B.A. Dartmouth 1967

Diploma in
Advanced Math Oxford 1969

Ph.D. Harvard 1972 (Adviser :
John Mather)

My office is in Phillips Hall 300. My office phone number is: (919) 962-9617.

You can also email me at jndamon@math.unc.edu.

My research has been in the area of singularity
theory and its application to nonlinear problems. It has
specifically concerned :

1) the relation between smooth and
topological stability of mappings

2) establishing the basic
theorems of singularity theory (unfolding, determinacy theorems, and
infinitesimal characterizations of local stability) for equivalences
preserving additional structures for smooth or holomorphic
mappings

3) establishing topological analogues of these
theorems with applications to topological stability and
equisingularity

4) applications to invariants and
classification for bifurcation theory

5) local structure of
nonlinear Fredholm operators

6) singular Milnor fibers and
their applications for nonisolated complete intersections, including
discriminants and nonlinear arrangements of hypersurfaces

7)
determining the freeness of discriminants and bifurcations sets for
versal unfoldings for general equivalence groups

8) solvable group representations yielding free divisors, and
their application to determining the vanishing topology of nonisolated
matrix singularities

9) Topology of exceptional orbit hypersurfaces
of prehomogeneous spaces, including the varieties of m x m singular matrices,
which are general, symmetric or skew-symmetric

10)singularity theory for solutions to PDE's with applications to
computer medical imaging

11) scale-based methods for
computer imaging

12) local and relative geometry of objects
and their boundaries from medial data; global geometry via skeletal
and medial integrals, and characterizing complexity of 3D regions via
graph structures

13) the analysis of multi-object configurations
via medial/skeletal linking structures capturing both shape and geometry of
individual objects and the positiona lgeometry of the configuration

14) determining the evolving self-intersections
of evolving surfaces defined by splines and the application to computing
medial axes for regions defined by splines

15) using singularity theory for mappings on special semianalytic
stratifications to determinine the local structure in natural images allowing
shade/shadow, geometric features, and apparent contours, for both stable views
and transitions under viewer movement.

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, (formerly titled "Characterizing Stable Local Features of Illuminated Surfaces and Their Generic Transitions from Viewer Movement"

Addenda to "Local Image Features
Resulting From 3-DimensionalGeometric Features, Illumination, and Movement: II"

Visibility Diagrams for Corner Transitions;
Animated Corner Transitions

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

"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

"Tree Structure for Contractible Regions in R^3", IJCV 74 no. 2 (2007) 103-116,

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.

"Determining the Geometry of Boundaries of Objects from Medial Data ", IJCV 63 no. 1 (2005) 45-64

joint with P. Dimitrov and K. Siddiqi, "Flux Invariants for Shape", Proc. CVPR (2003) 1063-1069

"Ridges and Cores for Two Dimensional Images", Jour. Math. Image and Vision 10, (1999) 163-174.

"Local Morse theory for Gaussian blurred functions", in "Gaussian Scale Space Theory ", Ed. J. Sporring et al., Kluwer Series in Comp. Science and Vision, Vol. 8, Kluwer Acad. Publ., (1997) 147-163.

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)

"Global Medial Structure of Regions in R^3", Geometry and Topology Vol 10 (2006) 2385- 2429

"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.

"A Global Weighted Version of Bezout's Theorem ", "Arnol'd Fest", Fields Communications Series 24 (1999) 115-129

"On the Legacy of Free Divisors: Discriminants and Morse Type Singularities", Amer. Jour. Math. 120, 1998, 453-492.

"Generic Structure of Two Dimensional Images under Gaussian Blurring", SIAM Jour. Appl. Math 59, 1998, 97-138.

"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

" Generic properties of solutions to partial differential equations", Arch. Rat. Mech. Anal. 140 (1997), 353-403.

" Singular Milnor fibers and higher multiplicities for nonisolated complete intersections", Int'l Sem. Sing. and Complex Geometry, AMS-IP Studies Adv. Math., Vol. 5 (1997), 28-53.

"Higher multiplicities and almost free divisors and complete intersections", Memoirs of the AMS, vol.123, no. 589 (1996)

"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 Equatiions and Applications, Vol.15 (1995), Birkhauser, 178-302.

" A Bezout theorem for determinantal modules ", Compositio Math. 98 (1995), 117-139.

Here is a Complete publication list

For comments/suggestions about this page, mail

jndamon@math.unc.edu

Last
modified: 1 September 2015