Professor James Damon

I am a Professor in the Mathematics Department.

Education

B.A. Dartmouth 1967
Diploma in Advanced Math Oxford 1969
Ph.D. Harvard 1972 (Adviser : John Mather)

How to find me.

My office is in Phillips Hall 374. My office phone number is: (919) 962-9617.
You can also email me at jndamon@math.unc.edu.

My research interests

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

I am a member of the AMS

Recent Preprints

"On the Number of Bounding Cycles for Nonlinear Arrangements", to appear Arrangements-Tokyo-1998, Adv. Stud. Pure Math.

"On the Freeness of Equisingular Deformations of Plane Curve Singularities", to appear Top. and Appl.

"On the Legacy of Free Divisors II : Free* Divisors and Complete Intersections", preprint

"On the Legacy of Free Divisors III : Functions and Divisors on Complete Intersections", preprint

"Nonlinear Sections of Nonisolated Complete Intersections", NATO Adv. Stud. Inst. , preliminary vers.

Recent Publications

"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.

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

"A Global Weighted Version of Bezout's Theorem ", "Arnol'dFest", 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

" 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.

" 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: 9 February 2000