Phillip Griffiths

Phillip Griffiths's AcademicInfluence.com Rankings

Phillip Griffiths

Mathematics

#92

World Rank

#253

Historical Rank

#36

USA Rank

Algebraic Geometry

#10

World Rank

#11

Historical Rank

USA Rank

Measure Theory

#285

World Rank

#442

Historical Rank

#124

USA Rank

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Mathematics

Phillip Griffiths's Degrees

PhD Mathematics Princeton University

Why Is Phillip Griffiths Influential?

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According to Wikipedia, Phillip Augustus Griffiths IV is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He is a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory, which forms part of transcendental algebraic geometry and which also touches upon major and distant areas of differential geometry. He also worked on partial differential equations, coauthored with Shiing-Shen Chern, Robert Bryant and Robert Gardner on Exterior Differential Systems.

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Phillip Griffiths's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Principles of Algebraic Geometry (1978) (7905)
Geometry of algebraic curves (1985) (2452)
Real homotopy theory of Kähler manifolds (1975) (913)
The intermediate Jacobian of the cubic threefold (1972) (779)
On the Periods of Certain Rational Integrals: II (1969) (631)
Principles of Algebraic Geometry: Griffiths/Principles (1994) (616)
Exterior Differential Systems (1990) (435)
Geometry of Algebraic Curves: Volume I (1984) (402)
Rational Homotopy Theory and Differential Forms (1981) (364)
Algebraic geometry and local differential geometry (1979) (277)
Exterior Differential Systems and the Calculus of Variations (1982) (273)
Periods of integrals on algebraic manifolds, III (some global differential-geometric properties of the period mapping) (1970) (262)
On Cartan’s method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry (1974) (253)
Locally homogeneous complex manifolds (1969) (246)
Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems (1970) (245)
Two Applications of Algebraic Geometry to Entire Holomorphic Mappings (1980) (242)
Nevanlinna theory and holomorphic mappings between algebraic varieties (1973) (222)
On the Periods of Integrals on Algebraic Manifolds (1968) (221)
On the variety of special linear systems on a general algebraic curve (1980) (210)
Topics in transcendental algebraic geometry (1984) (199)
Periods of Integrals on Algebraic Manifolds, I. (Construction and Properties of the Modular Varieties) (1968) (192)
Variations on a theorem of Abel (1976) (184)
Infinitesimal variations of hodge structure (I) (1983) (177)
PERIODS OF INTEGRALS ON ALGEBRAIC MANIFOLDS, II. (Local Study of the Period Mapping) (1968) (176)
Reshaping the graduate education of scientists and engineers. (1995) (175)
The Extension Problem in Complex Analysis II; Embeddings with Positive Normal Bundle (1966) (165)
Reduction for Constrained Variational Problems and κ 2 2 ds (1986) (159)
Introduction to Algebraic Curves (1989) (159)
A Defect Relation for Equidimensional Holomorphic Mappings Between Algebraic Varieties (1972) (154)
Geometry of Algebraic Curves: Volume II with a contribution by Joseph Daniel Harris (2011) (139)
Complex analysis and algebraic geometry (1979) (130)
On the Noether-Lefschetz theorem and some remarks on codimension-two cycles (1985) (121)
Analytic cycles and vector bundles on non-compact algebraic varieties (1975) (111)
PERIODS OF INTEGRALS ON ALGEBRAIC MANIFOLDS, II (2016) (109)
Characteristic cohomology of differential systems. I. General theory (1995) (97)
Residues and zero-cycles on algebraic varieties (1978) (95)
Hermitian differential geometry, Chern classes, and positive vector bundles (2015) (95)
Some Observations on the Infinitesimal Period Relations for Regular Threefolds with Trivial Canonical Bundle (1983) (94)
Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (2012) (91)
Characteristic cohomology of differential systems II: Conservation laws for a class of parabolic equations (1995) (90)
LINEARIZING FLOWS AND A COHOMOLOGICAL INTERPRETATION OF LAX EQUATIONS (1985) (89)
Exterior Differential Systems and Euler-Lagrange Partial Differential Equations (2002) (87)
