harris Moduli Spaces of Curves with Linear Series and the Slope Conjecture
2005 Jonathan Kaplan Shlomo Sternberg Morphlets; A Multiscale Representation for Diffeomorphisms
2005 Grigor Grigorov Richard Taylor Kato's Euler System and the Main Conjecture
2005 Peter Green Richard Taylor Geometricity of Local p-Adic Representations
2004 Stephanie Yang Joe Harris Special Linear Series in P2
2004 Nicholas Franklin Rogers Noam Elkies Elliptic Curves x3 + y3 = k with High Rank
2004 Daniel Rauch Cliff Taubes Perturbations of the D-bar Operator
2004 Nick Ramsey Barry Mazur Geometric and p-Adic Modular Forms of Half-Integral Weight
2004 Olga Plamenevskaya Peter Kronheimer Contact Structures and Floer Homology
2004 Maryam Mirzakhani Curtis McMullen Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves
2004 Alina Marian Shing-Tung Yau Intersection Theory on the Moduli Space of Stable Bundles via Morphism Spaces
2004 Ciprian Manolescu Peter Kronheimer A Spectrum Valued RQFT from the Seiberg-Witten Equations
2004 David Dumas Curtis McMullen Complex Projective Structures
2004 Izzet Coskun Joe Harris Degenerations of scrolls and Del Pezzo Surfaces and Applications to Enumerative Geometry
2003 Martin Weissman Benedict Gross The Fourier-Jacobi map and small representations
2003 Jacob Rasmussen Peter Kronheimer Floer Homology and Knot Complements
2003 Alexandru Popa Benedict Gross Central value of Rankin L-series over real quadratic fields
2003 Mark Lucianovic Benedict Gross Quaternion Rings
2003 Yu-Ru Liu Barry Mazur Generalization of the Turan and the Erdos-Kac Theorems
2003 Spiro Karigiannis Shing-Tung Yau Deformations of G2 and Spin(7) Structures on Manifolds
2003 David Jao Noam Elkies Supersingular primes for rational points on modular curves
2003 Peter Clark Barry Mazur Local and global points on moduli spaces of abelian surfaces with potential quaternionic multiplication
2003 Bing Cheng Shing-Tung Yau Li-Yau-Hamilton Estimate for the Ricci Flow
2003 Jiun-Cheng Chen Shing-Tung Yau Flops and Equivalences of derived Categories for Threefolds with only terminal Gorenstein Singularities
2002 Huan Yang Benedict Gross Hecke Algebra action on Siegel Modular Forms
2002 Mak Trifkovic Barry Mazur On u-Invariants of Elliptic Curves over Q
2002 Ralph Scott Cliff Taubes Closed Self-Dual Two-Forms on Four-Dimensional Handlebodies
2002 Elena Mantovan Richard Taylor On Certain Unitary Group Shimura Varieties
2002 Chiu-Chu Liu Shing-Tung Yau Moduli of J-Holomorphic Curves with Lagrangian Boundry Conditions
2002 Matvei Libine Wilfried Schmid A Localization Argument for Characters of Reductive Lie Groups
2002 Samuel Grushevsky Yum-Tong Siu Effective Schottky problem
2002 Laura DeMarco Curtis McMullen Holomorphic families of Rational Maps: Dynamics Geometry and Potential Theory
2002 Dmitro Arinkin David Kazhdan Fourier Transform for Quantized Completely Integrable Systems
2001 Vadim Vologodsky David Kazhdan Hodge Structure on the Fundemental Group and its Application to p-adic Integrarion
2001 David Savitt Richard Taylor Modularity of some potentially Barsotti-Tate Galois representations
2001 Robert Pollack Barry Mazur On the p-adic L-function of a Modular Form at a Supersingular Prime
2001 William Mann Richard Taylor Local Level-Raising for GLn
2001 Tomas Klenke Barry Mazur Modular Varieties and Visibility
2000 Nina Zipser Shing-Tung Yau The Global Nonlinear Stability of the Trivial Solution of the Einstein-Maxwell Equations
2000 Thomas Weston Barry Mazur On Selmer groups of geometric Galois Representations
2000 Christine Taylor Shing-Tung Yau Compact Manifolds with Exceptional Holonomy
2000 Jason Starr Joe Harris Rational Curves on Hypersurfaces in Pn
2000 Matthew Leingang Shlomo Sternberg Symmetric Space Valued Moment Maps
2000 Ian Dowker Peter Kronheimer PU(2) monopoles on Kahler surfaces
2000 Mark Dickinson Richard Taylor On the Modularity of Certain 2-adic Galois Representations
2000 Henry Cohn Noam Elkies New Bounds on Sphere Packings
2000 James Bernhard Raoul Bott Equivariant de Rham Theory and Statinary Phase Expansions
1999 Elizabeth Wilmer Joe Harris Exact Rates of Convergence for Some Simple Non-Reversible Markocv Chains
1999 Jianmei Wang Cliff Taubes Configuration space and Monopoles for Yang-Mills-Higgs Theory on R3/M
1999 Michael Szydlo Barry Mazur Flat Regular Models of Elliptic Schemes
1999 Heather Russell Joe Harris Monomial Ideals and Hilbert Schemes
1999 Catherine O'Neil Barry Mazur Jacobians of Curves of Genus One
1999 Adam Logan Joe Harris Moduli Spaces of Curves with Marked Points
1999 John Loftin Shing-Tung Yau Applications of Affine Differential Geometry to RP(2) Surfaces
1999 Gregory Landweber Cliff Taubes Dirac Operators on Loop Spaces
1999 Andrew Engelward Benedict Gross Models over Z for Locally Quasi-Split Algebraic Groups
1999 Charles Doran Shing-Tung Yau Picard-Fuchs Uniformation and Geometric Isomonodromic Deformations
1999 Mira Bernstein Joe Harris Moduli of curves with level structure
1999 David Ben-Zvi Edward Frenkel Spectral Curves
1998 Jared Wunsch Richard Melrose (MIT) Microlocal Analysis of the Time-Dependent Schroedinger Operator
1998 Kelly Wieand Persi Diaconis Eigenvalue Distribution of Random Matrices in Permutation Group and Compact Lie Groups
1998 Mu-Tao Wang Shing-Tung Yau Generalized Harmonic Maps and Representations of Discrete Groups
1998 Chin-lung Wang Shing-Tung Yau Topology of Birational Manifolds and Applications to Degeneration
1998 Ralph Teixeira David Mumford Curvature Motions, Medial Axes and Distance Transforms
1998 Michael Roth Joe Harris Calculations on the Moduli Space of Genus Zero Covers
1998 Leonid Positselski Koszul Property and Bogomolov's Conjecture
1998 David Pollack Benedict Gross Explicit Hecke Actions on Modular Forms
1998 Seth Padowitz Benedict Gross Traces of Hecke Operators
1998 Laila Maino Joe Harris Moduli Space of Enriched Stable Curves
1998 Joshua Lansky Benedict Gross Hecke rings of Groups over Local Fields
1998 Michael Hutchings Cliff Taubes Reidemeister Torsion in Generalized Morse Theory
1998 Susan Goldstine Benedict Gross Spin Representations and Lattices
1998 Wee-Tek Gan Benedict Gross Exceptional Theta Correspondences
1998 Matthew Emerton Barry Mazur 2-adic Modular Forms of Minimal Slope
1998 Jordan Ellenberg Barry Mazur Hilbert Modular Forms and the Galois Representations Associated to Hilbert-Blumenthal Abelian Varieties
1998 Thomas Brennan Benedict Gross Variation of capacity for Convex Domains in Euclidean Space
1997 Alexander Vishik David Kazhdan Integral Motives of Quadrics
1997 Ravi Vakil Joe Harris Enumerative Geometry of Curves via Degeneration Methods
1997 James Turetsky David Kazhdan Short Time Behavior of Logarithmic Derivatives of the Heat Kernel
1997 Svezdelina Stankova-Frenkel Joe Harris Moduli of Trigonal Curves
1997 Thomas Scanlon Ehud Hrushovski Model Theory of Valued D-Fields
1997 Igor Pak Persi Diaconis Random Walks on Groups: Strong Uniform Time Approach
1997 Adi Ofer Benedict Gross Abelian L-Functions Twisted by Algebraic Tori A+S=0
