Publications of James N. Damon

Current information as of Sept. 2019

  1. Doctoral Dissertation: "Thom Polynomials for Contact Class Singularities", Harvard University, 1972.
  2. "The Gysin homomorphism for flag bundles," Amer. J. Math., Vol. XCV, No. 3, Fall 1973, 643-659.
  3. "The Gysin homomorphism for flag bundles: Applications," Amer. J. Math., Vol. 96, No. 2, 246-260.
  4. (with A. Galligo) "A topological invariant for stable map germs," Invent. Math. 32, No. 2, 103-132.
  5. "A partial topological classification for stable map germs," Bull. of Amer. Math. Soc. 82 (1976), 105-107.
  6. "Topological stability in the nice dimensions, np," Bull. of Amer. Math. Soc. 82 (1976), 262-264.
  7. "Comparing C - zero and C - infinity stability," Cargese Conference on Singularities and Their Application, 1975, 137-142, available Univ. of Nice.
  8. "Topological properties of discrete algebra types, I: the Hilbert-Samuel function, " Adv. in Math., supp. ser. Vol. 5 (1978), 83-118.
  9. (with J. Mather) Book on Stability of Mappings, preliminary version.
  10. "The Relation between C - infinity and topological stability," I.M.P.A. Summer School of Singularities, Bol. Soc. Bras. Math. 8 (1977), 1-38.
  11. "Topological properties of discrete algebra types II: Real and Complex algebra types," Amer. J. Math. 101 (1979), 1219-1248.
  12. "Topological properties of real simple germs, curves, and the nice dimensions n > p," Math. Proc. Comb. Phil. Soc. 89 (1981), 457-47l.
  13. "Topological stability in the nice dimensions," Topology 18 (1979), 129-142.
  14. "Investigating the topological stratification of jet spaces," 11th Colloquium of Brazilian Math. Soc. (1977), 633-649.
  15. "On a theorem of Masushima," preprint, six pages.
  16. (with A. Galligo)"On the Hilbert-Samuel partition for stable map germs," Bull. Soc. Math. France, Vol. 111 (1983), 327-358.
  17. "Finite determinacy and topological triviality I," Invent. Math. 62 (1980), 299- 324.
  18. "Finite determinacy and topological triviality II: Sufficient conditions and topological stability," Compositio Math 47 (1982), 101-132.
  19. (with T. Gaffney)"Topological triviality of deformations of functions and Newton filtrations," Invent. Math. 72 (1983), 335-358.
  20. "The unfolding and determinacy theorem for subgroups of A and K," Proc. Sym. Pure Math. 40 (1983) 233-254.
  21. "Topological triviality in versal unfoldings," Proc. Sym. Pure Math. 40 (1983) 255-266.
  22. "The residue formula in Cobordism and decomposition of Thom polynomials," preprint, 31 pages.
  23. "Newton filtrations, monomial algebras and nonisolated and equivariant singularities," Proc. Sym. Pure Math. 40 (1983), 267-276.
  24. "The unfolding and determinacy theorems for subgroups of A and K," Memoirs Amer. Math. Soc. 306 (1984).
  25. "Topological triviality of versal unfoldings of complete intersections," Annales Inst. Fourier 34 (1984) 225-251.
  26. "A Theorem of Mather and the local structure of nonlinear Fredholm maps," Proc. Sym. Pure Math. 45 part I, (1986), 339-352.
  27. "Deformations of sections of singularities and Gorenstein surface singularities," Amer. J. Math. 109 (1987), 695-722.
  28. "Time dependent nonlinear oscillations with many periodic solutions," S.I.A.M. J. Math. Anal. 18 no. 5 (1987), 1294-1316.
  29. "On the Pham example and the universal topological stratification of singularities," in Singularities, Banach Center Publication 20 (1987), Polish Science Publishers, Warsaw, 161-168.
  30. "Topological triviality and versality for subgroups of A and K," Memoirs Amer. Math. Soc. no. 389, (1988).
  31. "Topological equivalence of bifurcation problems," Nonlinearity 1 (1988), 311-331.