Infinitesimal variations of Hodge structure and the global Torelli problem (1980) (83)
Infinitesimal variations of hodge structure (III) : determinantal varieties and the infinitesimal invariant of normal functions (1983) (79)
A poncelet theorem in space (1977) (79)
Entire Holomorphic Mappings in One and Several Complex Variables. (1976) (76)
Abel's Theorem and Webs. (1978) (74)
Complex-Analytic Properties of Certain Zariski Open Sets on Algebraic Varieties (1971) (69)
Two theorems on extensions of holomorphic mappings (1971) (59)
Topics in Transcendental Algebraic Geometry. (AM-106) (1984) (56)
Holomorphic curves and metrics of negative curvature (1976) (52)
The Gauss equations and rigidity of isometric embeddings (1983) (51)
Infinitesimal variations of hodge structure (II) : an infinitesimal invariant of hodge classes (1983) (50)
Néron models and limits of Abel–Jacobi mappings (2010) (49)
Complex differential and integral geometry and curvature integrals associated to singularities of complex analytic varieties (1978) (44)
A Theorem Concerning the Differential Equations Satisfied by Normal Functions Associated to Algebraic Cycles (1979) (43)
Characteristics and existence of isometric embeddings (1983) (42)
Holomorphic Mapping into Canonical Algebraic Varieties (1971) (42)
Differential Systems And Isometric Embeddings (1983) (41)
Hyperbolic exterior differential systems and their conservation laws, part II (1995) (39)
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (2005) (37)
The Extension Problem for Compact Submanifolds of Complex Manifolds I (1965) (36)
Mathematics at the Turn of the Millennium (2000) (35)
Hodge-theoretic invariants for algebraic cycles (2003) (34)
NÉRON MODELS AND BOUNDARY COMPONENTS FOR DEGENERATIONS OF HODGE STRUCTURE OF MIRROR QUINTIC TYPE (2008) (33)
On a theorem of Chern (1962) (30)
Some geometric and analytic properties of homogeneous complex manifolds (1963) (29)
An inequality for the rank of a web and webs of maximum rank (1978) (27)
Hodge Theory and Geometry (2004) (27)
The Legacy of Abel in Algebraic Geometry (2004) (26)
Holomorphic mappings: Survey of some results and discussion of open problems (1972) (26)
Algebraic Cycles and Motives: Algebraic Cycles and Singularities of Normal Functions (2007) (25)
An interesting 0-cycle (2003) (25)
Quotients of non-classical flag domains are not algebraic (2013) (24)
Some transcendental methods in the study of algebraic cycles (1971) (24)
Hodge Theory, Complex Geometry, and Representation Theory (2013) (22)
ALGEBRAIC CYCLES AND SINGULARITIES OF NORMAL FUNCTIONS, II (2006) (21)
Complete maps and differentiable coverings. (1963) (20)
Extremal degenerations of polarized Hodge structures (2014) (19)
Some Enumerative Global Properties of Variations of Hodge Structures (2009) (19)
Hyperbolic exterior differential systems and their conservation laws, part I (1995) (19)
Cycles over fields of transcendence degree 1 (2004) (18)
Mumford - Tate Domains (2010) (17)
Function theory of finite order on algebraic varieties. I(B) (1972) (16)
Complex Algebraic Varieties (2011) (16)
Some isometric embedding and rigidity results for Riemannian manifolds. (1981) (15)
On the Bezout Problem for Entire Analytic Sets (1974) (14)
Formal Deformation of Chow Groups (2004) (14)
Linear Differential Systems (1991) (13)
Positivity of vector bundles and Hodge theory (2018) (13)
Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results ? (2009) (13)
Inspired by S.S.Chern : a memorial volume in honor of a great mathematician (2006) (13)
Completion of Period Mappings and Ampleness of the Hodge bundle (2017) (13)
Differential Systems and Isometric Embeddings.(AM-114) (1987) (11)
The residue calculus and some transcendental results in algebraic geometry, I. (1966) (10)
ABEL'S DIFFERENTIAL EQUATIONS (2002) (9)
ON THE DIFFERENTIAL GEOMETRY OF HOMOGENEOUS VECTOR BUNDLES (1963) (9)
Deformations of G-structures (1964) (9)
Curvature properties of Hodge bundles (2018) (8)
An Introduction to the Theory of Special Divisors on Algebraic Curves (1980) (8)
The residue calculus and some transcendental results in algebraic geometry, ii. (1966) (8)