1997 Hung Loke Benedict Gross Exceptional Lie Groups and Lie Algebras
1997 Mikhail Grinberg Robert MacPherson A Generalization of Springer Theory using Nearby Cycles
1997 Jason Fulman Persi Diaconis Probability in the Classical Groups over Finite Fields: Symmetric Functions Stochastic Algorithms and Cycle Indices
1997 Keith Conrad Benedict Gross p-adic Gamma Functions
1997 Xi Chen Joe Harris Rational Curves of K3 Surfaces
1996 David Steinsaltz Persi Diaconis Socks and Boxes: Variations on Daniel Bernoulli's Marriage Problem
1996 Jeffrey Silver Persi Diaconis Weighted Poincare and Exhaustive Techniques for Scaled Metropolis-Hastings Algorithms and Spectral total Variation Convergence Bounds in Infinite Commutable Markov Chain Theory
1996 Alexander Polishchuk David Kazhdan Biextension Weil Representations on Derived Categories and Theta Functions
1996 Brad Mann Persi Diaconis Berry-Essen Central Limit Theorem for Markov Chains
1996 Nathan Lulov Persi Diaconis Random Walks on the Symmetric Group Generated by Conjugacy Classes
1996 Ai-Ko Liu Shing-Tung Yau Wall Crossing Formula of Seiberg-Witten Invariants and Symplectic Four Manifolds with b+1=1
1996 Brendan Hassett Joe Harris Special Cubic Hypersurfaces of Dimension Four
1995 Mikhail Verbitsky David Kazhdan Cohomology of compact Hyperkaehler Manifolds
1995 Francis Su Persi Diaconis Methods for Quantifying Rates of Convergence for Random Walks on Groups
1995 Henri Shahrouz Joe Harris The Grothendieck Quot Schemes and Composition Laws for Grassmannians
1995 Karl Rumelhart David Kazhdan Minimal Representations of Exceptional p-adic groups
1995 Wei-Dong Ruan Shing-Tung Yau On the Convergence of Kahler Metrics
1995 Eric Rains Persi Diaconis Topics in Probability on Compact Lie Groups
1995 David Grabiner Persi Diaconis Walks and Representation Theory
1995 Eugene Durenard Cliff Taubes A Mayer-Vietoris Principle for Monopoles
1994 Jiu-Kang Yu Benedict Gross A-divisible Modules
1994 Lan Wang Barry Mazur Canonical Heights and Rational Points on Varieties with Many Elliptic Fibrations
1994 Eric Twietmeyer Wilfried Schmid Real Forms of Quantum Groups and Harish-Chandra Modules
1994 Constantin Teleman Raoul Bott Lie Algebra Cohomology and the Fusion Rules
1994 Rahul Pandharipande Joe Harris A Compactification over the Moduli space of Stable curves of the Universal Moduli Space pf Slope-Semistable Vector Bundles
1994 Kok-onn Ng Joe Harris The Moduli Space of (3,3,3) Trilinear Forms
1994 Thomas Hagedorn Benedict Gross Multiplicities in restricted Representations of GLn (Fq) Un(Fq) and SO(Fq)
1994 Michael Finkelberg Joseph Bernstein Fusion Categories
1994 Constantine Costes Raoul Bott Some explicit Cocycles for Cohomology Classes of Groups of Diffeomorphisms Preserving a G-Structure
1994 James Bryan Cliff Taubes Symplectic Geometry and the Relative Donaldson Invariants of the Conjugate Projective Plan
1994 Eugen Angehrn Yum-Tong Siu An Effective Polynomial Bound for Base Point Freeness and Point Separation of Adjoint Bundles
1993 Rongguang Wang Cliff Taubes Essays on Vortices Knots and Monopoles
1993 Susan Tolman Raoul Bott Group Actions and Cohomology
1993 Du Nguyen David Kazhdan Graded Lie Algebras and conformal Field theories l: The Genus O Case
1993 David Maslen Persi Diaconis Fast Transforms and Sampling for Compact groups
1993 Peter Magyar J. Bernstein Formulas for Generalized Kazhdan-Lusztig Polynomials
1993 Kefeng Liu Shing-Tung Yau On Modular Invariants and Rigidity Theorems
1993 Yael Karshon Shlomo Sternberg Hamiltonian Actions of Lie Groups
1993 Jun-Muk Hwang Yum-Tong Siu Global Nondeformability of the Complex Hyperquadric
1993 Kaspar Ernst Cliff Taubes On the ends of the monopole Moduli Space
1993 Neil Dummigan Benedict Gross The 2nd Descent for Certain Families of Mordell-Weil Lattices
1993 Shun-Jen Cheng Victor Kac Differentiably Simple Lie Superalgebras
1993 Lucia Caporaso Joe Harris On a Compactification of the Universal Picard variety over the Moduli space of Stable Curves
1993 Eric Belsley Persi Diaconis Rates of Convergence of Markov Chains Related to Association Schemes
1992 Hon-Wai Wong Wilfried Schmid Dolbeault Cohomologies and Zuckerman Modules Associated with Finite Rank Representations
1992 Eric Weinstein Raoul Bott Extension of Self-Dual Yang-Mills Equations across the Eight Dimension
1992 Xuesung Wang Barry Mazur Higher-Order Characteristic Classes in Arithmetic Geometry
1992 Vladimir Voevodsky David Kazhdan Homology of Schemes and covariant Motives
1992 Andras Szenes Raoul Bott The Verlinde Formulas and Moduli Spaces of Vector Bundles
1992 Andrew J. Schwartz Heisuke Hironaka Functional Smoothing of Morphisms in Equal Characteristic 0
1992 Jeffrey Rosenthal Persi Diaconis Rates of Convergence for Gibbs Sampler and other Markov Chains
1992 Michael McQuillan Barry Mazur Division Points on Semi-Abelian Varieties
1992 David Kotz Benedict Gross A p-adic Computation of Singular Moduli
1992 Karen Chandler Joe Harris Hilbert and Functions of Zero-Dimensional Schemes in Uniform Position
1992 Pablo Azcue Joe Harris On the Dimension of the Chow Varieties
1991 Philip Spencer Cliff Taubes Yang-Mills Connections with Asymptotically Constant Curvature
1991 Keith Ramsey Barry Mazur Power-free Values of Polynomials
1991 James McKernan Joe Harris On the Hyperplane sections of a Variety in Projective Space
1991 Edward Frenkel Joseph Bernstein Affine Kac-Moody Algebras at the Critical Level and Quantum Drinfield-Sokolov Reduction
1991 Henri Darmon Benedict Gross Refined Class Formulas for Derivatives of L-Series
1991 Jean-Francois Burnol Barry Mazur Weierstrass Points on Arithmetic Surfaces
1991 Wayne Aitken Barry Mazur An Arithmetic Riemann-Roch Theorem for Singular Arithmetic Surfaces
1991 Dan Abramovich Joe Harris Subvarieties of Abelian Varieties and of Jacobians of Curves
1990 Yang Wang David Mumford Image Segmentation by Variational Methods and Elliptic Boundary Value Problems
1990 Ki-Seng Tan John Tate Refined Conjectures of the Birch and Swinnerton-Dyer Type
1990 Richard Stong Cliff Taubes Nonexistence of Almost Handebody Structures on Topological Four Manifold Pairs
1990 Edward Shipiz Joseph Bernstein Deligne's Conjecture in the Constant Coefficient Case
1990 Wan-Xiong Shi Shing-Tung Yau Ricci Deformation of the Metric on Complete Noncompact Kahler Manifolds
1990 Andrew D. Schwartz Barry Mazur Igusa Towers over Hilbert Modular Surfaces
1990 Zachary Robinson Mark Spivakovsky On Some Conditions of Regularity for Subanalytic Sets
1990 Steven Lu Shing-Tung Yau On Meromorthic Maps between Algebraic Varieties with Log-General Targets
1990 Jun Li Shing-Tung Yau Construction of Stable Vector Bundle on Surface of Low 2nd Chern Classification
1990 Alexandros Kouvidakis Joe Harris Divisors on Some Moduli Spaces
1990 Martin Hildebrand Persi Diaconis Rates of Convergence of Some Random Processes on Finite Groups
1990 Stephen DiPippo John Tate Spaces of Rational Functions on Curves over Finite Fields
