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Mumford, David Bryant

Author ID: mumford.david-b Recent zbMATH articles by "Mumford, David Bryant"
Published as: Mumford, David; Mumford, D.; Mumford, David B.
Homepage: http://www.dam.brown.edu/people/mumford/
External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef · theses.fr
Awards: Fields Medal (1974) · Shaw Prize (2006) · Wolf Prize (2008)
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Co-Authors

69 single-authored
9 Michor, Peter Wolfram
6 Nori, Madhav V.
4 Artin, Michael
4 Gleason, Andrew Mattei
4 Hughes-Hallett, Deborah
4 McCallum, William G.
4 Musili, C.
4 Osgood, Brad G.
4 Previato, Emma
4 Quinney, Douglas
4 Ramanujam, Chidambaram Padmanabhan
4 Stillman, Michael Eugene
4 Tecosky-Feldman, Jeff
4 Tucker, Thomas W.
3 Deligne, Pierre
3 Flath, Daniel Evans
3 Gordon, Sheldon P.
3 Kempf, George R.
3 Shiota, Takahiro
3 Tate, John Torrence jun.
3 Thrash, Joe B.
3 Zariski, Oscar
2 Ash, Avner
2 Barnsley, Michael Fielding
2 Bombieri, Enrico
2 Chai, Chingli
2 Chung, Fan
2 Falconer, Kenneth J.
2 Fogarty, John C.
2 Frame, Michael Lee
2 Jackson, Allyn
2 Knudsen, Finn Faye
2 Lee, Ann B.
2 Lock, Patti Frazer
2 Manin, Yuriĭ Ivanovich
2 Micheli, Mario
2 Neeman, Amnon
2 Nguyen Minh Chuong
2 Norman, Peter
2 Rapoport, Michael
2 Raskind, Wayne
2 Scott, Dana Stewart
2 Series, Caroline
2 Shah, Jayant
2 Stewart, Ian Nicholas
2 Tai, Yungsheng
2 Umemura, Hiroshi
2 Wright, David James
1 Abhyankar, Shreeram Shankar
1 Abhyankar, Yvonne
1 Adams, Malcolm R.
1 Arbarello, Enrico
1 Atiyah, Michael Francis
1 Bajai, Chanderjit
1 Balaji, Vikraman
1 Barrallo, Javier
1 Bass, Hyman
1 Bayer, David Allen
1 Bergman, George M.
1 Brothers, Harlan J.
1 Bruveris, Martins
1 Carrell, James B.
1 Cartier, Pierre
1 Chiossi, Simon G.
1 Ciarlet, Philippe Gaston
1 Cohen, Nathan
1 Coppens, Marc-Olivier
1 Cutkosky, Steven Dale
1 Davis, Philip J.
1 Demazure, Michel
1 Desolneux, Agnès
1 Dieudonné, Jean
1 Donagi, Ron Y.
1 Eglash, Ron
1 Egorov, Yuriĭ Vladimirovich
1 Furstenberg, Hillel
1 Giblin, Peter J.
1 Gidas, Basilis
1 Gieseker, David
1 Glazebrook, James F.
1 Gordon, Gaile G.
1 Greenberg, Marvin Jay
1 Gurdian, Rodolfo
1 Haboush, William J.
1 Hallinan, Peter W.
1 Harbater, Dale
1 Harris, Joseph Daniel
1 Hartshorne, Robin
1 Heinzer, William J.
1 Helgason, Sigurdur
1 Hironaka, Heisuke
1 Horrocks, Geoffrey
1 Howe, Roger Evans
1 Huang, Jinggang
1 Illusie, Luc
1 Jaffard, Stéphane
1 Jaffe, Arthur Michael
1 Jeffrey, Lisa Claire
1 Kalayciôglu, Selin
1 Katz, Nicholas Michael
...and 58 more Co-Authors
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Serials

14 Notices of the American Mathematical Society
9 American Journal of Mathematics
5 Inventiones Mathematicae
4 Ergebnisse der Mathematik und ihrer Grenzgebiete
4 Modern Birkhäuser Classics
3 International Journal of Computer Vision
3 Lecture Notes in Mathematics
3 Progress in Mathematics
2 Compositio Mathematica
2 Publications Mathématiques
2 Quarterly of Applied Mathematics
2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
2 Grundlehren der Mathematischen Wissenschaften
2 Mathematicians of Our Time
2 Tata Institute of Fundamental Research. Studies in Mathematics
2 Texts and Readings in Mathematics
1 Communications on Pure and Applied Mathematics
1 Journal d’Analyse Mathématique
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV)
