# zbMATH — the first resource for mathematics

## Mumford, David Bryant

Compute Distance To:
 Author ID: mumford.david-b Published as: Mumford, D.; Mumford, David; Mumford, David B. Homepage: http://www.dam.brown.edu/people/mumford/ External Links: MGP · Math-Net.Ru · Wikidata · GND · MacTutor Awards: Fields Medal (1974) · Shaw Prize (2006) · Wolf Prize (2008)
 Documents Indexed: 143 Publications since 1961, including 44 Books Biographic References: 5 Publications
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#### Co-Authors

 82 single-authored 9 Michor, Peter Wolfram 4 Frame, Michael L. 4 Gleason, Andrew Mattei 4 Hughes-Hallett, Deborah 4 McCallum, William G. 4 Osgood, Brad G. 4 Quinney, Douglas 4 Tecosky-Feldman, Jeff 4 Tucker, Thomas W. 3 Artin, Michael 3 Deligne, Pierre René 3 Flath, Daniel Evans 3 Gordon, Sheldon P. 3 Tate, John Torrence jun. 3 Thrash, Joe B. 2 Ash, Avner 2 Barnsley, Michael Fielding 2 Bombieri, Enrico 2 Chung Graham, Fan-Rong King 2 Falconer, Kenneth J. 2 Fogarty, John C. 2 Jackson, Allyn 2 Knudsen, Finn Faye 2 Lee, Ann B. 2 Lock, Patti Frazer 2 Micheli, Mario 2 Mulay, Shashikant B. 2 Nguyen Minh Chuong 2 Rapoport, Michael 2 Raskind, Wayne 2 Series, Caroline 2 Shah, Jayant 2 Stewart, Ian Nicholas 2 Tai, Yungsheng 1 Abhyankar, Yvonne 1 Atiyah, Michael Francis 1 Bajai, Chanderjit 1 Barrallo, Javier 1 Bass, Hyman 1 Bayer, David Allen 1 Berry, Michael Victor 1 Berry, Michael W. 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 Alexandre 1 Eglash, Ron 1 Egorov, Yuriĭ Vladimirovich 1 Furstenberg, Hillel 1 Giblin, Peter J. 1 Gidas, Basilis 1 Gordon, Gaile G. 1 Greenberg, Marvin Jay 1 Gurdian, Rodolfo 1 Hallinan, Peter W. 1 Harbater, Dale 1 Harris, Joseph Daniel 1 Hartshorne, Robin 1 Heinzer, William J. 1 Helgason, Sigurdur 1 Horrocks, Geoffrey 1 Howe, Roger Evans 1 Huang, Jinggang 1 Illusie, Luc 1 Jaffard, Stéphane 1 Jaffe, Arthur Michael 1 Kalayciôglu, Selin 1 Katz, Nicholas Michael 1 Kempf, George R. 1 Khrennikov, Andreĭ Yur’evich 1 Kirwan, Frances Clare 1 Kleiman, Steven Lawrence 1 Ladegaillerie, Yves 1 Lahme, Brigitte 1 Lascu, Alexandru T. 1 Lax, Peter David 1 Lesmoir-Gordon, Nigel 1 Lichtenbaum, Stephen 1 Liebermann, D. 1 Lochak, Pierre 1 Lomen, David O. 1 Lovelock, David 1 Lozano, Guadalupe I. 1 Matsusaka, Teruhisa 1 Mazur, Barry 1 Messing, William 1 Meyer, Yves F. 1 Morris, Jerry 1 Murre, Jacob P. 1 Newstead, Peter E. 1 Nitzberg, Mark ...and 31 more Co-Authors
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#### Serials

 11 Notices of the American Mathematical Society 8 American Journal of Mathematics 5 Inventiones Mathematicae 3 Lecture Notes in Mathematics 3 Progress in Mathematics 3 Modern Birkhäuser Classics 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 International Journal of Computer Vision 2 Ergebnisse der Mathematik und ihrer Grenzgebiete 2 Grundlehren der Mathematischen Wissenschaften 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 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 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

 70 Algebraic geometry (14-XX) 21 History and biography (01-XX) 16 General and overarching topics; collections (00-XX) 16 Computer science (68-XX) 10 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 Dynamical systems and ergodic theory (37-XX) 4 Commutative algebra (13-XX) 4 Real functions (26-XX) 3 Topological groups, Lie groups (22-XX) 3 Functions of a complex variable (30-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) 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 Mathematics education (97-XX)

#### Citations contained in zbMATH

116 Publications have been cited 9,017 times in 7,162 Documents Cited by Year
Geometric invariant theory. 3rd enl. ed. Zbl 0797.14004
Mumford, D.; Fogarty, J.; Kirwan, F.