1989 Fangyang Zheng Shing-Tung Yau Semipositive Threefolds and Threefolds with Universal covering C(3)
1989 Daniel Rockmore Persi Diaconis Fast Fourier Analysis for Finite Groups
1989 David Roberts Benedict Gross Shimura Curves Analogous to X (N)
1989 Dipendra Prasad Benedict Gross Trilinear Forms for GL (2) of a Local Field and Epsilon Factors
1989 Robert Morelli Raoul Bott Hilbert's Third Problem and the K Theory of Toric Varieties
1989 Rama Kocherlakota Raoul Bott Integral Homology of Real Flag Manifolds and Loop Spaces of Symmetric Spaces
1988 Boris Youssin Heisuke Hironaka Newton Polyhedra without Coordinates
1988 Charles Walter Robin Hartshorne Cohomology of Normal bundles of curves in P and other Topics
1988 Pirooz Vakili Raoul Bott Three Topics on Perturbation Analysis of Discrete Event Dynamic Systems
1988 Gang Tian Sing-Tung Yau Kaehler Metrics on Algebraic Manifolds
1988 Gordan Savin Limit Multiplications of Cusp Forms
1988 Zinovy Reichstein The Behavior of Stability under Equivariant Maps
1988 Alan Nadel Yum-Tong Siu Hyperbolic Surfaces
1988 Irwin Jungreis Ordered and unordered Periodic Points of Maps
1987 Dinesh Thakur John Tate Gamma Functions and Gauss Sums for Function Fields
1987 Carlos Simpson Wilfried Schmid Systems of Hodge Bundles and Uniformization
1987 Kevin Keating Benedict Gross Lifting Endomorphisms of Formal Groups
1987 John Jones Barry Mazur Iwasawa theory at Multiplicative Primes
1987 Rhonda Hatcher Benedict Gross Heights and L-Series
1987 Fernando Gouvea Barry Mazur Arithmetic of p-adic Modular Forms
1987 Ezra Getzler Arthur Jaffe Degree Theory of Wiener Maps and Supersymmetric Quantum Mechanics
1987 Alan Fekete Nancy Ann Lynch (MIT) Topics in Distributed Algorithms
1987 Noam Elkies Benedict Gross and Barry Mazur Supersingular Primes of a Given Elliptic Curve over a Number Field
1987 Nigel Boston Barry Mazur Deformation theory of Galois Representations
1987 Jonathan Block Raoul Bott Excursion in Cyclic Homology of Topological Algebras
1987 Rogerio Aguilar Rodriguez Wilfried Schmid Connections between Representations of Lie Groups and Sheaf Cohomology
1986 Akihiko Yukie David Mumford Applications of Equivariant Morse Stratifications
1986 Xian Wu Nondegeneracy of Infinitesimal Invariants Associated to Normal Functions
1986 Jeremy Teitelbaum John Tate p-adic Periods as Moduli for Schottky Curves of Genus Two
1986 Oscar Sanchez V. On Supergeometric Structures
1986 Miller Puckette Shannon Entropy and the Central Limit Theorem
1986 Carlos Gomez-Mont On Local Torelli for Extremal Varieties
1986 Kevin Corlette Stability and Canonical Metrics in Infinite Dimensions
1986 Gregory Call Local Heightson Families of Abelian Varieties
1985 Mark Spivakovsky Heisuke Hironaka Sandwiched Singularities and the Nash Resolution for Surfaces
1985 Igor Reider Bounds on Irregularity of Surfaces of General Type
1985 Stefanos Pantazis David Mumford Prym Varieties and the Geodesic Flow on SO(n)
1985 Renato Mirollo Heisuke Hironaka Rank Conditions on Sub-Varieties of Grassmannians
1985 Curtis McMullen David Mumford Families of Rational Maps and Iterative Root-Finding Algorithms
1985 Mitchell Laks David Kazhdan On the Characters of the Representations of Division Algebras over a Weak Field
1985 Robert Kuhn Barry Mazur On the Canonical Closure of the Universal Elliptic Curve over Xl(n)
1985 Robin Forman Raoul Bott Functional Determinants and Applications to Geometry
1985 Koji Cho Yum-Tong Siu Positivity of the Curvature of the Weil-Petersson Metric on the Moduli Space of Stable Vector Bundles
1985 Wing-Sum Cheung On Higher Order Conservation Laws
1985 Jen-Tseh Chang Wilfried Schmid Special K-Types and the Beilinson-Bernstein Realization
1984 Robin Ticciati Raoul Bott Singularities in Moduli Spaces of Yang-Mills Fields
1984 Takahiro Shiota Characterization of Jacobian Varieties in Terms of Soliton Equations
1984 William McCallum Barry Mazur The Tate-Shafarevich Group of the Jacobian of a Quotient of the Fermat Curve
1984 Thongchai Kengmana Wilfried Schmid Discrete Characters on Non-Riemannian Symmetric Spaces
1984 George Gilbert Barry Mazur Analytic Multiplicity One Theorems for GL (n)
1984 Edward Dunne Wilfried Schmid Hyperfunction Solutions of the Zero Rest Mass
1984 Boris Datakousky Barry Mazur On Zeta Functions Associated with the Space of Binary Cubic Forms with Coefficients in a Function Field
1984 Ching-Li Chai David Mumford Compactification of Siegel Moduli Schemes
1984 Colin Bailey Gerald Sacks B-Degrees for Weakly Inadmissible B
1983 Deane Yang Involutive Hyperbolic Differential Systems
1983 Paul Vojta Barry Mazur Integral Points on Varieties
1983 Michael Stillman David Mumford Construction of Holomorphic Differential Forms on the Moduli Space of Abelian Varieties
1983 Emma Previato David Mumford Hyperelliptic Curves and Solitons
1983 Yevsey Nisnevich David Kazhdan Etale Cohomology and Arithmetic of Semisimple Groups
1983 Amnon Neeman David Mumford Topics in Algebraic Geometry
1983 Lisa Mantini An Analogy of the Penrose Correspondence for Representations of U(p,q) on L2-Cohomology
1983 Mikhail Gurevich David Kazhdan Theory of e-representations
1983 Eric Grinberg Shlomo Sternberg Integral Geometry on Compact Symmetric Spaces
1982 David Wright Barry Mazur Dirichlet Series Associated with the Space of Binary Cubic Forms with Coefficients in a Number Field
1982 Joseph Silverman John Tate The Neron-Tate Height On Elliptic Curves
1982 Judith Packer George Mackey Von Neumann Algebras Associated to Ergodic Actions of Countable Groups
1982 Vijayakumar Murty John Tate Algebraic Cycles on Abelian Varieties
1982 Aharon Livne Barry Mazur On Certain Covers of the Universal Elliptic Curve
1982 Henry Laquer Raoul Bott Homogeneous Connections and Yang-Mils Theory on Homogeneous Spaces
1982 Nicholas Gunther Raoul Bott Hamiltonian Mechanics and Optimal Control
1982 Edmond Griffin Phillip Griffiths Special Fibers in Families of Plane Curves
1982 Peter Dordal Gerald Sacks Independence Results Concerning Some Combinatorial Properties of the Continuum
1982 Eric Berger The Gauss Map and Isometric Embedding
1982 Max Benson Heisuke Hironaka The Kahler Algebra and Analytic Equivalence of Isolated Hypersurfaces Singularities
1982 David Bayer Heisuke Hironaka The Division Algorithm and the Hilbert Scheme
1981 Glenn Stevens Barry Mazur On Congruences Satisfied by Special Values of L-functions
1981 Theodore Slaman Gerald Sacks Aspects of E-Recursion
1981 Karl Rubin On the Arithmetic of CM Elliptic Curves in Zp-Extensions
1981 Sheldon Kamienny Barry Mazur On J1(p) and the Arithmetic of the Kernel of the Eisenstein Ideal
1981 Bruce Jordan Barry Mazur On the Diophantine Arithmetic of Shimura Curves
1981 Nancy Hingston Raoul Bott Equivariant Morse Theory and Closed Geodesics
1981 Joseph Halpern Gerald Sacks Axiomatic Definitions of Programming Languages and Logics of Programs
1981 Marcia Groszek Akihiro Kanamori Iterated Perfect Set Forcing and Degrees of Constructibility
1981 Robert Friedman Phillip Griffiths Hodge Theory
