Tzuong-Tsieng Moh
PROFESSIONAL EXPERIENCE
Assistant Professor Purdue University 1969-71
Member Institute for Advanced Study 1971-72
Assistant Professor University of Minnesota 1972-75
Associate Professor University of Minnesota 1975-76
Associate Professor Purdue University 1975-83
Professor Purdue University 1983-
Visiting Professor Summer Inst., Beijing, China 1984
Visiting Professor National Taiwan U (Summer) 1985
Visitor Harvard U (Spring Semester) 1986
Visitor RIMS Kyoto University (6 weeks) 1986-87
Member MSRI, Berkeley, CA 1992
RESEARCH INTERESTS
Commutative algebra
Algebraic geometry
Power Series
Fourier Seriers
Summability
SELECTED PUBLICATIONS
2.Galois theory of power series rings. American Journal of
Mathematics. Volume 92, 1970, pp. 919-950.
3.(with S. S. Abhyankar) A reduction theorem for divergent
power series. Journal fur die reine und angewandte Mathematik.
Volume 241, 1970, pp. 27-33.
4.On a general Tauberian theorem. Proceedings of the American
Mathematical Society. Volume 36, 1972, pp. 167-172.
5.On characteristic pairs of algebraic plane curves of
characteristic p. bulletin of the Institute of Mathematics,
Academia Sinica. Volume 1, 1973, pp. 75-91.
6.(with S. S. Abhyankar) Newton-Puiseux expansion and generalized
Tschirnhausen transformation I. Journal fur die reine und angewandte
Mathematik. Volume 260, 1973, pp. 47-83.
7.(with S. S. Abhyankar), Newton-Puiseux expansion and generalized
Tschirnhausen transformation II.Journal Fur die reine und angewandte
Mathematik. Volume 261, 1973, pp. 29-53.
8.On analytic irreducibility at of a pencil of curves. Proceedings
of the American Mathematical Society. Volume 44, 1974, pp. 22-24.
9.On the unboundedness of generators of prime ideals in power
series rings of three variables. Journal of the Japan Mathematical
Society. Volume 26, 1974, pp. 722- 734.
10.(with S. S. Abhyankar) Embeddings of the line in the plane.
Journal fur die reine und angewandte Mathematik. Volume 276, 1975,
pp. 184-l66.
11.On approximate roots of a polynomial. Journal fur die reine und
angewandte Mathematik. Volume 278, 1974, pp. 301-306.
13.On Weierstrass points of analytic curves and a conjecture of
Mumford. Bulletin of the Institute of Mathematics, Academia Sinica.
Volume 7, 1979.
14.(with W. Heinzer) A generalized Luroth Theorem for curves.
Journal of the Japan Mathematical Society. Volume 31, 1979, pp. 85-86.
17.On the concept of approximate roots for algebra. Journal of
Agebra. Volume 65, 1980, pp. 347-360.
19.On the bound for DeFranchis-Severi Theorem. Michigan Mathematical
Journal 28, (1981). pp. 153-155.
22.On two fundamental theorems for the concept of approximate roots. J.
Japan Math. Soc., Vol 34, No. 4, 1982, pp. 637-652.
23.On the Jacobian conjecture and the configuration of roots. J. fur
die Reine and angewandte Mathematik, 340, 1983, pp. 140-212.
24.Set-theoretic complete intersections. Proc. Amer. Math. Soc.,
Vol. 94, No. 2, June 1985, pp. 19-21.
25: On a Stability theorem for local uniformixation in characteristic
p, RIMS, Kyoto U. Vol23, No 6. 1987, pp965-973
29.On the classification problem of embedded lines in
characteristic p. Algebraic Geometry and Commutative Algebra
in honor of Masayoshi Nagata, Kinokuniya Co. Tokyo, Vol. 1, 1989,
pp. 267-279.
30.Quasi-canonical uniformization of hypersurface singularities
of characteristic zero. Communication of Algebra, Vol 20 (11),
1992, pp. 3207-3251.