1 Uspekhi Matematicheskikh Nauk [N. S.]
1 Acta Mathematica
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Journal of Combinatorial Theory. Series B
1 Journal of Mathematics of Kyoto University
1 Mathematische Annalen
1 Mathematica Scandinavica
1 Proceedings of the American Mathematical Society
1 Proceedings of the London Mathematical Society. Third Series
1 Topology
1 Annals of Global Analysis and Geometry
1 Sūgaku
1 L’Enseignement Mathématique. 2e Série
1 Nova Acta Leopoldina. Neue Folge
1 Applied and Computational Harmonic Analysis
1 Izvestiya: Mathematics
1 Documenta Mathematica
1 European Mathematical Society Newsletter
1 Journal of the European Mathematical Society (JEMS)
1 Bulletin of the American Mathematical Society
1 Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino
1 Annals of Mathematics Studies
1 Lecture Notes in Computer Science
1 Monographies de l’Enseignement Mathématique
1 Science
1 SIAM Journal on Imaging Sciences
1 Foundations and Trends in Computer Graphics and Vision
1 Journal of Geometric Mechanics
1 Forum of Mathematics, Sigma
1 Classics in Mathematics
1 Springer Collected Works in Mathematics
1 Cambridge Mathematical Library
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Fields

78 Algebraic geometry (14-XX)
25 History and biography (01-XX)
19 General and overarching topics; collections (00-XX)
17 Computer science (68-XX)
12 Global analysis, analysis on manifolds (58-XX)
8 Partial differential equations (35-XX)
8 Statistics (62-XX)
7 Group theory and generalizations (20-XX)
7 Several complex variables and analytic spaces (32-XX)
6 Number theory (11-XX)
6 Differential geometry (53-XX)
6 Probability theory and stochastic processes (60-XX)
5 Commutative algebra (13-XX)
5 Real functions (26-XX)
5 Dynamical systems and ergodic theory (37-XX)
4 Functions of a complex variable (30-XX)
3 Topological groups, Lie groups (22-XX)
3 Information and communication theory, circuits (94-XX)
2 Combinatorics (05-XX)
2 Measure and integration (28-XX)
2 Special functions (33-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Operator theory (47-XX)
2 Convex and discrete geometry (52-XX)
2 Manifolds and cell complexes (57-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 Biology and other natural sciences (92-XX)
2 Mathematics education (97-XX)
1 Mathematical logic and foundations (03-XX)
1 Field theory and polynomials (12-XX)
1 Associative rings and algebras (16-XX)
1 Category theory; homological algebra (18-XX)
1 Difference and functional equations (39-XX)
1 Abstract harmonic analysis (43-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Geometry (51-XX)
1 General topology (54-XX)
1 Quantum theory (81-XX)
1 Relativity and gravitational theory (83-XX)
1 Astronomy and astrophysics (85-XX)

Publications by Year

Citations contained in zbMATH Open

123 Publications have been cited 11,447 times in 9,175 Documents Cited by Year
Geometric invariant theory. 3rd enl. ed. Zbl 0797.14004
Mumford, D.; Fogarty, J.; Kirwan, F.
849
1994
Optimal approximations by piecewise smooth functions and associated variational problems. Zbl 0691.49036
Mumford, David; Shah, Jayant
740
1989
The irreducibility of the space of curves of a given genus. Zbl 0181.48803
Deligne, Pierre; Mumford, D.
592
1969
Abelian varieties. Zbl 0223.14022
Mumford, David
585
1970
Toroidal embeddings. I. Zbl 0271.14017
Kempf, G.; Knudsen, F.; Mumford, D.; Saint-Donat, Bernard
511
1973
Lectures on curves on an algebraic surface. Zbl 0187.42701
Mumford, D.
471
1966
Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman. Zbl 0509.14049
Mumford, David
403
1983
Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura. Zbl 0549.14014
Mumford, David
375
1984
Geometric invariant theory. Zbl 0147.39304
Mumford, D.
366
1965
The topology of normal singularities of an algebraic surface and a criterion for simplicity. Zbl 0108.16801
Mumford, D.
302
1961
Geometric invariant theory. 2nd enlarged ed. Zbl 0504.14008
Mumford, D.; Fogarty, J.
269
1982
The projectivity of the moduli space of stable curves. I: Preliminaries on ”det” and ”Div”. Zbl 0343.14008
Knudsen, Finn; Mumford, David
241
1976
Towards an enumerative geometry of the moduli space of curves. Zbl 0554.14008
Mumford, David
238
1983
Algebraic geometry. I: Complex projective varieties. Zbl 0356.14002
Mumford, David
234
1976
On the Kodaira dimension of the moduli space of curves. Zbl 0506.14016
Harris, Joe; Mumford, David
228
1982
Varieties defined by quadratic equations (with an appendix by George Kempf). Zbl 0198.25801
Mumford, David
215
1970
Smooth compactification of locally symmetric varieties. Zbl 0334.14007
Ash, A.; Mumford, D.; Rapoport, M.; Tai, Y.
192
1975
On the equations defining Abelian varieties. I-III. Zbl 0219.14024
Mumford, D.
189
1966
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. 2nd ed. Zbl 0326.14012
Mumford, David
181
1974
Stability of projective varieties. Zbl 0363.14003
Mumford, David
168
1977
Some elementary examples of unirational varieties which are not rational. Zbl 0244.14017
Artin, M.; Mumford, D.
154
1972
Tata lectures on theta. III. Zbl 0744.14033
Mumford, David; Nori, Madhav; Norman, Peter
153
1991
Prym varieties. I. Zbl 0299.14018
Mumford, David
141
1974
The red book of varieties and schemes. Includes the Michigan lectures (1974) on “Curves and their Jacobians”. 2nd, expanded ed. with contributions by Enrico Arbarello. Zbl 0945.14001
Mumford, David
139
1999
Theta characteristics of an algebraic curve. Zbl 0216.05904
Mumford, David
137
1971
What can be computed in algebraic geometry? Zbl 0846.13017
Bayer, Dave; Mumford, David
130
1993
Hirzebruch’s proportionality theorem in the non-compact case. Zbl 0365.14012
Mumford, D.
126
1977
The red book of varieties and schemes. Zbl 0658.14001
Mumford, David
123
1988
Rational equivalence of O-cycles on surfaces. Zbl 0184.46603
Mumford, D.
119
1969
Riemannian geometries on spaces of plane curves. Zbl 1101.58005
Michor, Peter W.; Mumford, David
117
2006
Families of abelian varieties. Zbl 0199.24601
Mumford, D.
103
1966
Curves and their Jacobians. Zbl 0316.14010
Mumford, David
100
1975
Enriques’ classification of surfaces in char p. III. Zbl 0336.14010
Bombieri, E.; Mumford, D.
