David Mumford Ph.D.

National Medal of Science - Mathematics and Computer Science 2009

Mathematician. Algebraic geometry, Vision and Pattern Theory. Pure and Applied math. History and Philosophy of math, Math education. Sailing.

"Research enterprise depends on the free dissemination of scholarly material.

Publications

1. Research in Computer Vision: 1983-2007 PhD Students in Vision
2. Research on Geometry of Shape Spaces: 2001-2012 PhD Students in Shape
3. Research in the Biology and Psychology of Vision: 1983-2004 PhD Students in Computational Neurobiology
4. Papers in Algebraic Geometry: 1959-1982 PhD Students in Algebraic Geometry
5. Math Education, History of Math and Other Work

1. Research in Computer Vision: 1983-2007


1. The Representation of Shape (with A. Latto and J. Shah), in Proceedings of the 1984 IEEE Workshop on Computer Vision, pp. 183-191, 1984.
2. Boundary Detection by Minimizing Functionals I (with J. Shah), in Image Understanding 1989, Ablex Press, preliminary version in 1985 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 1985.
3. The Problem of Robust Shape Descriptors, in Proc of 1st IEEE International Conference on Computer Vision (ICCV), 1987, pp.602-606.
4. * Optimal Approximations of Piecewise Smooth Functions and Associated Variational Problems (with J. Shah), Comm. in Pure and Appl. Math., 1989, 42, pp.577-685.
5. The 2.1D Sketch (with M. Nitzberg), in Proc. of 3rd IEEE International Conference on Computer Vision (ICCV), 1990, pp.138-144.
6. Parametrizing Exemplars of Categories, J. Cognitive Neuroscience, 1991, 3, pp. 87-88.
7. Mathematical Theories of Shape: do they model perception?, in Proc. Conference 1570, Soc. Photo-optical & Ind. Engineers, 1991, pp. 2-10.
8. Texture Segmentation by Minimizing Vector-Valued Energy Functionals: the coupled membrane model (with Tai Sing Lee and Alan Yuille), Proc. European Conf. Comp. Vision, 1992, Lecture Notes in Computer Science 588, pp. 165-173.
9. A Bayesian Treatment of the Stereo Correspondence Problem Using Half-Occluded Regions, (with P. Belhumeur), Proc. IEEE Conf. Comp. Vision and Pattern Recognition, 1992 (CVPR), pp. 506-512.
10. Elastica and Computer Vision, in Algebraic Geometry and its Applications, ed. C. Bajaj, Springer-Verlag, 1993, pp. 507-518.
11. Commentary on Grenander & Miller "Representations of Knowledge in Complex Systems", Proc. Royal Stat. Soc., 1994.
12. Pattern Theory: a Unifying Perspective, in Proceedings 1st European Congress of Mathematics, Birkhauser-Boston, 1994. Revised version in Perception as Bayesian inference, ed. D.Knill and W.Richards, Cambridge Univ. Press, 1996, pp. 25-62.
13. Chordal completions of planar graphs (with F.R.K. Chung), J. of Combinatorics, 62, 1994, pp.96-106.
14. The Bayesian Rationale for Energy Functionals, in Geometry-Driven Diffusion in Computer Vision, Bart Romeny editor, Kluwer Academic, 1994, pp. 141-153.
15. The Statistical Description of Visual Signals, ICIAM 95 ed. K.Kirshgassner, O.Mahrenholtz & R.Mennicken, Akademie Verlag, 1996.
16. Review of Variational Methods in image segmentation, by J-M Morel & S. Solimini, Bull. Amer. Math. Soc., 33, 1996, 211-216.
17. Learning generic prior models for visual computation (with S.C.Zhu), Proc. IEEE Conf. Comp. Vision and Pattern Rec. 1997, 463-469, Comp Sci Press.
18. Minimax Entropy Principle and its Application to Texture Modeling (with S.C.Zhu and Y.N.Wu), Neural Computation, 9, 1997, 1627-60.
19. Prior Learning and Gibbs Reaction-Diffusion (with Song Chun Zhu), IEEE Trans. Patt. Anal. and Mach. Int., 19, 1997, 1236-50.
20. * FRAME: Filters, Random Field and Maximum Entropy, (with S.C.Zhu and Y.Wu), Int. J. Comp. Vis., 27, 1998.
21. The Statistics of Natural Images and Models (with J.Huang), Proc. IEEE Conf. Comp. Vision and Pattern Rec. 1999, pp.541-547, Comp Sci Press.
22. Statistics of range images (with Jinggang Huang and Ann Lee), Proc. IEEE Conf. Comp. Vision and Pattern Rec. 2000, pp. 324-331, Comp Sci Press.
23. * Stochastic Models for Generic Images (with Basilis Gidas), Quarterly Appl. Math., 59, 2001, pp.85-111.
24. Occlusion models for natural images: A statistical study of a scale-invariant dead-leaves model, (with Ann Lee and Jinggang Huang), Int. J. Computer Vision, 41, 2001, pp. 35-59.
25. Pattern Theory: The Mathematics of Perception, in Proceedings of ICM 2002, Beijing, vol. 1, 2002, pp.401-422.
26. The Nonlinear Statistics of High-contrast Patches in Natural Images (with Ann Lee and Kim Pedersen), Int. J. Comp. Vision, 54, 2003, pp.83-103.
27. Empirical Statistics and Stochastic Models for Visual Signals, in Brain and Systems: New Directions in Statistical Signal Processing, ed. by S.Haykin, J.Principe, T.Sejnowski, and J.McWhirter, MIT Press, 2006.
28. A stochastic grammar of images (with Song-Chun Zhu), Foundations and Trends in Computer Graphics and Vision, 2, 2007, pp. 259-362