  32. "Topological invariants of mu - constant deformations of complete intersection singularities," Quart. J. Math. Oxford 40 (1989), 139-159.
  33. "Topological equivalence for nonisolated singularities and global affine hypersurfaces", A.M.S. Contemp. Math. Vol. 90 (1989), 21-53.
  34. "On the number of branches for real and complex weighted homogeneous curve singularities", Topology 30 (1991), pp 223-229.
  35. "A-equivalence and the equivalence of sections of images and discriminants", Singularity Theory and Its Applications: Warwick 1989, Vol. 1, Springer Lecture Notes, 1462 (1991) pp 93-121.
  36. "Infinitesimal methods in topological equivalence of mappings," to appear in Proceedings of Baku Conference on Topology and Its Applications.
  37. "The versality discriminant and local topological equivalence of mappings," Annales Inst. Fourier 40 (1990), 965-1004.
  38. "Equivariant morsifications and bifurcations for finite groups," in Singularity Theory and Its Applications: Warwick 1989, vol. 2, Springer Lecture Notes, 1463 (1991), pp 80-106.
  39. "G-signature, G-degree, and the symmetries of branches of curve singularities," Topology, 30 (1991) pp 565-590.
  40. (with Andre Galligo) "Universal topological stratification for the Pham example," Bull. Soc. Math. France 121 (1993) pp. 153-181.
  41. (with D. Mond), "A-codimension and the vanishing topology of discriminants" Invent. math. 106 (1991), pp. 217-243.
  42. "Topological triviality and versality for subgroups of A and K, II: Applications and Sufficient Conditions, Nonlinearity 5, (1992) pp 373-412.
  43. "Local Morse theory for solutions to the heat equation and Gaussian blurring," Jour. Diff. Equations, 115 (1995) pp. 368-401.
  44. "Equisingularity for flat deformations and topological rigidity," Jour. Alg. Geo., 3 (1994), 399-409.
  45. "Applications of Singularity Theory to the Solutions of Nonlinear Equations," in Topological Nonlinear Analysis: Degree, Singularity and Variations, ed. M. Matzeu and A. Vignoli, Prog. Nonlinear Differential Equations and Applications, Vol. 15 (1995) Birkhauser, 178-302.
  46. "A Bezout Theorem for Determinantal Modules," Compositio Math., 98 (1995) 117-139.
  47. "Higher multiplicities and almost free divisors and complete intersections", Memoirs of AMS, Vol. 123, #589 (1996).
  48. "Local Morse Theory for Gaussian Blurred Functions in "Gaussian Scale Space Theory," ed J. Sporring, et al., Series in Comp. Science and Vision vol 8, Kluwer Acad. Publ. (1997) 147-163 .
  49. "Generic properties of solutions to partial differential equations," Arch Rat. Mech. Anal. 140 (1997) 353-403.
  50. "Singular Milnor Fibers and Higher Multiplicities for Nonisolated Complete Intersections," Int. Sem Sing. and Complex Geometry, AMS-IP Studies Adv. Math. vol 5 (1997), 28-53.
  51. "Singularities with Scale Threshold and Discrete Functions Exhibiting Generic Properties", Proc. Int. Workshop on Real and Complex Singularities, Sao Carlos, Maria Ruas Ed., Math. Contemp. vol 12, 1997, 45-65
  52. "Generic Structure of Two Dimensional Images under Gaussian Blurring", SIAM Jour. Appl. Math 59, 1998, 97-138.
  53. "On the Legacy of Free Divisors: Discriminants and Morse Type Singularities", Amer. Jour. Math. 120, 1998, 453-492.
  54. "A Global Weighted Version of Bezout's Theorem ", "Arnol'dFest", Fields Communications Series 24 (1999) 115-129
  55. "Ridges and Cores for Two Dimensional Images", Jour. Math. Imag and Vision 10, (1999) 163-174.
  56. "Critical points of Affine Multiforms on the Complements of Arrangements", Singularity Theory, Ed J.W.Bruce and D. Mond. Lond.Math. Soc. Lecture Notes, 263 (1999) Cambridge Univ. Press, 25-53.