96
1976
An analytic construction of degenerating curves over complete local rings. Zbl 0228.14011
Mumford, David
95
1972
Further pathologies in algebraic geometry. Zbl 0114.13106
Mumford, D.
93
1962
Elastica and computer vision. Zbl 0798.53003
Mumford, David
92
1994
The spectrum of difference operators and algebraic curves. Zbl 0502.58032
van Moerbeke, Pierre; Mumford, David
92
1979
An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Zbl 1116.58007
Michor, Peter W.; Mumford, David
90
2007
A stratification of the null cone via the moment map. (With an appendix by David Mumford). Zbl 0604.14006
Ness, Linda
89
1984
An analytic construction of degenerating Abelian varieties over complete rings. Zbl 0241.14020
Mumford, David
88
1972
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. Corrected reprint of the 2nd ed. 1974. Zbl 1177.14001
Mumford, David
86
2008
Algebraic surfaces. With appendices by S.S. Abhyankar, J. Lipman, and D. Mumford. 2nd suplemented ed. Zbl 0219.14020
Zariski, O.
84
1971
Algebraic Geometry. I: Complex projective varieties. Reprint of the corr. 2nd print. 1976. Zbl 0821.14001
Mumford, David
80
1995
A rank 2 vector bundle on P\(^4\) with 15,000 symmetries. Zbl 0255.14017
Horrocks, G.; Mumford, D.
75
1973
A remark on Mahler’s compactness theorem. Zbl 0215.23202
Mumford, D.
74
1971
A metric on shape space with explicit geodesics. Zbl 1142.58013
Younes, Laurent; Michor, Peter W.; Shah, Jayant; Mumford, David
73
2008
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Zbl 1083.58010
Michor, Peter W.; Mumford, David
72
2005
An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg de Vries equation and related non- linear equations. Zbl 0423.14007
Mumford, D.
70
1977
A note of Shimura’s paper: Discontinuous groups and Abelian varieties. Zbl 0169.23301
Mumford, D.
69
1969
Enriques’ classification of surfaces in char. \(p\). II. Zbl 0348.14021
Bombieri, E.; Mumford, D.
68
1977
Two fundamental theorems on deformations of polarized varieties. Zbl 0128.15505
Matsusaka, T.; Mumford, D.
67
1964
Smooth compactifications of locally symmetric varieties. With the collaboration of Peter Scholze. 2nd ed. Zbl 1209.14001
Ash, Avner; Mumford, David; Rapoport, Michael; Tai, Yung-Sheng
65
2010
Indra’s pearls. The vision of Felix Klein. With cartoons by Larry Gonick. Zbl 1141.00002
Mumford, David; Series, Caroline; Wright, David
61
2002
2D-shape analysis using conformal mapping. Zbl 1477.68492
Sharon, E.; Mumford, D.
59
2006
An algebraic surface with K ample, \((K^ 2)=9\), \(p_ g=q=O\). Zbl 0433.14021
Mumford, D.
57
1979
Filtering, segmentation and depth. Zbl 0801.68171
Nitzberg, Mark; Mumford, David; Shiota, Takahiro
53
1993
Pathologies. III. Zbl 0146.42403
Mumford, D.
48
1967
Abelian quotients of the Teichmüller modular group. Zbl 0173.22903
Mumford, D.
42
1967
Periods of a moduli space of bundles on curves. Zbl 0174.52902
Mumford, D.; Newstead, P.
39
1968
On the Kodaira dimension of the Siegel modular variety. Zbl 0527.14036
Mumford, David
33
1983
The nonlinear statistics of high-contrast patches in natural images. Zbl 1070.68661
Lee, Ann B.; Pedersen, Kim S.; Mumford, David
31
2003
Projective invariants of projective structures and applications. Zbl 0154.20702
Mumford, D.
31
1963
Introduction to the theory of moduli. Zbl 0242.14004
Mumford, David; Suominen, Kalevi
30
1972
Picard groups of moduli problems. Zbl 0187.42801
Mumford, D.
28
1965
Stochastic models for generic images. Zbl 1159.68598
Mumford, David; Gidas, Basilis
26
2001
Enriques’ classification of surfaces in char p. I. Zbl 0188.53201
Mumford, D.
25
1969
Bi-extensions of formal groups. Zbl 0216.33101
Mumford, D.
25
1969
Geodesic completeness for Sobolev metrics on the space of immersed plane curves. Zbl 1315.58009
Bruveris, Martins; Michor, Peter W.; Mumford, David
25
2014
Harmonic, wavelet and \(p\)-adic analysis. Based on the summer school, Quy Nhon, Vietnam, June 10–15, 2005. Zbl 1117.42001
24
2007
On Euler’s equation and ‘EPDiff’. Zbl 1274.35277
Mumford, David; Michor, Peter W.
23
2013
Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura. Reprint of the 1984 edition. Zbl 1112.14003
Mumford, David
23
2007
A remark on Mordell’s conjecture. Zbl 0151.27301
Mumford, D.
21
1965
Pattern theory. The stochastic analysis of real-world signals. Zbl 1210.94002
Mumford, David; Desolneux, Agnès
19
2010
A zoo of diffeomorphism groups on \(\mathbb R^n\). Zbl 1364.22009
Michor, Peter W.; Mumford, David
19
2013
A stochastic grammar of images. Zbl 1198.68160
Zhu, Song-Chun; Mumford, David
18
2006
Pattern theory: The mathematics of perception. Zbl 1057.91072
Mumford, David
17
2002
Tata lectures on theta. I. With the collaboration of C. Musili, M. Nori, E. Previato, and M. Stillman. Reprint of the 1983 edition. Zbl 1112.14002
Mumford, David
17
2007
Deformations and liftings of finite, commutative group schemes. Zbl 0179.49901
Oort, F.; Mumford, D.