PhD Students in Vision:

1989 Yang Wang, Image segmentation by variational methods and elliptic boundary value problems
1991 Gaile Gordon, Face recognition from depth and curvature
1991 Mark Nitzberg, Depth from overlap
1993 Peter Belhumeur, A Bayesian approach to the stereo correspondence problem
1993 David Fry, Shape recognition using metrics on the space of shapes
1995 Peter Hallinan, A deformable model for the recognition of human faces under arbitrary illumination.
1996 Song-Chun Zhu, Statistical and Computational Theories for Image Segmentation, Texture Modeling and Object recognition.
1998 Ralph Teixeira, Investigations on the Distance Transform and Medial axis.
2000 Artur Fridman, Mixed Markov Fields.
2000 Jinggang Huang, Statistics of Natural Images and Models.
2002 Ann Lee, Statistics, Models and Learning in BCM Theory of a Natural Visual Environment.

2. Research on Geometry of Shape Spaces: 2001-2012


1. Surface evolution under curvature flow (with Conglin Lu and Yan Cao), Special Issue on Partial Differential equations in Image Proc. Comp. Vision and Comp. Graphics, Journal of Visual Communication and Image Representation, 2001.
2. Geometric Structure Estimation of Axially Symmetric Pots from Small Fragments(with Yan Cao), in Proc. of Int. Conf. on Signal Processing, Pattern Recognition, and Applications, Crete, 2002.
3. * Riemannian Geometries on Spaces of Plane Curves (with Peter Michor), J. of the European Math. Society, 8, 2006, pp.1-48.
4. Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms (with Peter Michor), Documenta Mathematica, 10, 2005.
5. 2D-Shape Analysis using Conformal Mapping (with Eitan Sharon), Int. J. of Comp. Vision 70, 2006, pp.55-75; preliminary version in Proc. IEEE Conf. Comp. Vision and Patt. Rec. , 2004.
6. Stuff It! Review of Introduction to Circle Packing: The Theory of Discrete Analytic Functions by Kenneth Stephenson, The American Scientist, bf 94, 2006.
7. An overview of the Riemannian metrics on spaces of curves using the Hamiltonian Approach, (with Peter Michor), Applied and Computational Harmonic Analysis, 23, 2007, pp. 74-113.
8. A metric on shape space with explicit geodesics, (with Laurent Younes, Peter Michor and Jayant Shah), Rendiconti Lincei - Matematica e Applicazioni, 19, 2009, p. 2557.
9. Sectional Curvature in terms of the Co-Metric and with Applications to the Riemannian Manifolds of Landmarks (with M. Micheli and P. Michor), SIAM J. on Imaging Sciences, 5, 2012,, pp. 394- 433.
10. Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds (with Mario Micheli and Peter Michor), submitted.
11. Euler's equation and EPDiff (with Peter Michor), in preparation.