1993
Optimal approximations by piecewise smooth functions and associated variational problems. Zbl 0691.49036
Mumford, David; Shah, Jayant
1989
Abelian varieties. Zbl 0223.14022
Mumford, David
1970
The irreducibility of the space of curves of a given genus. Zbl 0181.48803
Deligne, Pierre; Mumford, D.
1969
Toroidal embeddings. I. Zbl 0271.14017
Kempf, G.; Knudsen, F.; Mumford, D.; Saint-Donat, Bernard
1973
Lectures on curves on an algebraic surface. Zbl 0187.42701
Mumford, D.
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
1983
Geometric invariant theory. Zbl 0147.39304
Mumford, D.
1965
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
1984
Geometric invariant theory. 2nd enlarged ed. Zbl 0504.14008
Mumford, D.; Fogarty, J.
1982
The topology of normal singularities of an algebraic surface and a criterion for simplicity. Zbl 0108.16801
Mumford, D.
1961
Algebraic geometry. I: Complex projective varieties. Zbl 0356.14002
Mumford, David
1976
The projectivity of the moduli space of stable curves. I: Preliminaries on ”det” and ”Div”. Zbl 0343.14008
Knudsen, Finn; Mumford, David
1976
Varieties defined by quadratic equations. Zbl 0198.25801
Mumford, D.
1970
Smooth compactification of locally symmetric varieties. Zbl 0334.14007
Ash, A.; Mumford, D.; Rapoport, M.; Tai, Y.
1975
On the Kodaira dimension of the moduli space of curves. Zbl 0506.14016
Harris, Joe; Mumford, David
1982
On the equations defining Abelian varieties. I-III. Zbl 0219.14024
Mumford, D.
1966
Towards an enumerative geometry of the moduli space of curves. Zbl 0554.14008
Mumford, David
1983
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. 2nd ed. Zbl 0326.14012
Mumford, David
1974
Stability of projective varieties. Zbl 0363.14003
Mumford, David
1977
Some elementary examples of unirational varieties which are not rational. Zbl 0244.14017
Artin, M.; Mumford, D.
1972
What can be computed in algebraic geometry? Zbl 0846.13017
Bayer, Dave; Mumford, David
1993
The red book of varieties and schemes. Zbl 0658.14001
Mumford, David
1988
Theta characteristics of an algebraic curve. Zbl 0216.05904
Mumford, David
1971
Tata lectures on theta. III. Zbl 0744.14033
Mumford, David; Nori, Madhav; Norman, Peter
1991
Rational equivalence of O-cycles on surfaces. Zbl 0184.46603
Mumford, D.
1969
Hirzebruch’s proportionality theorem in the non-compact case. Zbl 0365.14012
Mumford, D.
1977
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
1999
Curves and their Jacobians. Zbl 0316.14010
Mumford, David
1975
Riemannian geometries on spaces of plane curves. Zbl 1101.58005
Michor, Peter W.; Mumford, David
2006
Prym varieties. I. Zbl 0299.14018
Mumford, David
1974
The spectrum of difference operators and algebraic curves. Zbl 0502.58032
van Moerbeke, Pierre; Mumford, David
1979
Families of abelian varieties. Zbl 0199.24601
Mumford, D.
1966
Further pathologies in algebraic geometry. Zbl 0114.13106
Mumford, D.
1962
An analytic construction of degenerating curves over complete local rings. Zbl 0228.14011
Mumford, David
1972
An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Zbl 1116.58007
Michor, Peter W.; Mumford, David
2007
Elastica and computer vision. Zbl 0798.53003
Mumford, David
1994
A rank 2 vector bundle on P$$^4$$ with 15,000 symmetries. Zbl 0255.14017
Horrocks, G.; Mumford, D.
1973
Algebraic Geometry. I: Complex projective varieties. Reprint of the corr. 2nd print. 1976. Zbl 0821.14001
Mumford, David
1995
Enriques’ classification of surfaces in char p. III. Zbl 0336.14010
Bombieri, E.; Mumford, D.
1976
An analytic construction of degenerating Abelian varieties over complete rings. Zbl 0241.14020
Mumford, David
1972
A note of Shimura’s paper: Discontinuous groups and Abelian varieties. Zbl 0169.23301
Mumford, D.
1969
A remark on Mahler’s compactness theorem. Zbl 0215.23202
Mumford, D.
1971
A metric on shape space with explicit geodesics. Zbl 1142.58013
Younes, Laurent; Michor, Peter W.; Shah, Jayant; Mumford, David
2008
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Zbl 1083.58010
Michor, Peter W.; Mumford, David
2005
Two fundamental theorems on deformations of polarized varieties. Zbl 0128.15505
Matsusaka, T.; Mumford, D.