  57. "On the Number of Bounding Cycles for Nonlinear Arrangements", Arrangements-Tokyo-1998, Adv. Stud. Pure Math 27 (2000) 51-72.
  58. "Nonlinear Sections of Nonisolated Complete Intersections", New Developments in Singularity Theory, Eds. D. Siersma et al, NATO Conf. Series vol 21, Kluwer Pub.l (2001), 405-445.
  59. "On the Freeness of Equisingular Deformations of Plane Curve Singularities", Arrangements in Boston: Special Issue, Eds. D Cohen and A. Suciu, Top. and its Appl. 118 (2002), 31-43
  60. (joint with S. Pizer, K. Siddiqi, G. Szekely, and S. Zucker), "Multiscale Medial Loci and Their Properties", IJCV 55 no. 2-3 (2003), 155-179
  61. (joint with P. Dimitrov and K. Siddiqi), "Flux Invariants for Shape", Proc. CVPR (2003) 1063-1069
  62. "On the Legacy of Free Divisors II : Free* Divisors and Complete Intersections", Moscow Math. Jour. 3, Special Issue in honor of V. I. Arnol'd (2003) 361-395
  63. "On the Smoothness and Geometry of Boundaries Associated to Skeletal Structures I: Sufficient Conditions for Smoothness ", Annales Inst. Fourier 53 (2003), 1941-1985
  64. "On the Smoothness and Geometry of Boundaries Associated to Skeletal Structures II: Geometry in the Blum Case ", Compositio Mathematica 140 no. 6 (2004) 1657-1674
  65. "Determining the Geometry of Boundaries of Objects from Medial Data ", IJCV 63 no. 1 (2005) 45-64
  66. "On the Legacy of Free Divisors III : Functions and Divisors on Complete Intersections", Oxford Quart. Jour. Math. 57 (2006) 49-79
  67. (joint with Q. Han and S. Pizer) "Interpolation in Discrete Single Figure Medial Objects" Proc. MMBIA '06 (2006) 85 - 92
  68. "Global Medial Structure of Regions in R^3", Geometry and Topology Vol 10 (2006) 2385- 2429
  69. joint with X. Chen, E. Cohen, and R. Riesenfeld,"Theoretically based Algorithms for Robustly Tracking Intersection Curves of Deforming Surfaces", Proc. GMP '06 Springer LNCS 4077 (2006) 101-114
  70. Editor (joint with Jean Paul Brasselet, Le Dung Trang, and Mutsuo Oka)" Singularities in Geometry and Topology", Proc. 2005 ICTP Trieste Singularity Summer School and Workshop, World Scientific Publ. (2007)
  71. "Global Geometry of Regions and Boundaries via Skeletal and Medial Integrals" ,Comm. Anal. and Geom.15 No.2 (2007) 307-358
  72. "Tree Structure for Contractible Regions in R^3", IJCV 74 no. 2 (2007) 103-116
  73. joint with X. Chen, E. Cohen, and R. Riesenfeld, "Theoretically based Algorithms for Robustly Tracking Intersection Curves of Deforming Surfaces", Computer-Aided Design 39 No. 5 (2007) 389-397
  74. joint with T. Terriberry, S. Joshi, G. Gerig, and S. M. Pizer, "Population Based Fitting of Medial Shape Models with Correspondence Optimization", Proc. IPMI, LNCS 4584 (2007) 700-712
  75. joint with Qiong Han, D. Merck, J. Levy, C. Villarruel, E. L. Chaney, and S. M. Pizer "Geometrically Proper Models in Statistical Training", Proc. IPMI, LNCS 4584 (2007) 751-762
  76. "Swept Regions and Surfaces: Modeling and Volumetric Properties", Conf. Comput. Alg. Geom. in honor of Andre Galligo, Theor. Comp. Science 392 (2008) 66-91
  77. "Geometry and Medial Structure", chapter of book, Eds.S. Pizer and K. Siddiqi, "Medial Representations: Mathematics, Algorithms, and Applications", Vol. 37 Springer/Kluwer series Comp. Imag. and Vision, Springer-Verlag 2008