PhD Students in Shape:

2002 Conglin Lu, Curvature-based Multiscale Shape Analysis and Stochastic Shape Modeling.
2003 Yan Cao, Axial Representations of 3D shapes.
2004 Kathryn Leonard, Measuring Shape Space: _-entropy, adaptive coding and two-dimensional shape.
2008 Mario Micheli, The Differential Geometry of Landmark Space Manifolds: Metrics, Geodesics and Curvature.
2008 Matt Feizsli, Conformal Shape Representation.
2010 Sergey Kushnarev, The Geometry of the Space of 2D Shapes and the Weil-Petersson Metric.


3. Research in the Biology and Psychology of Vision: 1983-2004


1. Discriminating Figure from Ground: the role of edge detection and region growing (with S. Kosslyn, L. Hillger and R. Herrnstein), Proc. Nat. Acad. Sci., 1987, 84, pp.7354-7358.
2. Teaching Pigeons an Abstract Relational Rule: Insideness (with R. Herrnstein, W. Vaughan and S. Kosslyn), Perception and Psychophysics, 1989, 46, pp. 56-64.
3. * On the Computational Architecture of the Neocortex, I: The role of the thalamo-cortical loop, Biological Cybernetics, 1991, 65, pp.135-145; II: The role of cortico-cortical loops, Biological Cybernetics, 66, pp. 241-251.
4. Neuronal Architectures for Pattern-theoretic Problems, in Large Scale Neuronal Theories of the Brain, MIT Press, 1994, pp. 125-152.
5. Thalamus, in The Handbook of Brain Theory and Neural Networks, M. Arbib editor, MIT Press, 1995.
6. Neural correlates of boundary and medial axis representations in primate striate cortex, (with T.S.Lee, K.Zipser & P.H.Schiller), ARVO abstract, 1995.
7. Issues in the mathematical modeling of cortical functioning and thought, in The Legacy of Norbert Wiener: A Centennial Symposium, ed. D.Jerison et al, Amer. Math. Society, 1997, pp. 235-260.
8. Visual Search and Shape from Shading Modulate Contextual Processing in Macaque Early Visual Cortices, (with T.S.Lee, R.Romero, A.Tobias & T.Moore), Neuroscience Abstract, 1997.
9. The Role of V1 in Shape Representation (with Tai Sing Lee, Song Chun Zhu & Victor Lamme), Computational Neuroscience, ed. Bower, Plenum Press, 1997.
10. * The Role of Primary Visual Cortex in Higher Level Vision (with T.S.Lee, R.Romero and V.Lamme), Vision Research, 38, 1998, 2429-2454.
11. Thalamus, in MIT Encyclopedia of the Cognitive Sciences, MIT Press, 1999.
12. Neural activity in early visual cortex reflects behavioral experience and higher-order perceptual saliency (with Tai Sing Lee, C.Yang, R.Romero), Nature Neuroscience, 5, 2002, 589-597.
13. Hierarchical Bayesian Inference in the Visual Cortex, (with Tai Sing Lee), Journal of the Optical Society of America, 20, 2003, 1434-1448.
14. Modeling and Decoding Motor Cortical Activity using a Switching Kalman Filter, (with W.Wu, M.Black, Y.Gao, E.Bienenstock, J.Donoghue), IEEE Trans. on Biomed. Eng. , 51, pp. 933-942, 2004.
15. Movement Direction Decoding using Fast oscillation in Local Field Potential and Neural Firing, (with Wei Wu, W.Truccolo, M.Saleh and J.Donoghue), 13th Computational Neuroscience Meeting, 2004.
16. Minds must unite: Its time for experimentalists to stop ignoring computational modelers (with David Donoho and Bruno Olshausen), 'Opinion' section, The Scientist, June 6, 2005.

PhD Students in Computational Neurobiology:

1993 Tai Sing Lee, Surface inference by minimizing energy functionals: a computational framework for the visual cortex 2004 Wei Wu, Statistical Models of Neural Coding in Motor Cortex.