17
1968
Stability of projective varieties. Zbl 0497.14004
Mumford, David
16
1977
Indra’s pearls. The vision of Felix Klein. With cartoons by Larry Gonick. Reprint of the 2002 hardback edition. Zbl 1314.00007
Mumford, David; Series, Caroline; Wright, David
16
2015
Pathologies of modular algebraic surfaces. Zbl 0138.42002
Mumford, David
16
1961
Two- and three-dimensional patterns of the face. Zbl 0930.68140
Hallinan, Peter W.; Gordon, Gaile G.; Yuille, A. L.; Giblin, Peter; Mumford, David
15
1999
Lectures on curves on an algebraic surface. With a section by G. M. Bergman. Zbl 1079.14002
Mumford, David
15
2005
Chordal completions of planar graphs. Zbl 0809.05038
Chung, F. R. K.; Mumford, David
15
1994
Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds. Zbl 1280.58005
Micheli, M.; Michor, P. W.; Mumford, D.
14
2013
The dawning of the age of stochasticity. Zbl 0962.60003
Mumford, David
13
2000
Sectional curvature in terms of the cometric, with applications to the Riemannian manifolds of landmarks. Zbl 1276.37047
Micheli, Mario; Michor, Peter W.; Mumford, David
13
2012
Some footnotes to the work of C. P. Ramanujam. Zbl 0444.14002
Mumford, D.
13
1978
Tata lectures on theta III. In collaboration with Madhav Nori and Peter Norman. Reprint of the 1991 edition. Zbl 1124.14043
Mumford, David
13
2007
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. 2nd ed. Reprint. Zbl 0583.14015
Mumford, David
13
1985
The structure of the moduli spaces of curves and abelian varieties. Zbl 0222.14023
Mumford, David
12
1971
The self-intersection formula and the ’formule-clef’. Zbl 0341.14002
Lascu, A. T.; Mumford, D.; Scott, D. B.
11
1975
Introduction to commutative algebra and algebraic geometry. Transl. from the German by Michael Ackerman. With a preface by David Mumford. Reprint of the 1985 edition. Zbl 1263.13001
Kunz, Ernst
11
2013
Algebraic geometry II. Zbl 1325.14001
Mumford, David; Oda, Tadao
10
2015
Lectures on curves on a algebraic surface. Zbl 0187.42702
Mumford, D.
9
1968
A remark on the paper of M. Schlessinger. Zbl 0279.32007
Mumford, David
8
1973
Hilbert’s fourteenth problem - the finite generation of subrings such as rings of invariants. Zbl 0341.14019
Mumford, David
8
1976
Occlusion models for natural images: A statistical study of a scale-invariant dead leaves model. Zbl 1012.68715
Lee, Ann B.; Mumford, David; Huang, Jinggang
8
2001
Pathologies. IV. Zbl 0315.14012
Mumford, David
7
1975
Advances in deterministic and stochastic analysis. Proceedings of the 2nd international conference on abstract and applied analysis, Quy Nhon, Vietnam, June 4–9. 2005. Zbl 1115.35008
7
2007
Alexandre Grothendieck 1928–2014. I. Zbl 1338.01022
Atiyah, Michael; Bass, Hyman; Cartier, Pierre; Deligne, Pierre; Demazure, Michel; Greenberg, Marvin Jay; Hartshorne, Robin; Illusie, Luc; Katz, Nicholas; Kleiman, Steven L.
1
2016
Alexandre Grothendieck 1928–2014, part 2. Zbl 1338.01023
Ladegaillerie, Yves; Lichtenbaum, Stephen; Lochak, Pierre; Mazur, Barry; Messing, William; Murre, Jacob; Schneps, Leila
1
2016
Indra’s pearls. The vision of Felix Klein. With cartoons by Larry Gonick. Reprint of the 2002 hardback edition. Zbl 1314.00007
Mumford, David; Series, Caroline; Wright, David
16
2015
Algebraic geometry II. Zbl 1325.14001
Mumford, David; Oda, Tadao
10
2015
Geodesic completeness for Sobolev metrics on the space of immersed plane curves. Zbl 1315.58009
Bruveris, Martins; Michor, Peter W.; Mumford, David
25
2014
Shreeram Abhyankar (July 22, 1930 – November 2, 2012). Zbl 1338.13001
Abhyankar, Yvonne; Bajai, Chanderjit; Cutkosky, Steven Dale; Harbater, Dale; Heinzer, William; Shannon, David; Mulay, Shashikant; Mumford, David; Thakur, Dinesh
1
2014
On Euler’s equation and ‘EPDiff’. Zbl 1274.35277
Mumford, David; Michor, Peter W.
23
2013
A zoo of diffeomorphism groups on \(\mathbb R^n\). Zbl 1364.22009
Michor, Peter W.; Mumford, David
19
2013
Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds. Zbl 1280.58005
Micheli, M.; Michor, P. W.; Mumford, D.