  78. joint with S. Musuvathy, J-K. Seong, and E. Cohen "Tracing Ridges on B-spline Surfaces", Proc. 2009 SIAM/ACM Conf. Geom. and Phys. Modeling, ACM (2009) 55-66
  79. joint with P.Giblin and G.Haslinger "Local Image Features Resulting from 3-Dimensional Geometric Features, Illumination, and Movement:I", IJCV vol 82(1) (2009) 25-47
  80. joint with P.Giblin and G.Haslinger "Local Image Features Resulting From 3-Dimensional Geometric Features, Illumination, and Movement: II", SIAM Jour. Imaging Sciences vol 4 no 1 (2011) 386-412
  81. joint with S. Musuvathy, J-K. Seong, and E. Cohen "Principal Curvature Ridges and Geometrically Salient Regions of Parametric B-spline Surfaces", Computer-Aided Design 43(7) (2011) 756-770
  82. joint with B. Pike, "Solvable Group Representations and Free Divisors whose Complements are K(\pi, 1)'s", Proc. Valencia Conf. Generic Geom.in Top. and its Appl. 159 (2012) 437-449
  83. joint with S. Musuvathy and E. Cohen "Computing the Medial Axis of Generic 3D Regions Bounded by B-spline Surfaces", Computer-Aided Design 43(11) (2011) 1485-1495
  84. joint with S. Pizer,D. Goswami, J. Vicory, R. Chaudhuri, X. Zhao, S. Huckemann, S. Marron, "Nested Sphere Statistics of Skeletal Models", Innovations for Shape Analysis, Eds. M. Breuss, A. Bruckstein, and P. Maragos, Mathematics and Visualization series, Springer-Verlag (2013) 93-115.
  85. joint with J.S. Marron, "Backwards Principal Component Analysis and Principal Nested Relations" Jour. Math. Imag. Vision 50 (2014) 107-114
  86. joint with B. Pike,"Solvable Groups, Free Divisors and Nonisolated Matrix Singularities I:Towers of Free Divisors" Annales Inst. Fourier 65 no.3 (2015) 1251-1300
  87. joint with B. Pike,"Solvable Groups, Free Divisors and Nonisolated Matrix Singularities II: Vanishing Topology" Geometry and Topology 18 no. 2 (2014) 911-962
  88. "Semi-Coherence for SemiAnalytic Sets and Stratifications and Singularity Theory of Mappings on Stratifications" Proc. CIRM Conf. Geom. and Top. of Sing. Spaces, Jour. of Singularities vol 13 (2015) 42-56
  89. "Topology of Exceptional Orbit Hypersurfaces of Prehomogeneous Spaces"Jour. of Topology vol. 9 (3) (2016) 797-825
  90. joint with P. Giblin and G. Haslinger, "Local Features in Natural Images via Singularity Theory", Springer Lect. Notes in Mathematics vol 2165 (2016) 255 pages
  91. joint with Liyun Tu, Jared Vicory, Shireen Elhabian, Beatriz Paniagua, Juan Carlos Prieto, Ross Whitaker, Martin Styner and Stephen M. Pizer, "Entropy-based Correspondence Improvement of Interpolated Skeletal Models" Computer Vision and ImageUnderstanding 10 (2016) p 151- 163
  92. joint with E. Gasparovic, "Modeling Multi-object Configurations via Medial/Skeletal Linking Structures", IJCV 124 (2017) 255-272
  93. joint with E. Gasparovic, "Medial/Skeletal Linking Structures for Multi-Region Configurations", Memoirs of Amer. Math. Soc. vol 250 No. 1193 (2017)
  94. "Schubert Decomposition for Milnor Fibers of the Varieties of Singular Matrices" Special issue in honor of E. Brieskorn, Jour. of Singularities vol 18 (2018) 358-396
  95. joint with Ruibin Ma, Qingyu Zhao, Rui Wang, Julian Rosenman, and Stephen Pizer, "Deforming generalized cylinders without self-intersection bymeans of a parametric center curve" Computational Visual Media 4 No. 4 (2018) p 305-321
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