Period Mappings and Ampleness of the Hodge line bundle (2017) (8)
Cycles over fields of transcendence degree one (2002) (8)
Projectivity of the moduli space of stable curves (2011) (7)
Poincaré and algebraic geometry (1982) (6)
WHAT IS a Period Domain ? (2008) (6)
The moduli space of stable curves (2011) (6)
LOGARITHMIC HODGE STRUCTURES: (REPORT ON THE WORK OF KATO-USUI)∗ (2009) (5)
Variations of Hodge structures (2003) (5)
Some geometric and analytic properties of homogeneous complex manifolds (1963) (5)
Deformation Theory and Limiting Mixed Hodge Structures (2014) (5)
ON THE THEORY OF VARIATION OF STRUCTURES DEFINED BY TRANSITIVE, CONTINUOUS PSEUDOGROUPS (1964) (5)
Hodge Theory (MN-49) (2014) (4)
ON CERTAIN HOMOGENEOUS COMPLEX MANIFOLDS. (1962) (4)
The Hilbert Scheme (2011) (3)
Special Values of Automorphic Cohomology Classes (2014) (3)
A TRANSCENDENTAL METHOD IN ALGEBRAIC GEOMETRY (2010) (3)
Using Hodge theory to detect the structure of a compactified moduli space (2019) (3)
Hodge theory and moduli (2018) (3)
EXTERIOR DIFFERENTIAL SYSTEMS AND VARIATIONS OF HODGE STRUCTURES (2009) (2)
Enumerative Geometry of Curves (1985) (2)
Chapter XII. INFINITESIMAL VARIATION OF HODGE STRUCTURE AND THE GENERIC GLOBAL TORELLI THEOREM (1984) (2)
Shafarevich mappings and period mappings (2022) (2)
On the existence of a locally complete germ of deformation of certainG-structures (1965) (2)
The global asymptotic structure of period mappings (2020) (2)
Chapter XVII. INFINITESIMAL INVARIANT OF NORMAL FUNCTIONS (1984) (2)
Chapter II. CURVATURE PROPERTIES OF THE HODGE BUNDLES (1984) (2)
Completions of period mappings: progress report (2021) (2)
Chapter IV. ASYMPTOTIC BEHAVIOR OF A VARIATION OF HODGE STRUCTURE (1984) (2)
Deformations ofG-structures (1965) (1)
Chapter I. VARIATION OF HODGE STRUCTURE (1984) (1)
Some results on locally homogeneous complex manifolds. (1966) (1)
Applications of Commutative Algebra and Algebraic Geometry to the Study of Exterior Differential Systems (1991) (1)
Mathematics -- From Servant To Partner (1993) (1)
How Incompatible Worldviews Can Coexist (2014) (1)
Reshaping Graduate Education. (1995) (1)
The Basic Results of the Brill-Noether Theory (1985) (1)
Selected works of Phillip A. Griffiths with commentary (2003) (1)
MUMFORD-TATE GROUPS (2010) (1)
Line bundles on moduli (2011) (1)
A Theorem on Periods of Integrals of Algebraic Manifolds (1970) (1)
SOME REMARKS ON AUTOMORPHISMS, ANALYTIC BUNDLES, AND EMBEDDINGS OF COMPLEX ALGEBRAIC VARIETIES. (1963) (1)
Speculations on Hodge theory (2010) (0)
Chapter Ten. Speculations and Questions (2005) (0)
5. The isometric embedding system (1987) (0)
Donald C. Spencer (1912-2001), Volume 51, Number 1 (2003) (0)
HODGE DOMAINS AND AUTOMORPHIC COHOMOLOGY (2010) (0)
Chapter Eight. Tangents to Related Spaces (2005) (0)
The Characteristic Variety (1991) (0)
Completions of period mappings (2020) (0)
The Geometric Theory of Riemann’s Theta Function (1985) (0)
CW Homology Theorem (2013) (0)
Chapter III. INFINITESIMAL VARIATION OF HODGE STRUCTURE (1984) (0)
Some Reflections on the Mathematical Contributions of S. S. Chern (1996) (0)
Cartan-Kähler Theory (1991) (0)
Polarized Hodge structures and Mumford-Tate groups and domains (2013) (0)
Who Gave You the Epsilon?: Mathematics at the Turn of the Millennium (2009) (0)
Chapter III. The Mumford-Tate Group of a Variation of Hodge Structure (2012) (0)
A Classical Complex Analyst Encounters a Post-modern Mathematical Object (2001) (0)
Penrose transforms in the two main examples (2013) (0)
Chapter I. Mumford-Tate Groups (2012) (0)
Trends for Science and Mathematics in the 21st Century (2001) (0)
Intersection theory of tautological classes (2011) (0)
CHAPTER 2. THE APPEARANCE OF CURVATURE (1976) (0)
Chapter VII. Classification of Mumford-Tate Subdomains (2012) (0)
4. Quasi-linear Pfaffian differential system (1987) (0)
Homotopy Theory of DGAs (2013) (0)
CHAPTER 3. THE DEFECT RELATIONS (1976) (0)
Deformations of holomorphic mappings (1964) (0)
8. Embedding Cauchy-Riemann structures (1987) (0)
Moduli and Hodge Theory (2018) (0)
Chapter II. Period Domains and Mumford-Tate Domains (2012) (0)
Memorial for Robert Hermann (2021) (0)