4. Papers in Algebraic Geometry: 1959-1982


1. Topology of Normal Singularities and a Criterion for Simplicity, Publ. de l'Institut des Hautes Etudes Scientifiques, 1961, pp. 5-22.
2. Pathologies of Modular Geometry, Amer. J. of Math., 1961, pp. 339-342.
3. An Elementary theorem in Geometric Invariant Theory, Bull. Amer. Math. Soc., 1961, pp. 483-487.
4. Further Pathologies in Algebraic Geometry, Amer. J. of Math., 1962, pp. 642-648.
5. The Canonical Ring of an Algebraic Surface, an appendix to a paper by Oscar Zariski, Ann. Of Math., 76, 1962, pp. 612-615.
6. Topics in the Theory of Moduli, (in Japanese), Sugaku, 1963.
7. Projective Invariants of Projective Structures, International Congress of Mathematicians, Stockholm 1962, 1963, pp. 526-530.
8. Two Fundamental Theorem on Deformations of Polarized Varieties (with T. Matsusaka), Amer. J. of Math., 1964, pp. 668-684.
9. A Remark on Mordell's Conjecture, Amer. J. of Math., 1965, pp. 1007-1016.
10. Picard Groups of Moduli Problems, in Arithmetic Algebraic Geometry, (Proc. of a Conference in Purdue, 1963), Harper and Row, 1965.
11. * On the Equations Defining Abelian Varieties I, II, III, Inventiones Mathematicae, 1966, 1, pp. 287-384; 1967, 3, pp. 75-135 and pp. 215-244.
12. Families of Abelian Varieties, in Proc. of Symposium in Pure Math., 9, Amer. Math. Soc., 1966.
13. Pathologies III, Amer. J. of Math., 1967, 89, pp. 94-104.
14. Abelian Quotients of the Teichmuller Modular Group, Journal d'Analyse, 1967, 28, pp. 227-244.
15. Deformations and Liftings of Finite Commutative Group Schemes (with F. Oort), Inventiones Mathematicae, 1968, 5, pp. 317-334.
16. Periods of Moduli Spaces of Bundles on Curves (with P. Newstead), Amer. J. of Math., 1968, 90, pp. 1200-1208.
17. Enriques' Classification of Surfaces in Char. p, I, in Global Analysis (papers in honor of K. Kodaira), Spencer and Iyanaga editors, U. of Tokyo Press, 1969, pp. 325-339.
18. Bi-extensions of Formal Groups, in Algebraic Geometry, Oxford University Press, 1969, pp. 307-322.
19. A Note on Shimura's paper "Discontinuous Groups and Abelian Varieties", Math. Annalen, 1969,181, pp. 345-351.
20. Rational Equivalences of 0-cycles on Surfaces, J. of Math. of Kyoto Univ., 1969, 9, pp. 195-204.
21. * The Irreducibility of the Space of Curves of Given Genus (with P. Deligne), Publ. Math. De l'I.H.E.S., 1969, 36, pp. 75-109.
22. Varieties Defined by Quadratic Equations, in Questions on Algebraic Varieties, C.I.M.E., 1969, publ. by Editioni Cremonese, 1970.
23. 6 Appendices to Algebraic Surfaces, by O. Zariski, 2nd edition, Springer-Verlag, 1971.
24. Theta Characteristics of an Algebraic Curve, Annales de l'Ecole Norm. Sup., 1971, pp. 181-192.
25. A Remark on Mahler's Compactness Theorem, Proc. Amer. Math. Soc., 1971., 28, pp. 289-194.
26. The Structure of the Moduli Spaces of Curves and Abelian Varieties, Actes du Congress Int. du Math., Nice, 1970; Gauthier-Villars, 1971.
27. An Analytic Construction of Degenerating Curves Over Complete Local Rings, Composito Math., 1972, 24, pp. 129-174
28. An Analytic Construction of Degenerating Abelian Varieties over Complete Rings, Composito Math., 1972, 24, pp. 239-272.
29. Some Elementary Examples of Unirational Varieties which are not Rational (with M. Artin), J.London Math. Soc., 1972, 25, pp. 75-95.
30. Introduction to the Theory of Moduli (with K. Suominen), in Algebraic Geometry, Oslo 1970, F. Oort editor, Wolters-Noordhoff, 1972, pp. 171-222.
31. Introduction to Oscar Zariski: Collected Works, vol. I, MIT Press, 1972 and vol. II, MIT Press, 1973.
32. A Rank 2 Vector Bundle on P4 with 15,000 Symmetries (with G. Horrocks), Topology, 1973, 12, pp. 63-81.