14
2013
Introduction to commutative algebra and algebraic geometry. Transl. from the German by Michael Ackerman. With a preface by David Mumford. Reprint of the 1985 edition. Zbl 1263.13001
Kunz, Ernst
11
2013
Sectional curvature in terms of the cometric, with applications to the Riemannian manifolds of landmarks. Zbl 1276.37047
Micheli, Mario; Michor, Peter W.; Mumford, David
13
2012
Glimpses of Benoît B. Mandelbrot (1924–2010). Zbl 1284.01047
Stewart, Ian; Mumford, David; Falconer, Kenneth; Eglash, Ron; Brothers, Harlan; Lesmoir-Gordon, Nigel; Barrallo, Javier; Berry, Michael; Frame, Michael
1
2012
The influence of Benoît B. Mandelbrot on mathematics. Zbl 1284.01048
Stewart, Ian; Mumford, David; Howe, Roger; Furstenberg, Hillel; Falconer, Kenneth; West, Bruce J.; Coppens, Marc-Olivier; Cohen, Nathan; Jaffard, Stéphane; Berry, Michael; Frame, Michael
1
2012
Intuition and rigor and Enriques’s quest. Zbl 1268.14003
Mumford, David
6
2011
Smooth compactifications of locally symmetric varieties. With the collaboration of Peter Scholze. 2nd ed. Zbl 1209.14001
Ash, Avner; Mumford, David; Rapoport, Michael; Tai, Yung-Sheng
65
2010
Pattern theory. The stochastic analysis of real-world signals. Zbl 1210.94002
Mumford, David; Desolneux, Agnès
19
2010
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. Corrected reprint of the 2nd ed. 1974. Zbl 1177.14001
Mumford, David
86
2008
A metric on shape space with explicit geodesics. Zbl 1142.58013
Younes, Laurent; Michor, Peter W.; Shah, Jayant; Mumford, David
73
2008
An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Zbl 1116.58007
Michor, Peter W.; Mumford, David
90
2007
Harmonic, wavelet and \(p\)-adic analysis. Based on the summer school, Quy Nhon, Vietnam, June 10–15, 2005. Zbl 1117.42001
24
2007
Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura. Reprint of the 1984 edition. Zbl 1112.14003
Mumford, David
23
2007
Tata lectures on theta. I. With the collaboration of C. Musili, M. Nori, E. Previato, and M. Stillman. Reprint of the 1983 edition. Zbl 1112.14002
Mumford, David
17
2007
Tata lectures on theta III. In collaboration with Madhav Nori and Peter Norman. Reprint of the 1991 edition. Zbl 1124.14043
Mumford, David
13
2007
Advances in deterministic and stochastic analysis. Proceedings of the 2nd international conference on abstract and applied analysis, Quy Nhon, Vietnam, June 4–9. 2005. Zbl 1115.35008
7
2007
Riemannian geometries on spaces of plane curves. Zbl 1101.58005
Michor, Peter W.; Mumford, David
117
2006
2D-shape analysis using conformal mapping. Zbl 1477.68492
Sharon, E.; Mumford, D.
59
2006
A stochastic grammar of images. Zbl 1198.68160
Zhu, Song-Chun; Mumford, David
18
2006
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Zbl 1083.58010
Michor, Peter W.; Mumford, David
72
2005
Lectures on curves on an algebraic surface. With a section by G. M. Bergman. Zbl 1079.14002
Mumford, David
15
2005
The nonlinear statistics of high-contrast patches in natural images. Zbl 1070.68661
Lee, Ann B.; Pedersen, Kim S.; Mumford, David
31
2003
Indra’s pearls. The vision of Felix Klein. With cartoons by Larry Gonick. Zbl 1141.00002
Mumford, David; Series, Caroline; Wright, David
61
2002
Pattern theory: The mathematics of perception. Zbl 1057.91072
Mumford, David
17
2002
Stochastic models for generic images. Zbl 1159.68598
Mumford, David; Gidas, Basilis
26
2001
Occlusion models for natural images: A statistical study of a scale-invariant dead leaves model. Zbl 1012.68715
Lee, Ann B.; Mumford, David; Huang, Jinggang
8
2001
The dawning of the age of stochasticity. Zbl 0962.60003
Mumford, David
13
2000
The dawning of the age of stochasticity. Zbl 1149.00309
Mumford, David
2
2000
The red book of varieties and schemes. Includes the Michigan lectures (1974) on “Curves and their Jacobians”. 2nd, expanded ed. with contributions by Enrico Arbarello. Zbl 0945.14001
Mumford, David
139
1999
Two- and three-dimensional patterns of the face. Zbl 0930.68140
Hallinan, Peter W.; Gordon, Gaile G.; Yuille, A. L.; Giblin, Peter; Mumford, David
15
1999
Calculus. Single and multivariable. 2nd ed. Zbl 0913.26003
Hughes-Hallett, Deborah; Gleason, Andrew M.; McCallum, William G.; Flath, Daniel E.; Lock, Patti Frazer; Gordon, Sheldon P.; Lomen, David O.; Lovelock, David; Mumford, David; Osgood, Brad G.; Pasquale, Andrew; Quinney, Douglas; Tecosky-Feldman, Jeff; Thrash, Joe B.; Thrash, Karen R.; Tucker, Thomas W.
1
1998
Trends in the profession of mathematics. Zbl 1288.00054
Mumford, David
1
1998
Multivariable calculus. Zbl 0892.26002
McCallum, William G.; Hughes-Hallett, Deborah; Gleason, Andrew M.; Flath, Daniel; Gordon, Sheldon P.; Mumford, David; Osgood, Brad G.; Quinney, Douglas; Raskind, Wayne; Tecosky-Feldman, Jeff; Thrash, Joe B.; Tucker, Thomas W.
1
1997
Algebraic Geometry. I: Complex projective varieties. Reprint of the corr. 2nd print. 1976. Zbl 0821.14001
Mumford, David
80
1995
Geometric invariant theory. 3rd enl. ed. Zbl 0797.14004
Mumford, D.; Fogarty, J.; Kirwan, F.