From the Past to the Future through the Present: Conversations with Historians at the Institute for Advanced Study. Princeton, N.J: Institute for Advanced Study, 1992. (1992) (0)
Discrete series and -cohomology (2013) (0)
Miscellaneous topics and some questions (2013) (0)
New Geometric Invariants Arising from Hodge Theory (2018) (0)
Two Results in the Global Theory of Holomorphic Mappings (1974) (0)
Eilenberg–MacLane Spaces, Cohomology, and Principal Fibrations (2013) (0)
The Varieties of Special Linear Series on a Curve (1985) (0)
Linear Differential Operators (1991) (0)
First consequences of the cellular decomposition (2011) (0)
Brill–Noether theory on a moving curve (2011) (0)
Mathematics and the Sciences: is Interdisciplinarity Research possible? (2000) (0)
Chapter IV. Hodge Representations and Hodge Domains (2012) (0)
Chapter V. Hodge Structures With Complex Multiplication (2012) (0)
Smooth Galois covers of moduli spaces (2011) (0)
Research: A New Agenda. (1987) (0)
Geometry of flag domains: Part II (2013) (0)
Chapter Four. Absolute Differentials (I) (2005) (0)
Riemann Surfaces and Algebraic Curves (2011) (0)
Annals of Mathematics Residues and Zero-Cycles on Algebraic Varieties (2010) (0)
The Teichmüller point of view (2011) (0)
Book Review: Multidimensional residues and their applications (1994) (0)
The Whitehead Theorem and the Hurewicz Theorem (2013) (0)
Chapter Nine. Applications and Examples (2005) (0)
Topics in Algebraic and Analytic Geometry. (MN-13): Notes From a Course of Phillip Griffiths (1974) (0)
Chapter VIII. Arithmetic of Period Maps of Geometric Origin (2012) (0)
Period Mapping at Infinity (2020) (0)
HODGE THEORY AND REPRESENTATION THEORY ( APPLICATION OF SOME WORK OF CARAYOL ) (2010) (0)
INDEX OF NOTATIONS (1976) (0)
Chapter Two. The Classical Case When n = 1 (2005) (0)
The Quadric Line Complex (2011) (0)
CHAPTER 1. ORDERS OF GROWTH (1976) (0)
Chapter Five Geometric Description of T̳Zn(X) (2005) (0)
DGAs and Rational Homotopy Theory (2013) (0)
Masatake Kuranishi (1924–2021) (2022) (0)
Examples and Computations (2013) (0)
Poincar and algebraic geometry (1982) (0)
Introduction to Special Divisors (1985) (0)
Commonly used notation (1987) (0)
3. Pfaffian differential systems (1987) (0)
Global properties of period mappings on the boundary (2020) (0)
The classical theory: Part II (2013) (0)
Losing Faculties (2008) (0)
Differential of a period mapping at a singularity (2022) (0)
Chapter Six. Absolute Differentials (II) (2005) (0)
Differential Graded Algebras (2020) (0)
Spectral Sequence of a Fibration (2013) (0)
Euler-Lagrange Equations for Differential Systems with One Independent Variable (1983) (0)
Quillen’s Work on Rational Homotopy Theory (2013) (0)
The Existence and Connectedness Theorems for W d r ( C ) (1985) (0)
TWAS nl (2010) (0)
7. Isometric embeddings of space forms (1987) (0)
Natural line bundles on completions of period mappings (2021) (0)
Chapter VI. Arithmetic Aspects of Mumford-Tate Domains (2012) (0)
Principles of algebraic geometry / Philip Griffiths and Joseph Harris (1978) (0)
Postnikov Towers and Rational Homotopy Theory (2013) (0)
Comparisons between the Hodge-theoretic and algebro-geometric approaches to limiting mixed Hodge structures (2019) (0)
The Fundamental Group (2013) (0)
First Integrals of the Euler-Lagrange System; Noether’s Theorem and Examples (1983) (0)
Euler Equations for Variational Problems in Homogeneous Spaces (1983) (0)
Deformations of G-Structures Part B : Deformations of Geometric G-Structures (2005) (0)
Hodge representations and Hodge domains (2013) (0)
2. Structure equations of Xn ⊂ EN (1987) (0)
Cellular decomposition of moduli spaces (2011) (0)
Review: Shoshichi Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings (1972) (0)
Endpoint Conditions; Jacobi Equations and the 2nd Variation; the Hamilton-Jacobi Equation (1983) (0)
Elementary deformation theory and some applications (2011) (0)
Chapter Seven. The Ext-definition of TZ2(X) for X an Algebraic Surface (2005) (0)
Cycles in the moduli spaces of stable curves (2011) (0)
deRham’s Theorem for Simplicial Complexes (2013) (0)
Chapter Three. Differential Geometry of Symmetric Products (2005) (0)
The Hirsch Lemma (2013) (0)

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