33. An Example of a Unirational 3-fold which is not Rational, Accad. Naz. dei Lincei, 1973.
34. A Remark on the Paper of M. Schlessinger, in Complex Analysis, 1972, Rice University Studies, 1973, pp. 113-117.
35. Prym Varieties I, in Contributions to Analysis, Academic Press, 1974, pp. 325-350.
36. A New Approach to Compactifying Locally Symmetric Varieties, in Discrete Subgroups of Lie Groups, (Proc. of International Colloquium Bombay, 1973), Oxford University Press, 1975, pp. 211-224.
37. Matsusaka's Big Theorem (with D. Lieberman), in Algebraic Geometry, Arcata 1974, AMS Proc. of Symposia in Pure Math., 29, 1975, pp. 513-530.
38. The Self-Intersection Formula and the "Formule-Clef" (with A.T. Lascu and D.B. Scott), Math. Proc. Camb. Phil. Soc., 1975, 78, pp. 117-123.
39. Pathologies IV, Amer. J. of Math., 1975, 97, pp. 847-849.
40. Hilbert's 14th Problem - The Finite Generation of Subgroups such as Rings of Invariants, in Proc. of a Conference on Hilbert's Problems, (Dekalb, 1974), Amer. Math. Society, 1976.
41. The projectivity of the moduli space of stable curves, I: Preliminaries on "det" and "Div", Math. Scand., 1, 1976, pp.19-55.
42. Enriques Classification of Surfaces in Char. p, III (with E. Bombieri), Invent. Math., 1976, 35, pp. 197-232.
43. Enriques Classification of Surfaces in Char. p, II (with E. Bombieri, in Complex Analysis and Algebraic Geometry, Baily and Shioda editors, Cambridge Univ. Press, 1977, pp. 23-42.
44. Stability of Projective Varieties, Monographie No. 24 de L'Enseignement Math., 23, 1977, pp. 39-110.
45. Hirzebruch's Proportionality Theorem in the non-compact case, Invent. Math., 1977, 42., pp. 239-272.
46. An Algebro-Geometric Construction of Commuting Operators and of Solutions to the Toda Lattice Equation, Korteweg de Vries Equation and Related Non-Linear Equations, in Proc. of the Int. Symp. on Alg. Geom., (Kyoto, 1977), Kinokuniya, Tokyo 1978, pp.115-153.
47. Some Footnotes to the Work of C.P. Ramanujam, in C.P. Ramanujam- A Tribute, Studies in Math. No 8, Tata Institute of Fundamental Research, 1978, pp.247-262.
48. The Work of C.P.Ramanujam in Algebraic Geometry, in C.P. Ramanujam- A Tribute, Studies in Math. No 8, Tata Institute of Fundamental Research, 1978, pp.8-10.
49. An Instinct for the Key Idea (with John Tate), Science, 1978, 202, pp. 737-739.
50. An Algebraic Surface with K ample, (K2) = 9, pg = q = 0, Amer. J. of Math., 1979, 101, pp. 233-244.
51. The Spectrum of Difference Operators and Algebraic Curves (with Pierre Van Moerbeke), Acta Math., 1979, 143, pp. 93-154.
52. * On the Kodaira Dimension of the Moduli Space of Curves (with Joe Harris and an appendix by William Fulton), Inv. Math., 1982, pp.23-88.
53. On the Kodaira Dimension of the Siegel Modular Variety, in Algebraic Geometry - Open Problems, (Ravello, 1982), Lecture Notes in Mathematics 997, Springer-Verlag 1983, pp.348-375.
54. * Towards an Enumerative Geometry of Moduli Space of Curves, in Arithmetic and Geometry, edited by M. Artin, J. Tate, Birkhauser-Boston, 1983, pp.271-326.
55. A Stratification of the Null Cone via the Moment Map (with Linda Ness), Amer. J. of Math., 106, 1984, pp.1281-1329.
56. Oscar Zariski: 1899-1986, Notices of the Amer. Math. Society, 33, 1986, pp.891-894.
57. Oscar Zariski and his Work, AMS-MAA joint meeting, 1988, VHS cassette, Amer. Math. Society, 1988.
58. Foreword for non-mathematicians, in The Unreal Life of Oscar Zariski, by Carol Parikh, Academic Press, 1990.
59. What can be Computed in Algebraic Geometry? (with Dave Bayer), in Computational Algebraic Geometry and Commutative Algebra, ed. D.Eisenbud & L.Robbiano, Camb Univ. Press, 1993, pp. 1-48.