1964
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. Corrected reprint of the 2nd ed. 1974. Zbl 1177.14001
Mumford, David
2008
Indra’s pearls. The vision of Felix Klein. With cartoons by Larry Gonick. Zbl 1141.00002
Mumford, David; Series, Caroline; Wright, David
2002
An algebraic surface with K ample, $$(K^ 2)=9$$, $$p_ g=q=O$$. Zbl 0433.14021
Mumford, D.
1979
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.
1977
Pathologies. III. Zbl 0146.42403
Mumford, D.
1967
Enriques’ classification of surfaces in char. $$p$$. II. Zbl 0348.14021
Bombieri, E.; Mumford, D.
1977
Filtering, segmentation and depth. Zbl 0801.68171
Nitzberg, Mark; Mumford, David; Shiota, Takahiro
1993
Abelian quotients of the Teichmüller modular group. Zbl 0173.22903
Mumford, D.
1967
Periods of a moduli space of bundles on curves. Zbl 0174.52902
Mumford, D.; Newstead, P.
1968
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
2010
The nonlinear statistics of high-contrast patches in natural images. Zbl 1070.68661
Lee, Ann B.; Pedersen, Kim S.; Mumford, David
2003
Stochastic models for generic images. Zbl 1159.68598
Mumford, David; Gidas, Basilis
2001
A remark on Mordell’s conjecture. Zbl 0151.27301
Mumford, D.
1965
Geodesic completeness for Sobolev metrics on the space of immersed plane curves. Zbl 1315.58009
Bruveris, Martins; Michor, Peter W.; Mumford, David
2014
Introduction to the theory of moduli. Zbl 0242.14004
Mumford, David; Suominen, Kalevi
1972
On the Kodaira dimension of the Siegel modular variety. Zbl 0527.14036
Mumford, David
1983
Picard groups of moduli problems. Zbl 0187.42801
Mumford, D.
1965
On Euler’s equation and ‘EPDiff’. Zbl 1274.35277
Mumford, David; Michor, Peter W.
2013
A zoo of diffeomorphism groups on $$\mathbb R^n$$. Zbl 1364.22009
Michor, Peter W.; Mumford, David
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
2007
A stochastic grammar of images. Zbl 1198.68160
Zhu, Song-Chun; Mumford, David
2006
Stability of projective varieties. Zbl 0497.14004
Mumford, David
1977
Deformations and liftings of finite, commutative group schemes. Zbl 0179.49901
Oort, F.; Mumford, D.
1968
Bi-extensions of formal groups. Zbl 0216.33101
Mumford, D.
1969
Projective invariants of projective structures and applications. Zbl 0154.20702
Mumford, D.
1963
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
2015
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
2007
Lectures on curves on an algebraic surface. With a section by G. M. Bergman. Zbl 1079.14002
Mumford, David
2005
Enriques’ classification of surfaces in char p. I. Zbl 0188.53201
Mumford, D.
1969
Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds. Zbl 1280.58005
Micheli, M.; Michor, P. W.; Mumford, D.
2013
Pattern theory. The stochastic analysis of real-world signals. Zbl 1210.94002
Mumford, David; Desolneux, Agnès
2010
Two- and three-dimensional patterns of the face. Zbl 0930.68140
Hallinan, Peter W.; Gordon, Gaile G.; Yuille, A. L.; Giblin, Peter; Mumford, David
1999
Some footnotes to the work of C. P. Ramanujam. Zbl 0444.14002
Mumford, D.
1978
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
2012
Harmonic, wavelet and $$p$$-adic analysis. Based on the summer school, Quy Nhon, Vietnam, June 10–15, 2005. Zbl 1117.42001
Nguyen Minh Chuong (ed.); Egorov, Yu. V. (ed.); Khrennikov, A. (ed.); Meyer, Y. (ed.); Mumford, D. (ed.)
2007
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. 2nd ed. Reprint. Zbl 0583.14015
Mumford, David
1985
Pathologies of modular algebraic surfaces. Zbl 0138.42002
Mumford, D.
1961
Pattern theory: The mathematics of perception. Zbl 1057.91072
Mumford, David
2002
The dawning of the age of stochasticity. Zbl 0962.60003
Mumford, David
2000
Chordal completions of planar graphs. Zbl 0809.05038
Chung, F. R. K.; Mumford, David
1994
The structure of the moduli spaces of curves and abelian varieties. Zbl 0222.14023
Mumford, David
1971
Tata lectures on theta III. In collaboration with Madhav Nori and Peter Norman. Reprint of the 1991 edition. Zbl 1124.14043
Mumford, David
2007
The self-intersection formula and the ’formule-clef’. Zbl 0341.14002
Lascu, A. T.; Mumford, D.; Scott, D. B.