1981 Theodore Chinburg John Tate Stark's Conjecture
1980 Loring Tu Phillip Griffiths Variation of Hodge Structure and the Local Torelli Problem
1980 David Morrison Phillip Griffiths Semistable Degenerations of Enriques and Hyperelliptic Surfaces
1980 Curt Monash Andrew Gleason Stochastic Games: The Minmax Theorem
1980 Farshid Jamshidian Shlomo Sternberg Integral Geometry of Plane Complexes
1980 Max Benson The Kaehler algebra and analytic equivalence of isolated hypersurface singularities
1979 Dan Willard Gerald Sacks Predicate-Oriented Database Search Algorithms
1979 Terrie Stevens Andrew Gleason Weakened Topologies for Lie Groups
1979 Giuseppe Canuto Phillip Griffiths Associated Curves and Plucker Formulas in Grassmannians
1978 Dale Peterson Shlomo Sternberg Geometry of the Adjoint Representation of a Complex Semisimple Lie Algebra
1978 Carl Offner Andrew Gleason Zeros and Growth of Entire Functions of Order One and Maximal Type With an Application to the Random Signs Problem
1978 Ian Morrison David Mumford Projective Stability of Ruled Surfaces
1978 William Lang David Mumford Quasi-Elliptic Surfaces in Characteristic Three
1978 Joe Harris Phillip Griffiths A Bound on the Geometric Genus of Projective Varieties
1978 Benedict Gross John Tate Arithmetic on Elliptic Curves with Complex Multiplication
1978 Henri Gillet The Applications of Algebraic K-Theory to Intersection Theory
1978 Ofer Gabber Barry Mazur Some Theorems on Azumaya Algebras
1978 Moshe Breiner Essential Singularities of Entire Analytic Varieties
1977 William Wilson Richard Brauer Fusion in Nonabelian Groups of Order p3
1977 James Weisinger John Tate Some Results on Classical Eisenstein Series and Modular Forms over Function Fields
1977 Jerrold Tunnell John Tate On the Local Langlands Conjecture for GL(2)
1977 Robert Kottwitz John Tate Orbital Integrals on GL3
1977 Jerome Hoffman The Hodge Theory of Flat Vector Bundles on a Complex Torus
1977 Michael Harris Barry Mazur On p-adic Representations Arising From Descent on Abelian Varieties
1977 David Goss Barry Mazur P-adic Eisenstein Series for Function Fields
1977 Daniel Flath John Tate A Comparison of the Automorphic Representations of GL (3) and its Twisted Forms
1977 Ron Donagi Phillip Griffiths On the Geometry of Grassmannians
1977 Don Coppersmith Lars Ahlfors Deformations of Lie Groups and Lie Algebras
1977 Joe Buhler John Tate Icosahedral Galois Representations
1977 Robert Brooks Raoul Bott On the Smooth Cohomology of Groups of Diffeomorphisms
1976 Richard Weiss Raoul Bott Refined Chern Classes for Foliations
1976 Allen Tannenbaum Heisuke Hironaka Deformations of L-cycles and the Chow Scheme
1976 Yung-Sheng Tai David Mumford On Arithmetic Quotients of Bounded Symmetric Domains
1976 Caroline Series George Mackey Ergodic Actions of Product Groups
1976 Peter Olver Garrett Birkhoff Symmetry Groups of Partial Differential Equations
1976 Fred Kochman Shlomo Sternberg Bernstein Polynomials and the Gauss-Manin Connection
1976 Naomi Jochowitz Barry Mazur Congruences Between Modular Forms and Implications for the Hecke Algebra
1976 Kenneth Baclawski Heisuke Hironaka Homology and Combinatorics of Ordered Sets
1975 Robert Zimmer George Mackey Ergodic Group Actions with Generalized Discrete Spectrum
1975 Sandy Zabell Shlomo Sternberg A Limit Theorem for Conditional Expectations with Applications to Probability Theory and Statistical Mechanics
1975 William Symes Phillip Griffiths Holomorphic Pseudogroup Structures on Quasiprojective Varieties
1975 Walter Stromquist Andrew Gleason Some Aspects of the Four Color Problem
1975 Zenaida Ramos Analytic Theory of Elliptic Curves with Split Multiplicative Reduction over Complete Rings
1975 Ulf Persson David Mumford On Degenerations of Algebraic Surfaces
1975 James Perchik Raoul Bott Cohomology of Hamiltonian and Related Formal Vector Field Lie Algebras
1975 Linda Ness David Mumford Curvature on Algebraic Plane Curves
1975 Mark Mostow Raoul Bott Continuous Cohomology of Spaces with Two Topologies
1975 Victor Miller Barry Mazur Diophantine and p-adic Analysis of Elliptic Curves and Modular Forms
1975 Peter Hahn George Mackey Haar Measure and Convolution Algebras on Ergodic Groupoids
1975 Walter Griffith David Mumford Cohomology of Flag Varieties on Characteristic p
1975 William Gordon Barry Mazur Linking the Conjectures of Artin-Tate and Birch-Swinnerton-Dyer
1975 Frederick Fuglister Richard Brauer On a Problem of E. Artin
1975 Robert Fisher David Mumford Endomorphisms of Abelian Schemes
1975 Alain Damlamian Lynn Loomis Non-Linear Evolution Equations with Variable Norms
1975 Donald Cohn Andrew Gleason Topics in Liftings and Stochastic Processes
1975 Daniel Cohen Andrew Gleason Small Rings in Critical Maps
1975 Robert Brody Phillip Griffiths Intrinsic Metrics and Measures on Compact Complex Manifolds
1975 Avner Ash David Mumford Polyhedral Reduction Theory in Self-Adjoint Homogeneous Cones
1975 John Adams Phillip Griffiths On the Theorem of Frenet
1974 George Shapiro Lynn Loomis Some Aspects of Balayage of Fourier Transforms
1974 Henry Pinkham David Mumford Deformations of Algebraic Varieties with Gm Action
1974 Francis Myers David Mumford P-adic Schottky Groups
1974 Kenneth Kramer John Tate Two-descent for Elliptic Curves in Characteristic Two
1974 Colin Godfrey Shlomo Sternberg Ideals of Orbits of Nilpotent Lie Algebras
1974 Johh Garberson Raoul Bott The Cohomology of Certain Algebraic Varieties
1974 Frederick Fuglister Richard Brauer On a problem of E. Artin
1974 Persi Diaconis Frederick Mosteller Weak and Strong Averages in Probability and the Theory of Numbers
1974 William Carter Saunders Mac Lane On the Cohomology Theory of Fields
1974 Joseph Carroll On the 2-primary Part of K2O and on Z2-extensions for Imaginary Quadratic Fields
1974 Michael Buchner Stability of the Cut Locus
1973 Thomas Wieting George MacKey Ergodic Affine Lebesgue G-Spaces
1973 Helen Wang Andrew Gleason Function Algebra Extensions and Analytic Structures
1973 George Shapiro Some Aspects of Balayage of Fourier transforms
1973 Lawrence Risman Subalgebras of Division Algebras
1973 Kenneth Ribert Galois Action on Division Points of Abelian Varieties with Many Real Multiplications
1973 Michael O'Hare
1973 Jerome Myers David Mumford p-Adic Schottky Groups
1973 Edward Miller Raoul Bott Local Isomorphism of Riemannian Hermitian and Combinatorial Manifolds
1973 Robert Metcalfe
1973 Robert May Transversality Properties of Topologically Stable Mappings
1973 George Markowsky Combinatorial Aspects of Lattice Theory with Applications for the Enumeration of Free Distributive Lattices
1973 Gerald MacCollum Shlomo Sternberg Topics on Universal Algebra
1973 Stacy Langston David Mumford Valuative Criteria for Families of Vector Bundles on Algebraic Varieties
1973 Daniel Kubert Barry Mazur Universal Bounds on the Torsion and Isogenics of Elliptic Curves
1973 Eric Kronstadt Andrew Gleason Interpolating Sequences in Polydisks
1973 Joel Hirsh
1973 Ronald Hirschorn