31.On a Newton polygon approach to the uniformization of
singularities of characteristic p., Bulletin of La Rabida
Symposium, 1995 pp 53-101
32.On Jacobian Conjecture. Algebra and Grometry, International
press, 1997
33.A Public Key System with Signature and Master Key Functions.
Communications in Algebra, 27(5), 2207-2222 (1999).
34.A Fast Public Key System With Signature And Master Key Functions.
CrypTEC'99 (Proc. International Workshop on Cryptographic
Techniques & E-commerce), City University of Hong Kong Press, July, 1999.
35. An Application of Algebraic Geometry to Encryption: Tame
Transformation Method. Revista Matematica Iberoanericana, Vol 19 No. 2
Ano 2003.
37. On the Signature Scheme TTMs,
The monograph entitled ``Affine Algebraic Geometry'' in honor of
Professor Masayoshi Miyanishi published by Osaka U, Japan.
2006. .
38.Comment on a Paper by Yucai Su On Jacobian Conjecture (Dec 30, 2005)
Arxiv, math.AG/0512472, 2006.
A short description of my researchs is as follows,
(1): Algebraic Geometry: Abhyankar-Moh theorem, [6],[7],[10].
(2): Algebraic Geometry: Study of plane curves in characteristic p,
[2],[5].
(3): Commutative Algebra: Moh's model, [9].
(4): Commutative Algebra: Approximate roots, [11],[17],[22].
(5): Fourier Analysis: Beurling-Moh theorem, [4].
(6): Algebraic Geometry: Jacobian Conjecture, [23],[38].
(7): Algebraic Geometry: Resolution of Singularities, [30],[31].
(8): Encryption: [33],[34],[35],[37] with patents on TTM
crytosystem.
Besides the above, I believe that I am familiar with "Coding
theory". I have taught two semesters' graduate courses on it.
BOOKS
"Algebra"
World Scientific Publishing Co 1993 (viii+350 pages)
Coding Theory. In preparation.
INVITED ADDRESSES:
1. Notre Dame University 1969
2. Louisiana State University 1970
3. Michigan State University 1970
4. AMS Meeting, Chicago 1971
5. AMS Meeting, Kansas University 1972
6. AMS Meeting, Northwestern University 1973
7. Conference, University of Minnesota 1974
8. Kentucky University 1974
9. AMS National Meeting, Washington D.C. 1975
10. AMS Meeting, Chicago 1975
11. Conference, Northwestern University 1975
12. AMS Meeting, Tallahassee, Florida 1976
13. Kyoto University, Japan 1977
14. Michigan State University 1979
15. AMS Meeting, Wisconsin 1980
16. National Taiwan University, R.O.C. 1982
17. Academia Sinica, R.O.C. 1982
18. Ching-Hwa University, R.O.C. 1982
19. AMS Meeting, Northwestern University 1983
20. Fudan University, Shanghai, China 1984
21. Academia Sinica, Beijing, China 1984
22. Peking University, Beijing, China 1984
23. AMS Meeting, Massachusetts 1985
24. Harvard University 1986
25. Oakland University, Detroit, Michigan 1986
26. Washington University, St. Louis, MI 1986
27. Tokyo Symposium, Tokyo, Japan 1987
28. University of Illinois at Chicago 1987
29. Conference, Univ of Illinois at Chicago 1988
30. Academia Sinica, Beijing, China 1988
31. AMS Meeting, Kansas 1988
32. Conference, St. Louis, Missouri 1989
33. Rabida Symposium, La Rabida, Spain 1991
34. AMS Meeting, Springfield, Missouri 1992
35. UC Berkeley 1992
36. Technion, Israel 1993
37. Conference, NTU 1996
38. AMS Meeting, Louisville, KY 1998
39 MAGC meeting, Illinois U 1999
40 Columbia, Mo 2000
41. Peking University 2000
42. Miami University 2001
43: Seville, Spain 2001
44. CERIAS, Purdue U 2002
45. Cincinnati University 2004