1975
Lectures on curves on a algebraic surface. Zbl 0187.42702
Mumford, D.
1968
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
Nguyen Minh Chuong (ed.); Ciarlet, P. G. (ed.); Lax, P. (ed.); Mumford, D. (ed.); Phong, D. H. (ed.)
2007
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
2001
Pattern theory: A unifying perspective. Zbl 0939.68820
Mumford, David
1994
Matsusaka’s big theorem. Zbl 0321.14004
Liebermann, D.; Mumford, D.
1975
Pathologies. IV. Zbl 0315.14012
Mumford, David
1975
A remark on the paper of M. Schlessinger. Zbl 0279.32007
Mumford, David
1973
Algebraic geometry II. Zbl 1325.14001
Mumford, David; Oda, Tadao
2015
Hilbert’s fourteenth problem - the finite generation of subrings such as rings of invariants. Zbl 0341.14019
Mumford, David
1976
A new approach to compactifying locally symmetric varieties. Zbl 0322.32016
Mumford, David
1975
The irreducibility of the space of curves of a given genus. Zbl 0233.14008
Deligne, Pierre; Mumford, D.
1972
Alexandre Grothendieck 1928–2014, part 2. Zbl 1338.01023
Artin, Michael (ed.); Jackson, Allyn (ed.); Mumford, David (ed.); Tate, John (ed.); Ladegaillerie, Yves; Lichtenbaum, Stephen; Lochak, Pierre; Mazur, Barry; Messing, William; Murre, Jacob; Schneps, Leila
2016
Alexandre Grothendieck 1928–2014. I. Zbl 1338.01022
Artin, Michael (ed.); Jackson, Allyn (ed.); Mumford, David (ed.); Tate, John (ed.); Atiyah, Michael; Bass, Hyman; Cartier, Pierre; Deligne, Pierre; Demazure, Michel; Greenberg, Marvin Jay; Hartshorne, Robin; Illusie, Luc; Katz, Nicholas; Kleiman, Steven L.
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
2015
Algebraic geometry II. Zbl 1325.14001
Mumford, David; Oda, Tadao
2015
Geodesic completeness for Sobolev metrics on the space of immersed plane curves. Zbl 1315.58009
Bruveris, Martins; Michor, Peter W.; Mumford, David
2014
Shreeram Abhyankar (July 22, 1930 – November 2, 2012). Zbl 1338.13001
Mulay, Shashikant (ed.); Sathaye, Avinash (ed.); Abhyankar, Yvonne; Bajai, Chanderjit; Cutkosky, Steven Dale; Harbater, Dale; Heinzer, William; Shannon, David; Mulay, Shashikant; Mumford, David; Thakur, Dinesh
2014
On Euler’s equation and ‘EPDiff’. Zbl 1274.35277
Mumford, David; Michor, Peter W.
2013
A zoo of diffeomorphism groups on $$\mathbb R^n$$. Zbl 1364.22009
Michor, Peter W.; Mumford, David
2013
Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds. Zbl 1280.58005
Micheli, M.; Michor, P. W.; Mumford, D.
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
2012
The influence of Benoît B. Mandelbrot on mathematics. Zbl 1284.01048
Barnsley, Michael F. (ed.); Frame, Michael (ed.); Stewart, Ian; Mumford, David; Howe, Roger; Furstenberg, Hillel; Falconer, Kenneth; West, Bruce J.; Coppens, Marc-Olivier; Cohen, Nathan; Jaffard, Stéphane; Berry, Michael; Frame, Michael
2012
Glimpses of Benoît B. Mandelbrot (1924–2010). Zbl 1284.01047
Barnsley, Michael F. (ed.); Frame, Michael (ed.); Stewart, Ian; Mumford, David; Falconer, Kenneth; Eglash, Ron; Brothers, Harlan; Lesmoir-Gordon, Nigel; Barrallo, Javier; Berry, Michael; Frame, Michael
2012
Intuition and rigor and Enriques’s quest. Zbl 1268.14003
Mumford, David
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
2010
Pattern theory. The stochastic analysis of real-world signals. Zbl 1210.94002
Mumford, David; Desolneux, Agnès
2010
A metric on shape space with explicit geodesics. Zbl 1142.58013
Younes, Laurent; Michor, Peter W.; Shah, Jayant; Mumford, David
2008
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. Corrected reprint of the 2nd ed. 1974. Zbl 1177.14001
Mumford, David
2008
An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Zbl 1116.58007
Michor, Peter W.; Mumford, David
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
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
2007
Harmonic, wavelet and $$p$$-adic analysis. Based on the summer school, Quy Nhon, Vietnam, June 10–15, 2005. Zbl 1117.42001
Nguyen Minh Chuong (ed.); Egorov, Yu. V. (ed.); Khrennikov, A. (ed.); Meyer, Y. (ed.); Mumford, D. (ed.)