1973 Charles Getchell Andrew Gleason Construction of Rings in Modular Lattices
1973 Peter Forrest George Mackey On the Virtual Groups Defined by Ergodic Actions of Rn and Zn
1973 Gerald Edgar Convergence from an Algebraic Point of View
1973 Peter Chen
1973 Alan Candiotti Iwasawa Invariants in Z1 extensions of Number Fields
1972 Neil White The Bracket Ring and Combinatorial Geometry
1972 Francisco Thayer-Fabrega George Mackey Liftings in the Category of C* Algebras
1972 Peter Shalen Triangulation of 3-Manifolds: A Piecewise Linear Approach
1972 Charles Setzer John Coates Elliptic Curves of Prime Conductor
1972 Steven Schnider Shlomo Sternberg Invariant Theory and the Cohomology of Infinite Lie Algebras
1972 Mary Schaps David Mumford Non-singular Deformations of Space Curves using Determinantal Schemes
1972 Carl Pomerance John Tate Odd Perfect Numbers are Divisible by at least Seven Distinct Primes
1972 Arthur Ogus Local Cohomology Dimension of Algebraic Varieties
1972 Lee Mondshein
1972 Daniel Marcus Andrew Gleason Direct Decompositions of Commutative Monoids
1972 Finn Knudsen David Mumford Towards Projectivity of the Space of Moduli of Stable Curves of a Given Genus
1972 Lewis Josephs
1972 David Harris David Mumford A Study of Three-Dimensional Principally-Polarized Abelian Varieties
1972 Peter Gilkey Raoul Bott Curvature and the Eigenvalues of the Laplacian for Geometrical Elliptic Complexes
1972 Stephen Fisk Triangulations of Two Manifolds with Local Properties
1972 James Damon Thom Polynomials for Contact Class Singularities
1972 Stephen Crick David Mumford Local Moduli of Abelian Varieties
1972 Jerry Bona Cauchy Problems with Random Initial Values in the Space of Tempered Distributions
1971 Alan Waterman General-Valued Polarities
1971 Jonathan Wahl David Mumford Deformations of Branched Covers and Equisingularity
1971 Richard Stanley Ordered Structures and Partitions
1971 Satish Shirali Lynn Loomis Complex Involutory Banach Algebras
1971 Michael Razar John Tate The Non-vanishing of L(1) for Certain Elliptic Curves
1971 Richard Goodman Round-off Error in the Numerical Solution of Retarded Ordinary Differential Equations
1971 Michael Connnolly
1970 Joel Spencer Lars Ahlfors Probabilistic Methods in Combinatorial Theory
1970 Richard Rochberg Andrew Gleason Properties of Isometrics and Almost Isometrics of Some Function Algebras
1970 Vern Poythress Partial Algebras
1970 Robert MacPherson Raoul Bott Singularities of Maps and Characteristic Classes
1970 Raleigh Stanton Hales Jr Numerical Invariants and Gamma Products of Graphs
1970 David Gieseker David Mumford Contributions to the Theory of Positive Embeddings in Algebraic Geometry
1970 John Fay Lars Ahlfors Special Moduli and Theta Relations
1970 Julia Brown Andrew Gleason Homologies and Elations of Finite Projective Planes
1970 Andreas Blass Raoul Bott Orderings of Ultrafilters
1969 Peter Taylor Andrew Gleason The Structure Space of a Choquet Simplex
1969 Joel Roberts David Mumford Ordinary Singularities of Projective Varieties
1969 Richard Rasala Barry Mazur On the Structure of Purely Inseparable Field Extensions
1969 David Pincus Andrew Gleason Individuals in Zermelo-Fraenkel Set Theory
1969 Donald Olivier
1969 Robert Oberg Andrew Gleason Functional Differential Equations with General Perturbation of Argument
1969 John Lindsey II Richard Brauer Finite Linear Groups in Six Variables
1969 Emmett Keeler Mathematical Models of Economic Growth
1969 Birger Iversen Numerical Invariants and Multiple Planes
1969 Herbert Gintis
1969 Stephen Gewirtz David Mumford The Picard Scheme of a Quotient Problem
1969 Richard Brown Raoul Bott Cobordism
1969 Morris Brooks Raoul Bott The Cohomology of the Complement of a Submanifold
1968 William Waterhouse John Tate Abelian Varieties over Finite Fields
1968 Walter Taylor Compactness in Relational Structures
1968 Leslie Roberts Barry Mazur Algebraic K of Vector Bundles
1968 Lawrence Roberts On the Flat Cohomology of Finite Group Schemes
1968 John McCabe P-adic Theta Functions
1968 Ravindra Kulkarni Shlomo Sternberg Curvature and Metric
1968 Keith Josephson The Structure of a Banach Algebra Invariant for Measure Preserving Automorphisms
1968 Christopher Henrich Nonunitary Representations and Harmonic Analysis of Some Solvable Lie Groups
1968 Charles Feifeld Shlomo Sternberg The Coholomogy Theory of Transitive Moduales over the Primitive Infinite Lie Algebras
1968 Lawrence Corwin George Mackey Measures on Locally Compact Groups with Certain Transformation Properties
1968 Paul Chernoff Semigroup Product Formulas and Addition of Unbounded Operators
1968 Lawrence Brown David Mumford On the Structure of Locally Compact Groups
1968 George Bergman Commuting Elements in Free Algebras and Related T+E225opics in Ring Theory
1967 Robert Warfield Complete Abelian Groups and Direct Sum Decompositions
1967 David Wales Richard Brauer Finite Linear Groups in Seven Variables
1967 George Sethares Lars Ahlfors The External Property of Certain Teichmüller Mappings
1967 Shankar Sen John Tate On Automorphisms of Local Fields
1967 David Ragozin Andrew Gleason Approximation Theory on Compact Manifolds and Lie Groups with Applications to Harmonic Analysis
1967 Tadao Oda David Mumford Abelian Varieties over a Perfect Field and Dieudonne` Modules
1967 James Milne The Conjecture of Birch and Swinnerton-Dyer for Constant Abelian Varieties over Function Fields
1967 Nelson Max Homemorphisms of Sn x Sl
1967 Sandy Grabiner Andrew Gleason Radical Banach Algebras and Formal Power Series
1967 Hubert Goldschmidt Shlomo Sternberg Overdetermined Systems of Analytic Partial Difference Equations
1967 Gustave Efroymson Cohomology Rings of Commutative Formal Groups
1966 Herry Wente Existence Theorems for Surfaces of Constant Mean Curvature and Perturbations of a Liquid Globule in Equilibrium
1966 Stuart Sidney Andrew Gleason Powers of Maximal Ideals in Function Algebras
1966 Theodore Palmer Lynn Loomis Unbounded Normal Operators on Banach Spaces
1966 Connor Lazarov Raoul Bott Secondary Characteristic Classin K-Theory
1966 John Fogarty David Mumford On Hilbert Schemes
1966 Stephen Cook On the Minimum Computation Time of Functions
1966 Kirby Baker Topological Methods in the Algebraic Theory of Vector Lattices
1966 Steadman Bagby Lars Ahlfors Conformal Invariants for Condensers
1965 Martin Schultz The Convergence of Difference Approximations to Cauchy Problems in the Space of Tempered Distributions
1965 Joseph Lipman Quasi-ordinary Singularities of Embedded Surfaces
1965 Peter Landweber Raoul Bott Kunneth Formulas for Bordism Theories
1965 John Labute Classification of Demushkin Groups
1965 Steven Kleiman Oscar Zariski Toward a Numerical Theory of Ampleness
1965 William Jones Lynn Loomis Types of Completeness in Locally Convex Spaces
1965 Herbert Halperin Lynn Loomis Decomposition of Centrally Reducible and of Reducible Functionals
1965 Ethan Bolker Andrew Gleason Functions Resembling Quotients of Measures
1964 Richard Turyn Richard Brauer Character Sums and Difference Sets