849
1994
Elastica and computer vision. Zbl 0798.53003
Mumford, David
92
1994
Chordal completions of planar graphs. Zbl 0809.05038
Chung, F. R. K.; Mumford, David
15
1994
Pattern theory: A unifying perspective. Zbl 0939.68820
Mumford, David
5
1994
What can be computed in algebraic geometry? Zbl 0846.13017
Bayer, Dave; Mumford, David
130
1993
Filtering, segmentation and depth. Zbl 0801.68171
Nitzberg, Mark; Mumford, David; Shiota, Takahiro
53
1993
Tata lectures on theta. III. Zbl 0744.14033
Mumford, David; Nori, Madhav; Norman, Peter
153
1991
Optimal approximations by piecewise smooth functions and associated variational problems. Zbl 0691.49036
Mumford, David; Shah, Jayant
740
1989
The red book of varieties and schemes. Zbl 0658.14001
Mumford, David
123
1988
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. 2nd ed. Reprint. Zbl 0583.14015
Mumford, David
13
1985
Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura. Zbl 0549.14014
Mumford, David
375
1984
A stratification of the null cone via the moment map. (With an appendix by David Mumford). Zbl 0604.14006
Ness, Linda
89
1984
Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman. Zbl 0509.14049
Mumford, David
403
1983
Towards an enumerative geometry of the moduli space of curves. Zbl 0554.14008
Mumford, David
238
1983
On the Kodaira dimension of the Siegel modular variety. Zbl 0527.14036
Mumford, David
33
1983
Geometric invariant theory. 2nd enlarged ed. Zbl 0504.14008
Mumford, D.; Fogarty, J.
269
1982
On the Kodaira dimension of the moduli space of curves. Zbl 0506.14016
Harris, Joe; Mumford, David
228
1982
Algebraic geometry. I: Complex projective varieties. Corr. 2nd printing. Zbl 0456.14001
Mumford, David
1
1980
The spectrum of difference operators and algebraic curves. Zbl 0502.58032
van Moerbeke, Pierre; Mumford, David
92
1979
An algebraic surface with K ample, \((K^ 2)=9\), \(p_ g=q=O\). Zbl 0433.14021
Mumford, D.
57
1979
Some footnotes to the work of C. P. Ramanujam. Zbl 0444.14002
Mumford, D.
13
1978
Fields Medals. IV: An instinct for the key idea. Zbl 1225.01080
Mumford, David; Tate, John
1
1978
Stability of projective varieties. Zbl 0363.14003
Mumford, David
168
1977
Hirzebruch’s proportionality theorem in the non-compact case. Zbl 0365.14012
Mumford, D.
126
1977
An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg de Vries equation and related non- linear equations. Zbl 0423.14007
Mumford, D.
70
1977
Enriques’ classification of surfaces in char. \(p\). II. Zbl 0348.14021
Bombieri, E.; Mumford, D.
68
1977
Stability of projective varieties. Zbl 0497.14004
Mumford, David
16
1977
Stability of projective varieties. Zbl 0376.14007
Mumford, David
4
1977
The projectivity of the moduli space of stable curves. I: Preliminaries on ”det” and ”Div”. Zbl 0343.14008
Knudsen, Finn; Mumford, David
241
1976
Algebraic geometry. I: Complex projective varieties. Zbl 0356.14002
Mumford, David
234
1976
Enriques’ classification of surfaces in char p. III. Zbl 0336.14010
Bombieri, E.; Mumford, D.
96
1976
Hilbert’s fourteenth problem - the finite generation of subrings such as rings of invariants. Zbl 0341.14019
Mumford, David
8
1976
Smooth compactification of locally symmetric varieties. Zbl 0334.14007
Ash, A.; Mumford, D.; Rapoport, M.; Tai, Y.
192
1975
Curves and their Jacobians. Zbl 0316.14010
Mumford, David
100
1975
The self-intersection formula and the ’formule-clef’. Zbl 0341.14002
Lascu, A. T.; Mumford, D.; Scott, D. B.
11
1975
Pathologies. IV. Zbl 0315.14012
Mumford, David
7
1975
Matsusaka’s big theorem. Zbl 0321.14004
Liebermann, D.; Mumford, D.
7
1975
A new approach to compactifying locally symmetric varieties. Zbl 0322.32016
Mumford, David
3
1975
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. 2nd ed. Zbl 0326.14012
Mumford, David
181
1974
Prym varieties. I. Zbl 0299.14018
Mumford, David
141
1974
Geometrische Invariantentheorie. (Geometriceskaja teorija invariantov.) Übersetzung aus dem Englischen von A. N. Parsin. Zbl 0284.14002
Dieudonné, Jean A.; Carrell, James B.; Mumford, David
1
1974
Toroidal embeddings. I. Zbl 0271.14017
Kempf, G.; Knudsen, F.; Mumford, D.; Saint-Donat, Bernard
511
1973
A rank 2 vector bundle on P\(^4\) with 15,000 symmetries. Zbl 0255.14017
Horrocks, G.; Mumford, D.
75
1973
A remark on the paper of M. Schlessinger. Zbl 0279.32007
Mumford, David
8
1973
Collected papers. Volume II: Holomorphic functions and linear systems. Ed. by M. Artin and D. Mumford. Zbl 0564.14001
Zariski, Oscar
4
1973
Some elementary examples of unirational varieties which are not rational. Zbl 0244.14017
Artin, M.; Mumford, D.