2007
Tata lectures on theta III. In collaboration with Madhav Nori and Peter Norman. Reprint of the 1991 edition. Zbl 1124.14043
Mumford, David
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
Nguyen Minh Chuong (ed.); Ciarlet, P. G. (ed.); Lax, P. (ed.); Mumford, D. (ed.); Phong, D. H. (ed.)
2007
Riemannian geometries on spaces of plane curves. Zbl 1101.58005
Michor, Peter W.; Mumford, David
2006
A stochastic grammar of images. Zbl 1198.68160
Zhu, Song-Chun; Mumford, David
2006
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Zbl 1083.58010
Michor, Peter W.; Mumford, David
2005
Lectures on curves on an algebraic surface. With a section by G. M. Bergman. Zbl 1079.14002
Mumford, David
2005
The nonlinear statistics of high-contrast patches in natural images. Zbl 1070.68661
Lee, Ann B.; Pedersen, Kim S.; Mumford, David
2003
Indra’s pearls. The vision of Felix Klein. With cartoons by Larry Gonick. Zbl 1141.00002
Mumford, David; Series, Caroline; Wright, David
2002
Pattern theory: The mathematics of perception. Zbl 1057.91072
Mumford, David
2002
Stochastic models for generic images. Zbl 1159.68598
Mumford, David; Gidas, Basilis
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
2001
The dawning of the age of stochasticity. Zbl 0962.60003
Mumford, David
2000
The dawning of the age of stochasticity. Zbl 1149.00309
Mumford, David
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
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
1999
Trends in the profession of mathematics. Zbl 1288.00054
Mumford, David
1998
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.
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.
1997
Algebraic Geometry. I: Complex projective varieties. Reprint of the corr. 2nd print. 1976. Zbl 0821.14001
Mumford, David
1995
Elastica and computer vision. Zbl 0798.53003
Mumford, David
1994
Chordal completions of planar graphs. Zbl 0809.05038
Chung, F. R. K.; Mumford, David
1994
Pattern theory: A unifying perspective. Zbl 0939.68820
Mumford, David
1994
Geometric invariant theory. 3rd enl. ed. Zbl 0797.14004
Mumford, D.; Fogarty, J.; Kirwan, F.
1993
What can be computed in algebraic geometry? Zbl 0846.13017
Bayer, Dave; Mumford, David
1993
Filtering, segmentation and depth. Zbl 0801.68171
Nitzberg, Mark; Mumford, David; Shiota, Takahiro
1993
Tata lectures on theta. III. Zbl 0744.14033
Mumford, David; Nori, Madhav; Norman, Peter
1991
Optimal approximations by piecewise smooth functions and associated variational problems. Zbl 0691.49036
Mumford, David; Shah, Jayant
1989
The red book of varieties and schemes. Zbl 0658.14001
Mumford, David
1988
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. 2nd ed. Reprint. Zbl 0583.14015
Mumford, David
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
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
1983
Towards an enumerative geometry of the moduli space of curves. Zbl 0554.14008
Mumford, David
1983
On the Kodaira dimension of the Siegel modular variety. Zbl 0527.14036
Mumford, David
1983
Geometric invariant theory. 2nd enlarged ed. Zbl 0504.14008
Mumford, D.; Fogarty, J.
1982
On the Kodaira dimension of the moduli space of curves. Zbl 0506.14016
Harris, Joe; Mumford, David
1982
Algebraic geometry. I: Complex projective varieties. Corr. 2nd printing. Zbl 0456.14001
Mumford, David
1980
The spectrum of difference operators and algebraic curves. Zbl 0502.58032
van Moerbeke, Pierre; Mumford, David
1979
An algebraic surface with K ample, $$(K^ 2)=9$$, $$p_ g=q=O$$. Zbl 0433.14021
Mumford, D.
1979
Some footnotes to the work of C. P. Ramanujam. Zbl 0444.14002
Mumford, D.
1978
Fields Medals. IV: An instinct for the key idea. Zbl 1225.01080
Mumford, David; Tate, John
1978
Stability of projective varieties. Zbl 0363.14003
Mumford, David
1977
Hirzebruch’s proportionality theorem in the non-compact case. Zbl 0365.14012
Mumford, D.
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.
1977
Enriques’ classification of surfaces in char. $$p$$. II. Zbl 0348.14021
Bombieri, E.; Mumford, D.