PhD Students in Algebraic Geometry:

1966 John Fogarty, Some remarks on Hilbert Schemes
1967 Tadao Oda, Abelian varieties over a perfect field and Dieudonne modules
1968 Leslie Roberts, Algebraic K1 of vector bundles
1969 Joel Roberts, Ordinary singularities of projective varieties
1969 Steve Gewirtz, Picard scheme of a quotient problem
1969 Birger Iverson, Numerical invariants and multiple planes
1971 Jonathon Wahl, Deformations of branched covers and equisingularity
1971 Finn Knudsen, Towards projectivity of thew space of moduli of stable curves
1972 David Harris, A study of 3 dimensional principally polarized abelian varieties
1972 Stacy Langton, Valuative criterion of families of vector bundles on algebraic varieties
1972 Mary Schaps, Non-singular deformations of space curves using determinental schemes
1973 Bernard Saint-Donat, Projective models of curves and K3 surfaces
1973 Stephen Crick, Local moduli of abelian varieties
1973 Jerome Myers, Schottky groups over fields complete with respect to discrete valuations
1974 Henry Pinkham, Deformations of algebraic varieties with Gm-action
1975 Robert Fisher, Endomorphisms of abelian schemes
1975 Ulf Persson, On degenerations of algebraic surfaces
1975 Linda Ness, Curvature of algebraic plane curves
1975 Avner Ash, Polyhedral reduction theorems in self-adjoint homogeneous cones
1975 Larry Griffith, Cohomology of flag varieties in characteristic p
1975 Y.-S. Tai, On arithmetic quotients of bounded symmetric domains
1978 Ian Morrison, Projective stability of ruled surfaces
1978 Henri Gillet, Applications of algebraic K-theory to intersection theory
1978 William Lang, Quasi-elliptic surfaces in characteristic 3
1983 Amnon Neeman, Topics in algebraic geometry
1983 Emma Previato, Hyperelliptic curves and solitons
1983 Michael Stillman, Construction of holomorphic differential forms on the moduli space of abelian Varieties
1984 Ching-Li Chai, Compactification of the Siegel moduli schemes
1986 Akihiko Yukie, Applications of equivariant Morse stratifications

5. Math Education, History of Math and Other Work


1. Contributor to Multi-variable Calculus, The Calculus Consortium based at Harvard, Wiley, 1995.
2. Calculus Reform - For the Millions, Notices Amer. Math. Soc., May 1997, pp. 559-563.
3. Trends in the Profession of Mathematics, Mitteilungen der Deutsche Mathemtiker Verein REF, 1998.
4. The Dawning of the Age of Stochasticity, in Mathematics: Frontiers and Perspectives, edited by V.Arnold, M.Atiyah, P.Lax and B.Mazur, AMS, 2000.
5. Mathematics in the Near East, some personal observations, Notices of the AMS, May 2005.
6. Mathematics Belongs in a Liberal Education, The Arts and Humanities in Higher Education, 5, 2006, pp.21-32.
7. Henri's Crystal Ball (with Phil Davis), Notices of the AMS, 55, 2008, pp. 458-466.
8. Why I am a Platonist, Newsletter of European Math. Soc., December 2008, pp. 27-30.
9. Review of Mathematics in India by Kim Plofker, Notices of the AMS, 2010, pp. 385-390.
10. Passages to India, Mathematics Intelligencer, Hyderabad edition, 2010, pp.51-55.
11. What's so Baffling about Negative Numbers - a Cross-Cultural Comparison, in Studies in the History of Indian Mathematics, C. S. Seshadri editor, Hindustan Book Agency (distr. in US by AMS), 2010.
12. Intuition and Rigor and Enriques's Quest, Notices of the AMS, 58, 2011, pp. 250-260.
13. How to Fix Our Math Education (with Sol Garfunkel), OpEd contribution to New York Times, August 25, 2011.
14. "Yu laid out the lands": georeferencing the Chinese Yujitu [Map of the Tracks of Yu] of 1136 (with Alexander Akin), Cartography and Geographic Information Science Journal, Vol 39, No.3, 2012, pp. 154-169."
15. Foreword to The Best Writing on Mathematics 2012, edited by Mircea Pitici, Princteon Univ. Press, eBook ISBN: 9781400844678.

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