1964 John Schlessinger John Tate Infinitesimal Deformations of Singularities
1964 Daniel Quillen Raoul Bott Formal Theory of Linear overdetermined Systems of Partial Differential Equations
1964 Donald Passman Richard Brauer Groups and Group Rings
1964 Stephen Lichtenbaum John Tate Curves over Discrete Valuation Rings
1964 Karl Kronstein Richard Brauer Characters and Systems of Subgroups
1964 Bernard Kripkee Lynn Loomis Modules of Holomorphic Vector-Valued Functions
1964 Irving Isaacs Richard Brauer P-Solvable Linear Groups
1964 Richard Holzsager Raoul Bott Classification of certain Types of Spaces
1964 Deborah Haimo Integral Equations Associated with Hankel Convolutions
1964 Jerry Fields Rational Approximations to Generalized Hypergeometric Functions
1964 John Dauns Convolution Transforms whose Inversion Functions have Complex Roots
1963 Joseph Zilber Raoul Bott Categories in Homotopy Theory
1963 Charles Sims Enumerating p-Groups
1963 Ralph Rockafellar Convex Functions and Dual Extremum Problems
1963 Judith Obermayer John Tate Curves of Genus 3 over Characteristic 2
1963 Victor Manjarrez Polynomial Bases for Compact Sets in the Plane
1963 Saul Lubkin Theory of Covering Spaces
1963 Jonathan Lubin John Tate One-parameter Formal Lie Groups over p-adic Integer Rings
1963 Joseph Kitchen Jr Lynn Loomis Almost Periodic Functionals in the Conjugate Space of a Banach Algebra
1963 Roger Kirchner Lars Ahlfors Elementary Moduli for Teichmüller Space
1963 John Kennison Andrew Gleason Natural Functors in Topology and Generalizations
1963 Judith Hirschfield The Curves of Genus 3 Defined over Z/2Z
1963 Seymour Hayden Richard Brauer On Finite Linear Groups whose Order contains a Prime Larger than the Degree
1963 John Denton Applications of the Herbrand Theorem
1963 Lawrence Conlon Raoul Bott Spaces of Paths on a Symmetric Space
1963 David Bloom Richard Brauer On the Subgroups of SL (3,q)
1962 Harold Ward Richard Brauer On Ree's Series of Simple Groups
1962 Stephen Shatz Cohomology of Artinian Group Schemes over Local Fields
1962 Dorothy Shaffer The Shape of Level Loci of Green's Function and other Harmonic Functions
1962 Rohit Parikh Recursive Well Orderings and Transfinite Progressions
1962 Arlan Ramsay Lynn Loomis Existence and Applications of Dimension Functions in Lattices
1962 David Mumford Oscar Zariski Existence of the Moduli Scheme for Curves of any Genus
1962 Albert Marden Lars Ahlfors An External Length Problem and the Bilinear Relation on Open Riemann Surfaces
1962 Florence MacWilliams Andrew Gleason Combinatorial Problems of Elementary Abelian Groups
1962 Malcolm MacLaren Lynn Loomis Atomic Orthocomplemented Lattices
1962 Stanley Kaplan On the Global Existence of Solutions of Quasi-Linear Parabolic Equations
1962 Victor Guillemin Shlomo Sternberg Theory of Finite G-Structures
1962 Herbert Enderton Hierarchies in Recursive Function Theory
1962 Edward Effros On the Representations of C-Algebras
1962 Clifford Earle Jr Lars Ahlfors Teichmüller Spaces of Groups of the Second Kind
1962 Thomas Brown The Asymptotic Behavior of Some Non-linear Autonomous Systems
1961 Vincent Williams On Conformal Maps of Regions of Infinite Connectivity
1961 Andrew Ogg John Tate Cohomology of Abelian Varieties over Function Fields
1961 Samuel Holland Jr Lynn Loomis The Radon-Nikodym Theorem in Dimension Lattices
1961 Peter Falb On Differentials in Function Fields
1961 Harold Edwards Raoul Bott Applications of Intersection Theory to Boundary Value Problems
1961 Edward Curtis Raoul Bott The Lower Central Series for Free Group Complexes
1961 James Cohn Some Results in the Cohomology Theory of Finite Groups
1960 Johnathan Richards Lars Ahlfors A Classification of Noncompact Surfaces
1960 Calvin Moore John Moore Extensions and Cohomology Theory of Locally Compact Groups
1960 Thomas Knapp Minimal and Relatively Minimal Models for the Function Field of an Algebraic Surface
1960 Adam Kleppner George Mackey Multipliers on Abelian Groups
1960 Heisuke Hironaka Oscar Zariski On the Theory of Birational Blowing-Up
1960 Stevens Heckschner A Characterization of Certain Banach Function Spaces
1960 Morton Harris Some Results on a Generalization of the Character Table of a Finite Group
1960 Marshall Freimer Truncated Policies in Dynamic Programming
1960 Leonard Evens The Cohomology Ring of a Finite Group
1960 Michael Artin Oscar Zariski On Enriques' surfaces
1959 Neal Zierler George Mackey On General Measure Theory
1959 Paul Yale Andrew Gleason A Characterization of Congruence Groups in Geometries of the Euclidean Type
1959 Warren Wong Richard Brauer On the Irreducible Modulat Representations of Finite Classical Groups
1959 Ralph Krause Minimal Metric Spaces
1959 Dale Husemoller Lars Ahlfors Automorphisms and Coverings of Riemann Surfaces Mappings
1959 Paul Fong Richard Brauer On the Characters of Finite Solvable Groups
1959 Gerald Bilodeau Lars Ahlfors Inversion and Representation Theory of the Weierstrass Transform
1958 Louis Solomon Richard Brauer The Representation of Finite Groups in Algebraic Number Fields
1958 Marvian Pour-El Computable Functionals
1958 Mason Phelps Andrew Gleason Closed Subalgebras of a Commutative Algebra over the Real Numbers
1958 Donald Newman Some aspects on Polynomial Approximation
1958 Thomas Mullikin Mixed Cauchy Problems and C-Semigroups
1958 Peter Martin External Metrics for a Class of Varational Problems Related to Extended Length
1958 Henry Leonard Jr Richard Brauer A Generalization of a Theorem of Blichfeldt
1958 Glen Bredon Andrew Gleason Some Theories on Transformation Groups
1958 Leonard Baum Lynn Loomis Derivations in Commutative Semi-Simple Banach Algebras
1958 Edward Assmus On the Homology of Local Rings
1958 Robert D. Accola Lars Ahlfors The Bilinear Relation on Open Riemann Surfaces
1957 Avrum Weinzweig Andrew Gleason On Fibre Spaces and Fibre Bundles
1957 Stephen Smale Raoul Bott Regular Curves on Riemann Manifolds
1957 Henry Landau On Canonical Conformal Maps of Multiply Connected Regions
1957 Solomon Golomb Problems in the Distribution of the Prime Numbers
1956 Mishael Zedek On Generalized Tchebycheff Polynomials
1956 Richard Palais Andrew Gleason A Global Formulation of the Lie Theory of Transformation Group
1956 Richard Goldberg Generalized Lambert Transforms
1956 Marguerite Frank New Simple Lie Algebras
1955 Calvin Wilcox The scattering of electromagnetic radiation by a cyclindrical shell of finite length
1955 Eoin L. Whitney Lars Ahlfors Variability Regions for the Univalent Functions and their Derivatives
1955 Seth Warner George Mackey Locally M-Convex Algebras
1955 Ernest Schlesinger Lars Ahlfors Conformal Invariants and Prime Ends
1955 Parfeny Saworotnow On the generalization of the notion of H*-algebra: Complemented algebras
1955 Roger Pinkham Inversion of the Laplace and Stieltjes transforms utilizing difference operators
1955 Robert Osserman Lars Ahlfors Contributions to the Problem of Type
1955 John Kalman George Mackey Some Inequalities Related to Holder Inequality and Some Contributions to Lattice Theory