154
1972
An analytic construction of degenerating curves over complete local rings. Zbl 0228.14011
Mumford, David
95
1972
An analytic construction of degenerating Abelian varieties over complete rings. Zbl 0241.14020
Mumford, David
88
1972
Introduction to the theory of moduli. Zbl 0242.14004
Mumford, David; Suominen, Kalevi
30
1972
The irreducibility of the space of curves of a given genus. Zbl 0233.14008
Deligne, Pierre; Mumford, D.
3
1972
Collected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities. Edited by H. Hironaka and D. Mumford. Zbl 0234.14001
Zariski, Oscar
3
1972
An analytic construction of degenerating curves over complete local rings. Zbl 0243.14010
Mumford, David
3
1972
Rational equivalence of 0-cycles on surfaces. Zbl 0228.14005
Mumford, D.
2
1972
Theta characteristics of an algebraic curve. Zbl 0216.05904
Mumford, David
137
1971
Algebraic surfaces. With appendices by S.S. Abhyankar, J. Lipman, and D. Mumford. 2nd suplemented ed. Zbl 0219.14020
Zariski, O.
84
1971
A remark on Mahler’s compactness theorem. Zbl 0215.23202
Mumford, D.
74
1971
The structure of the moduli spaces of curves and abelian varieties. Zbl 0222.14023
Mumford, David
12
1971
Abelian varieties. Zbl 0223.14022
Mumford, David
585
1970
...and 23 more Documents
all top 5

Cited by 8,137 Authors

56 Ballico, Edoardo
48 Biswas, Indranil
45 Geng, Xianguo
44 Zarkhin, Yuriĭ Gennad’evich
32 Bauer, Martin
28 Brion, Michel
25 Tai, Xuecheng
23 Lange, Herbert
22 Pirola, Gian Pietro
21 Abramovich, Dan
21 Catanese, Fabrizio M. E.
21 Farkas, Gavril
21 Hulek, Klaus
21 Michor, Peter Wolfram
20 Bruveris, Martins
20 Harris, Joseph Daniel
20 Previato, Emma
19 Eisenbud, David
19 Katsura, Toshiyuki
19 Oort, Frans
19 Pandharipande, Rahul
19 Srivastava, Anuj
18 Kollár, János
18 Reichstein, Zinovy B.
18 Voisin, Claire
17 Schröer, Stefan
17 Van der Geer, Gerard
16 Debarre, Olivier
16 Mumford, David Bryant
15 Beauville, Arnaud
15 Ciliberto, Ciro
15 Ichikawa, Takashi
15 Kannan, Senthamarai
15 Salvati Manni, Riccardo
15 Silverman, Joseph Hillel
15 Xu, Chenyang
14 Duong, Dao Van
14 Nguyen Minh Chuong
14 Renner, Lex E.
13 Chen, Ke
13 Donagi, Ron Y.
13 Edidin, Dan
13 Grushevsky, Samuel
13 Gurjar, Rajendra Vasant
13 Kirwan, Frances Clare
13 Kleiman, Steven Lawrence
13 Rumpf, Martin
13 Verra, Alessandro
13 Zuo, Kang
12 Alexeev, Valery A.
12 Alper, Jarod
12 Caporaso, Lucia
12 Chen, Dawei
12 Cremers, Daniel
12 Dolgachev, Igor’ Vladimirovich
12 Kumar, Shrawan
12 Lesfari, Ahmed
12 Melo, Margarida
12 Nicaise, Johannes
12 Noma, Atsushi
12 Odaka, Yuji
12 Sommese, Andrew John
12 Van den Bergh, Michel
12 Viehweg, Eckart
12 Vistoli, Angelo
12 Viviani, Filippo
12 Yang, Di
12 Yu, Chia-Fu
12 Zeng, Xin
12 Zhu, Wei
11 Arapura, Donu
11 Brodmann, Markus P.
11 Cavalieri, Renzo
11 Chambolle, Antonin
11 Duits, Remco
11 Esnault, Hélène
11 Gritsenko, Valeriĭ Alekseevich
11 Gross, Mark
11 Harris, Michael Howard
11 Hassett, Brendan
11 Hausen, Jürgen
11 He, Guoliang
11 Katzarkov, Ludmil
11 Matsutani, Shigeki
11 Naranjo, Juan-Carlos
11 Polishchuk, Alexander Evgen’evich
11 Robert, Damien
11 Sankaran, Gregory Kumar
11 Sturmfels, Bernd
11 Tschinkel, Yuri
11 van Moerbeke, Pierre
11 Weinmann, Andreas
11 Yeung, Sai-Kee
10 Adler, Mark
10 Bastianelli, Francesco
10 Bismut, Jean-Michel
10 Bost, Jean-Benoît
10 Braides, Andrea
10 Ellia, Philippe
10 Fan, Engui
...and 8,037 more Authors
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Cited in 612 Serials

380 Mathematische Annalen
363 Inventiones Mathematicae
316 Journal of Algebra
282 Transactions of the American Mathematical Society
268 Advances in Mathematics
258 Compositio Mathematica
233 Duke Mathematical Journal
197 Journal of Pure and Applied Algebra
187 Mathematische Zeitschrift
166 Annales de l’Institut Fourier
154 Manuscripta Mathematica
147 Proceedings of the American Mathematical Society
126 Communications in Mathematical Physics
113 Journal of Algebraic Geometry
109 Journal of Mathematical Imaging and Vision
104 Journal of Geometry and Physics
101 Journal of Number Theory
91 Communications in Algebra
89 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
89 Journal für die Reine und Angewandte Mathematik
85 Tôhoku Mathematical Journal. Second Series
84 Journal of High Energy Physics
79 Journal of the American Mathematical Society
75 International Journal of Mathematics
70 Geometriae Dedicata
63 Nuclear Physics. B
61 Journal of Symbolic Computation
60 Israel Journal of Mathematics
58 Michigan Mathematical Journal
58 Selecta Mathematica. New Series
58 Transformation Groups
57 International Journal of Computer Vision
57 Geometry & Topology
53 Nagoya Mathematical Journal
53 Algebra & Number Theory
51 SIAM Journal on Imaging Sciences
50 European Journal of Mathematics
48 Annali di Matematica Pura ed Applicata. Serie Quarta
47 Journal of Mathematical Physics
47 Mathematische Nachrichten
46 Bulletin de la Société Mathématique de France
46 Publications of the Research Institute for Mathematical Sciences, Kyoto University
46 Bulletin of the American Mathematical Society. New Series
46 Annals of Mathematics. Second Series