1977
Stability of projective varieties. Zbl 0497.14004
Mumford, David
1977
Stability of projective varieties. Zbl 0376.14007
Mumford, David
1977
Algebraic geometry. I: Complex projective varieties. Zbl 0356.14002
Mumford, David
1976
The projectivity of the moduli space of stable curves. I: Preliminaries on ”det” and ”Div”. Zbl 0343.14008
Knudsen, Finn; Mumford, David
1976
Enriques’ classification of surfaces in char p. III. Zbl 0336.14010
Bombieri, E.; Mumford, D.
1976
Hilbert’s fourteenth problem - the finite generation of subrings such as rings of invariants. Zbl 0341.14019
Mumford, David
1976
Smooth compactification of locally symmetric varieties. Zbl 0334.14007
Ash, A.; Mumford, D.; Rapoport, M.; Tai, Y.
1975
Curves and their Jacobians. Zbl 0316.14010
Mumford, David
1975
The self-intersection formula and the ’formule-clef’. Zbl 0341.14002
Lascu, A. T.; Mumford, D.; Scott, D. B.
1975
Matsusaka’s big theorem. Zbl 0321.14004
Liebermann, D.; Mumford, D.
1975
Pathologies. IV. Zbl 0315.14012
Mumford, David
1975
A new approach to compactifying locally symmetric varieties. Zbl 0322.32016
Mumford, David
1975
Abelian varieties. With appendices by C. P. Ramanujam and Yuri Manin. 2nd ed. Zbl 0326.14012
Mumford, David
1974
Prym varieties. I. Zbl 0299.14018
Mumford, David
1974
Toroidal embeddings. I. Zbl 0271.14017
Kempf, G.; Knudsen, F.; Mumford, D.; Saint-Donat, Bernard
1973
A rank 2 vector bundle on P$$^4$$ with 15,000 symmetries. Zbl 0255.14017
Horrocks, G.; Mumford, D.
1973
A remark on the paper of M. Schlessinger. Zbl 0279.32007
Mumford, David
1973
Some elementary examples of unirational varieties which are not rational. Zbl 0244.14017
Artin, M.; Mumford, D.
1972
An analytic construction of degenerating curves over complete local rings. Zbl 0228.14011
Mumford, David
1972
An analytic construction of degenerating Abelian varieties over complete rings. Zbl 0241.14020
Mumford, David
1972
Introduction to the theory of moduli. Zbl 0242.14004
Mumford, David; Suominen, Kalevi
1972
The irreducibility of the space of curves of a given genus. Zbl 0233.14008
Deligne, Pierre; Mumford, D.
1972
Rational equivalence of 0-cycles on surfaces. Zbl 0228.14005
Mumford, D.
1972
An analytic construction of degenerating curves over complete local rings. Zbl 0243.14010
Mumford, David
1972
Theta characteristics of an algebraic curve. Zbl 0216.05904
Mumford, David
1971
A remark on Mahler’s compactness theorem. Zbl 0215.23202
Mumford, D.
1971
The structure of the moduli spaces of curves and abelian varieties. Zbl 0222.14023
Mumford, David
1971
Abelian varieties. Zbl 0223.14022
Mumford, David
1970
Varieties defined by quadratic equations. Zbl 0198.25801
Mumford, D.
1970
The irreducibility of the space of curves of a given genus. Zbl 0181.48803
Deligne, Pierre; Mumford, D.
1969
Rational equivalence of O-cycles on surfaces. Zbl 0184.46603
Mumford, D.
1969
A note of Shimura’s paper: Discontinuous groups and Abelian varieties. Zbl 0169.23301
Mumford, D.
1969
Bi-extensions of formal groups. Zbl 0216.33101
Mumford, D.
1969
Enriques’ classification of surfaces in char p. I. Zbl 0188.53201
Mumford, D.
1969
Periods of a moduli space of bundles on curves. Zbl 0174.52902
Mumford, D.; Newstead, P.