1955 James Howland Induced potentials
1955 Shreeram Abhyankar Local uniformization of algebraic surfaces over modular ground fields
1954 Richard Varga Properties of a special set of entire functions and their respective partial sums
1954 William Reynolds Richard Brauer On Finite Groups Related to Permutation Groups of Prime Degrees
1954 Arthur Hinton Read Lars Ahlfors External Problems on Riemann Surfaces
1954 Jacqueline Evans On approximation and interpolation by functions analytic in a given region and an application to orthonormal systems
1954 James Eells Geometric aspects of integration theory
1953 Lawrence Rosenfeld On distortion at the boundary of a conformal mapping
1953 Theodore Rivlin Overconvergent Taylor Series and the zeros of related polynomials
1953 Robert Kozelka On some special order statistics from a multinomial distribution
1953 Samuel Kneale Axially symmetric stokes flows
1953 Harry Gonshor Lynn Loomis Spectral Theory for a Class of Non-Linear Operators
1953 Irwin Fischer The totality of curves of genus g
1953 Frederic Cunningham Jr L1-structure in Banach Spaces
1952 Norman Zachary
1952 Lawrence Markus A topological analysis of differential equations in the large
1952 Alan Kay Methods in the location of zeros of families of polynomials of unbounded degree in circles sectors and other regions
1952 Robert Graves The Fredholm Theory in Banach Spaces
1952 William Fishback On the theorem of Bertini on the variable singular points of a linear system
1952 Edward Block
1951 John Wermer On the harmonic analysis of certain groups and semi-groups of operators
1951 Halsey Royden Lars Ahlfors Harmonic Functions on Open Riemann Surfaces
1951 Israel Rose On the Cohomology theory of associative algebras
1951 Henry Pollak Some estimates for external distance
1951 Henry Nelson
1951 Graham Murray
1950 David Young Jr Iterative methods for solving partial difference equations of elliptic type
1950 John Sopka On the characterization of Reynolds operators on the normed algebra of all continuous real-valued functions defined on a compact Hausdorff space
1950 Parfeny Saworothow Lynn Loomis On the Generalization of the Notion of H*-Algebra: Complex Algebra
1950 Maxwell Rosenlicht Equivalence concepts on an algebraic curve
1950 Allen Devinatz Lars Ahlfors Transformations in Reproducing
1950 Philip Davis
1950 H. Chandler Davis
1949 Vitar Michael Wolontis Lars Ahlfors Properties of Conformal Invariants
1949 George Springer Lars Ahlfors Representations of Finite Groups
1949 Morton Slater Hausdorff measure in abstract metric spaces
1948 James H. Wolfe Tensor fields associated with Lipschitz cochains
1948 George Mostow The extensibility of local Lie groups of transformations and groups on surfaces
1948 James Jenkins Some problems in conformal mapping
1948 Margaret Elliott Joseph Walsh On the Degree of Approximation to Harmonic Functions by Harmonic Polynomials
1948 Harvey Cohn Lars Ahlfors Diophantine Aspects of Poincare Theta Functions
1947 Frank Stewart Non-commutative integration and abstract differential equations
1947 Paul Olum Homology with operators and mapping theory
1947 Ivan Hershner Jr The Moduli of univalence and of p-valence of functions analytic in the unit circle
1947 Albert Harvey Some studies of functions of exponential type
1947 Thomas Caywood Axially symmetric harmonic functions
1947 Edwin Akutowicz The third iterate of the Laplace transform
1946 Pesi Masani Multiplicative Riemann integration in normed rings
1945 Choy-Tak Taam On the solutions of ordinary linear homogeneous differential equations of the second order in the complex domain
1945 Richard Arens Topologies for spaces of transformations
1936 Walter Sewell Generalized derivatives and approximation by polynomials
1936 Arthur Sard On the measure of the critical values of functions
1936 Joel Brenner The linear homogeneous group modulo p
1935 George Van Schaack Topics in the theory of critical points
1935 Yu-Cheng Shen On interpolation and approximation to an analytic function by rational functions with preassigned poles
1935 Arthur Pitcher Certain invariants of closed extremals
1935 Holbrook MacNeille Extensions of partially ordered sets
1935 Walter Leighton The minimizing of a singular quadratic functional
1935 John Curtiss I. Interpolation in transforms of the roots of unity II. The Jacobi interpolation series on the lemniscate of convergence
1934 Frederick Steen On a class of polynomials which minimize definite integrals
1934 Thomas Downs On the planer points of an analytic surface
1934 Nancy Cole The index form associated with an extremaloid
1934 Donald Ballou A class of completely monotonic functions every positive power of which is also completely monotonic
1934 Allen Anderson Topics in the theory of binary forms
1933 Ruth Peters Parallelism and equidistance in Riemannian geometry
1933 Lester Moston Invariant methods in the infinitesimal geometry of surfaces
1933 James Frame The theory of tables of group characteristics
1932 Hassler Whitney The coloring of graphs
1932 Mildred Sullivan On the derivations of Newtonian and logarithmic potentials near the acting masses
1932 Helen Russell On the degree of convergence and overconvergence of polynomials of best simultaneous approximation to several functions analytic in distinct regions
1932 Griffith Price On the double pendulum and similar dynamical systems
1932 Sumner Myers Sufficient conditions in the problem of the calculus of variations in n-space in parametric form and under general end conditions
1932 Daniel Lewis Infinite systems if ordinary differential equations with applications to certain second order non-linear partial differential equations of hyperbolic type
1932 Spofford Kimball On rigid motions in four dimensions with applications to the Laguerre geometry of three dimensions
1932 Joseph Doob The boundary values of analytic functions
1931 Turner Smith The Birkhoff fluid theory of electricity
1931 Charles Morrey Invariant functions of conservative surface transformations
1931 Cecil Holmes The approximation of harmonic functions in three dimensions by harmonic polynomials
1930 Charles Wexler On the theory of quadratic fields
1930 Chin-Nien Liu Contributions to the restricted problem of three bodies
1930 Tsai-Han Kiang Existence of critical points of harmonic functions of three variables
1930 Gustav Hedlund (a) Geodesics on a two-dimensional Riemannian manifold with periodic coefficients (b) Poincare's rotation number and Morse's type number
1930 Orin Farrell (a) on the expansion of harmonic functions in terms of harmonic polynomials (b) On approximation to an arbitrary function of a complex variable by polynomials
1930 Edward Cutler Some properties of genesubspaces of a Riemannian space
1930 Albert Currier The problem if the calculations in m-space with end points variable on two manifolds
1930 Stewart Cairns The cellular division and approximation of regular spreads