45 Archiv der Mathematik
43 Proceedings of the Japan Academy. Series A
42 Letters in Mathematical Physics
41 Computer Methods in Applied Mechanics and Engineering
41 Publications Mathématiques
41 Journal of the European Mathematical Society (JEMS)
39 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
39 Comptes Rendus. Mathématique. Académie des Sciences, Paris
38 Mathematics of Computation
36 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
36 Linear Algebra and its Applications
35 Journal de Théorie des Nombres de Bordeaux
34 The Journal of Geometric Analysis
33 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
33 Journal of the London Mathematical Society. Second Series
33 Journal of Scientific Computing
32 Functional Analysis and its Applications
31 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
31 Calculus of Variations and Partial Differential Equations
30 Journal of Mathematical Sciences (New York)
30 Forum of Mathematics, Sigma
28 Journal de Mathématiques Pures et Appliquées. Neuvième Série
28 Documenta Mathematica
28 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
27 Rendiconti del Seminario Matematico della Università di Padova
27 Pattern Recognition
27 Indagationes Mathematicae. New Series
27 Journal of the Institute of Mathematics of Jussieu
26 Mathematical Proceedings of the Cambridge Philosophical Society
26 Annals of Global Analysis and Geometry
26 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
26 Proceedings of the Steklov Institute of Mathematics
25 Communications in Contemporary Mathematics
24 Memoirs of the American Mathematical Society
23 Archive for Rational Mechanics and Analysis
23 Mathematical Notes
23 Theoretical and Mathematical Physics
23 Acta Mathematica
23 Bulletin of the London Mathematical Society
23 Osaka Journal of Mathematics
23 Bulletin des Sciences Mathématiques
23 Kyoto Journal of Mathematics
22 Applied Mathematics and Computation
22 Journal de l’École Polytechnique – Mathématiques
21 Journal of the Mathematical Society of Japan
21 Physica D
21 Advances in Geometry
21 Bulletin of the American Mathematical Society
21 Inverse Problems and Imaging
20 Differential Geometry and its Applications
20 Applied and Computational Harmonic Analysis
19 Computers & Mathematics with Applications
19 Journal of Mathematical Analysis and Applications
19 Journal of Functional Analysis
19 Topology and its Applications
19 Expositiones Mathematicae
...and 512 more Serials
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Cited in 63 Fields

5,791 Algebraic geometry (14-XX)
1,287 Number theory (11-XX)
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643 Differential geometry (53-XX)
600 Commutative algebra (13-XX)
526 Computer science (68-XX)
508 Dynamical systems and ergodic theory (37-XX)
473 Group theory and generalizations (20-XX)
432 Information and communication theory, circuits (94-XX)
423 Partial differential equations (35-XX)
420 Quantum theory (81-XX)
392 Numerical analysis (65-XX)
355 Global analysis, analysis on manifolds (58-XX)
341 Manifolds and cell complexes (57-XX)
298 Calculus of variations and optimal control; optimization (49-XX)
296 Functions of a complex variable (30-XX)
244 Associative rings and algebras (16-XX)
228 Topological groups, Lie groups (22-XX)
216 Nonassociative rings and algebras (17-XX)
156 Mechanics of deformable solids (74-XX)
153 Category theory; homological algebra (18-XX)
147 Algebraic topology (55-XX)
135 Combinatorics (05-XX)
135 Field theory and polynomials (12-XX)
124 Statistics (62-XX)
121 Biology and other natural sciences (92-XX)
115 Linear and multilinear algebra; matrix theory (15-XX)
113 Convex and discrete geometry (52-XX)
99 \(K\)-theory (19-XX)
91 Operator theory (47-XX)
89 Special functions (33-XX)
87 Relativity and gravitational theory (83-XX)
84 Mechanics of particles and systems (70-XX)
80 Ordinary differential equations (34-XX)
80 Functional analysis (46-XX)
75 Operations research, mathematical programming (90-XX)
69 Harmonic analysis on Euclidean spaces (42-XX)
68 Probability theory and stochastic processes (60-XX)
59 Geometry (51-XX)
54 Statistical mechanics, structure of matter (82-XX)
46 Difference and functional equations (39-XX)
40 Mathematical logic and foundations (03-XX)
39 Systems theory; control (93-XX)
38 Fluid mechanics (76-XX)
37 History and biography (01-XX)
36 Measure and integration (28-XX)
29 Real functions (26-XX)
28 General and overarching topics; collections (00-XX)
25 Abstract harmonic analysis (43-XX)
21 Approximations and expansions (41-XX)
18 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
14 Potential theory (31-XX)
11 Order, lattices, ordered algebraic structures (06-XX)
10 Optics, electromagnetic theory (78-XX)
9 General topology (54-XX)
8 Integral transforms, operational calculus (44-XX)
7 Mathematics education (97-XX)
6 General algebraic systems (08-XX)
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4 Integral equations (45-XX)
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1 Sequences, series, summability (40-XX)
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