1968
...and 16 more Documents
all top 5

#### Cited by 6,478 Authors

 50 Ballico, Edoardo 39 Biswas, Indranil 37 Geng, Xianguo 32 Zarkhin, Yuriĭ Gennad’evich 24 Bauer, Martin 23 Brion, Michel 20 Harris, Joseph Daniel 20 Michor, Peter Wolfram 19 Abramovich, Dan 19 Lange, Herbert 19 Oort, Frans 18 Bruveris, Martins 17 Eisenbud, David 17 Hulek, Klaus 17 Pirola, Gian Pietro 17 Voisin, Claire 16 Catanese, Fabrizio M. E. 16 Kollár, János 16 Mumford, David Bryant 16 Reichstein, Zinovy B. 15 Beauville, Arnaud 15 Farkas, Gavril 15 Katsura, Toshiyuki 15 Previato, Emma 15 Renner, Lex E. 14 Debarre, Olivier 14 Ichikawa, Takashi 14 Tai, Xuecheng 13 Kleiman, Steven Lawrence 13 Pandharipande, Rahul 13 Salvati Manni, Riccardo 13 Zuo, Kang 12 Chen, Ke 12 Kumar, Shrawan 12 Viehweg, Eckart 11 Alper, Jarod 11 Brodmann, Markus P. 11 Chen, Dawei 11 Duits, Remco 11 Grushevsky, Samuel 11 Gurjar, Rajendra Vasant 11 Harris, Michael Howard 11 Hausen, Jürgen 11 Kannan, Subramaniam Senthamarai 11 Katzarkov, Ludmil 11 Lesfari, Ahmed 11 Nicaise, Johannes 11 Schröer, Stefan 11 Silverman, Joseph Hillel 11 Srivastava, Anuj 11 van Moerbeke, Pierre 10 Adler, Mark 10 Arapura, Donu 10 Bismut, Jean-Michel 10 Braides, Andrea 10 Caporaso, Lucia 10 Chardin, Marc 10 Ciliberto, Ciro 10 Cremers, Daniel 10 Donagi, Ron Y. 10 Edidin, Dan 10 Ford, Timothy J. 10 Hassett, Brendan 10 Korotkin, Dmitrii A. 10 Leaci, Antonio 10 Matsutani, Shigeki 10 Melo, Margarida 10 Nguyen Minh Chuong 10 Sankaran, Gregory Kumar 10 Sommese, Andrew John 10 Soulé, Christophe 10 Srinivas, Vasudevan 10 Sturmfels, Bernd 10 Van der Geer, Gerard 10 Viviani, Filippo 10 Vogel, Wolfgang 10 Weinmann, Andreas 10 Zeng, Xin 9 Alexeev, Valery A. 9 Bastianelli, Francesco 9 Bloch, Spencer J. 9 Bost, Jean-Benoît 9 Carriero, Michele 9 Chambolle, Antonin 9 Dolgachev, Igor’ Vladimirovich 9 Ellia, Philippe 9 Fan, Engui 9 Fried, Michael David 9 Gross, Mark 9 Jonsson, Mattias 9 Kani, Ernst J. 9 Kato, Fumiharu 9 Kirwan, Frances Clare 9 Lan, Kai-Wen 9 Lee, Yongnam 9 Lieblich, Max David 9 Liedtke, Christian 9 Mabuchi, Toshiki 9 Malaspina, Francesco 9 Manin, Yuri Ivanovich ...and 6,378 more Authors
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#### Cited in 517 Serials

 347 Mathematische Annalen 341 Inventiones Mathematicae 286 Journal of Algebra 248 Transactions of the American Mathematical Society 232 Compositio Mathematica 216 Duke Mathematical Journal 211 Advances in Mathematics 160 Journal of Pure and Applied Algebra 145 Annales de l’Institut Fourier 143 Mathematische Zeitschrift 133 Proceedings of the American Mathematical Society 124 Manuscripta Mathematica 112 Communications in Mathematical Physics 98 Journal of Algebraic Geometry 88 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 87 Journal of Number Theory 82 Journal of Geometry and Physics 80 Communications in Algebra 78 Tohoku Mathematical Journal. Second Series 74 Journal of the American Mathematical Society 66 Journal für die Reine und Angewandte Mathematik 65 Journal of Mathematical Imaging and Vision 64 International Journal of Mathematics 63 Nuclear Physics. B 59 Geometriae Dedicata 49 Journal of High Energy Physics 48 Journal of Symbolic Computation 47 Israel Journal of Mathematics 47 Michigan Mathematical Journal 44 Transformation Groups 43 Nagoya Mathematical Journal 43 Proceedings of the Japan Academy. Series A 43 Bulletin of the American Mathematical Society. New Series 42 Publications of the Research Institute for Mathematical Sciences, Kyoto University 41 Annali di Matematica Pura ed Applicata. Serie Quarta 40 Archiv der Mathematik 40 SIAM Journal on Imaging Sciences 38 Journal of Mathematical Physics 38 Geometry & Topology 37 Publications Mathématiques 37 Annals of Mathematics. Second Series 35 Bulletin de la Société Mathématique de France 34 Letters in Mathematical Physics 33 Mathematics of Computation 33 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 31 Mathematische Nachrichten 31 International Journal of Computer Vision 31 Journal of the European Mathematical Society (JEMS) 30 Selecta Mathematica. New Series 30 Comptes Rendus. Mathématique. Académie des Sciences, Paris 27 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 27 Linear Algebra and its Applications 27 Pattern Recognition 27 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 27 Calculus of Variations and Partial Differential Equations 27 Journal of Mathematical