1929 Robin Robinson On the differential geometry of surfaces in non-Euclidean space
1929 Clarence Lubin Singular points of second order systems of real differential equations
1929 John Hinrichsen The problem of n bodies
1929 Carl Coe Exterior motion in the restricted problem of three bodies
1929 Arthur Brown Relations between the critical points of a real analytic function of n independent variables
1929 Andrew Berry Fourier representations
1928 Fred Perkins On the oscillation of harmonic functions
1928 Morris Marden On the location of the roots of the Jacobian of two binary forms and of the derivative of a rational function
1927 Isidor Sheffer On the theory of linear differential equations of infinite order
1926 Marshall Stone Ordinary linear homogeneous differential equations of order n and the related expansion problems
1926 Morris Slotnick Fundamental transformations of surfaces
1926 Bernard Koopman On rejection to infinity and exterior motion in the restricted Problem of Three Bodies
1926 Miltiades Demos The group characteristics of the general and special quaternary linear homogeneous groups
1926 Arthur Copeland Studies on the gyroscope
1925 Lewis Ward Boundary value problems of the third order and the allied expansions
1925 Heinrich Brinkmann Contributions to the theory of Riemann spaces
1924 David Widder Some mean-value theorems connected with Cote's Method of Mechanical Quadature
1924 Julian Holley Linear spaces and their fixed points.
1923 Forrest Murray (a) on certain differential equations of the second order (b) on certain systems of differential equations containing a parameter
1923 Ben Linfield On the theory of discrete varieties
1923 Carl Garabedian A method of series in elastic with applications (I) to circular plates of constant or variable thickness
1922 Eleanor Pairman Expansion theorems for solution of a Fredholm homogeneous integral equation of the second kind with kernel of non-symmetric type
1922 Rudolph Langer (a) Developments associated with a boundary problem not linear in the parameter (b) the boundary problems and developments associated with a system of ordinary linear differential equations of the first order
1922 Bancroft Brown The equilong transformations of Euclidean space
1922 Clarence Adams The general theory of the linear partial q-difference equation and of the linear partial difference equation of the intermediate type
1921 Rachel Blodgett The determination of the coefficients in interpolation formulae and a study of the approximate solution of integral equations
1920 Joseph Walsh On the location of the roots of the Jacobian of two binary forms
1920 Hyman Ettlinger (a) Existence Theorems for the General Real Self-Adjoint Linear System of the Second Order (b) Oscillation Theorems for the Real Self-Adjoint Linear System of the Second Order
1919 Tsoo Tsiang The Geometry of a Non-Euclidean Line-Sphere Transformation
1919 Clarence Reynolds On the Zeros of Solutions of Linear Differential Equations
1919 Louis Brand (a) On Linear equations with an Infinite Number of Variables (b) on Infinite Systems of Linear Integral Equations (c) Flexural Deflections and Statically Indeterminate Beams
1917 Marston Morse Certain types of geodesic motion on a surface of negative curvature
1917 Minfu Hu Linear integro-differential equations with a boundary condition
1917 Lester Ford On rational approximations to an irrational complex number
1917 Mary Curtis Curves invariant under point-transformations of special type
1916 Norman Miller Some problems connected with the linear connectivity of manifolds
1916 Alton Miller Systems of pencils of lines in ordinary space
1916 Raymond Brink Some integral tests for the convergence and divergence of infinite series
1916 Paul Batchelder The hypergeometric difference equation
1915 Levi Wilson Conformal transformation of curvilinear angles
1915 Charles Wilder Problems in the theory of ordinary linear differential equations with auxiliary conditions at more than two points
1915 William Milne On the degree of convergence of Birkhoff's series
1914 Rainard Robbins The calculus of variations as the limit of a problem in minimizing an algebraic sum
1914 Edward Allen Su alcuni caratteri di una serie algebriea e la formola di de Jonquieres per serie qualsiasi
1913 Joseph Slepian On the functions of a complex variable defined by an ordinary differential equation of the first order and first degree
1913 Roger Johnson An analytic treatment of the conic as an element of space of three dimensions
1913 Guy Clements Implicit functions defined by equations with vanishing Jacobian
1913 David Barrow Oriented circles in space
1912 Tomlinson Fort Problems connected with linear difference equations of the second order with special reference to equations with periodic coefficients
1911 Samuel Urner Certain singularities of point-transformations in space of three-dimensions
1910 Frank Hitchcock Vector functions of a point
1910 Griffith Evans Volterra's integral equation of the second kind with discontinuous kernel
1909 Edson Taylor On some problems in conformal mapping
1909 Louis Dederick Certain singularities of transformations of two real variables
1908 Charles Moore On the theory of convergence factors and some of its applications
1908 Frank Irwin The invariants of linear differential expressions
1907 William Brenke A contribution to the theory of trigonometric and zonal harmonic series
1906 William Roever Brilliant points
1905 Walter Ford On the problem of analytic extension as applied to the functions defined by power series
1904 Lewis Ames An arithmetic treatment of some problems in analysis situs
1903 David Curtiss Binary Families in a triply connected region with especial reference to hypergeometric families
1902 Otto Dunkel Regular singular points of a system of homogeneous linear differential equations of the first order
1901 Charles Haskins On the invariants of quadratic differential forms
1901 Charles Black The parametric representation of the neighborhood of a singular point of an analytic surface
1898 Donald Campbell On linear differential equations of the third and fourth orders in whole solutions exist certain homogeneous relations
1898 Harry Benedict The variation of latitude
1897 Frederick Safford Systems of revolution and their relation to conical systems in the theory of Lame's products
1897 Milton Porter On the Roots of the hypergeometric and Bessel's Functions
1895 James Glover On the Properties of functions defined by the partial equation
1889 Joseph Markley Bessel's Functions
1887 George Johnson Surfaces having the principal radii of curvature at each point numberically equal but of opposite sign
1886 Frank Cole A contribution to the theory of the general equation of the sixth degree
1879 Leonard Waldo The investigation of the constants of the micrometirc apparatus of the Merz equatorial of the observatory of Harvard College together with the discussion of the observations of the satellites of Mars observed therewith
1873 William Byerly The heat of the sun