Sciences (New York) 26 Functional Analysis and its Applications 26 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 26 Journal de Théorie des Nombres de Bordeaux 25 Rendiconti del Seminario Matematico della Università di Padova 25 Journal of Scientific Computing 24 Journal de Mathématiques Pures et Appliquées. Neuvième Série 23 Acta Mathematica 23 Indagationes Mathematicae. New Series 23 European Journal of Mathematics 22 Computer Methods in Applied Mechanics and Engineering 22 Annals of Global Analysis and Geometry 21 Theoretical and Mathematical Physics 21 Osaka Journal of Mathematics 21 The Journal of Geometric Analysis 21 Bulletin of the American Mathematical Society 20 Mathematical Notes 20 Mathematical Proceedings of the Cambridge Philosophical Society 20 Algebra & Number Theory 20 Kyoto Journal of Mathematics 19 Archive for Rational Mechanics and Analysis 19 Applied Mathematics and Computation 19 Topology and its Applications 19 Bulletin des Sciences Mathématiques 19 Proceedings of the Steklov Institute of Mathematics 18 Physics Letters. A 17 Chaos, Solitons and Fractals 17 Journal of Soviet Mathematics 17 Differential Geometry and its Applications 17 Applied and Computational Harmonic Analysis 17 Communications in Contemporary Mathematics 17 Inverse Problems and Imaging 16 Journal of Functional Analysis 16 Geometric and Functional Analysis. GAFA 16 Documenta Mathematica 16 Central European Journal of Mathematics 16 Journal of the Institute of Mathematics of Jussieu 15 Journal of Mathematical Analysis and Applications 15 Journal of the Mathematical Society of Japan 15 Acta Applicandae Mathematicae 15 Physica D 15 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 15 International Journal of Number Theory 14 Computers & Mathematics with Applications 14 Computer Aided Geometric Design ...and 417 more Serials
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#### Cited in 61 Fields

 4,537 Algebraic geometry (14-XX) 970 Number theory (11-XX) 811 Several complex variables and analytic spaces (32-XX) 491 Differential geometry (53-XX) 483 Commutative algebra (13-XX) 388 Dynamical systems and ergodic theory (37-XX) 377 Computer science (68-XX) 368 Group theory and generalizations (20-XX) 332 Quantum theory (81-XX) 318 Partial differential equations (35-XX) 317 Information and communication theory, circuits (94-XX) 298 Numerical analysis (65-XX) 297 Global analysis, analysis on manifolds (58-XX) 274 Manifolds and cell complexes (57-XX) 237 Calculus of variations and optimal control; optimization (49-XX) 230 Functions of a complex variable (30-XX) 188 Topological groups, Lie groups (22-XX) 187 Associative rings and algebras (16-XX) 168 Nonassociative rings and algebras (17-XX) 118 Category theory; homological algebra (18-XX) 113 Algebraic topology (55-XX) 108 Field theory and polynomials (12-XX) 103 Mechanics of deformable solids (74-XX) 96 Biology and other natural sciences (92-XX) 88 Statistics (62-XX) 85 Combinatorics (05-XX) 84 Linear and multilinear algebra; matrix theory (15-XX) 77 Convex and discrete geometry (52-XX) 76 Mechanics of particles and systems (70-XX) 67 Special functions (33-XX) 66 $$K$$-theory (19-XX) 62 Operator theory (47-XX) 60 Ordinary differential equations (34-XX) 59 Relativity and gravitational theory (83-XX) 57 Operations research, mathematical programming (90-XX) 51 Functional analysis (46-XX) 49 Probability theory and stochastic processes (60-XX) 47 Geometry (51-XX) 44 Harmonic analysis on Euclidean spaces (42-XX) 39 Statistical mechanics, structure of matter (82-XX) 36 Systems theory; control (93-XX) 31 Difference and functional equations (39-XX) 27 Fluid mechanics (76-XX) 25 Mathematical logic and foundations (03-XX) 24 History and biography (01-XX) 24 Real functions (26-XX) 23 Measure and integration (28-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Abstract harmonic analysis (43-XX) 16 General and overarching topics; collections (00-XX) 16 Approximations and expansions (41-XX) 11 Potential theory (31-XX) 9 General topology (54-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 6 Mathematics education (97-XX) 5 General algebraic systems (08-XX) 5 Integral transforms, operational calculus (44-XX) 5 Optics, electromagnetic theory (78-XX) 5 Geophysics (86-XX) 2 Integral equations (45-XX) 2 Classical thermodynamics, heat transfer (80-XX)

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