Vita of George B

1

Vita of George B. Purdy

Dept. of Electrical Engineering and Computing systems

Mail Location 30

University of Cincinnati

Cincinnati, Ohio 45221

513-556-1811

Education:

B.Sc. With First Class Honors, Mathematics, 1964

University of Reading, England

M.Sc,, Mathematics, 1967

University of Reading, England

Ph.D., Mathematics, 1972

University of Illinois at Urbana-Champaign,

Urbana, Illinois

Employment:

2006-present: Professor, Dept. of Computer Science, University of Cincinnati.

1994--2006: Professor, Dept. of Electrical and Computer Engineering and Computer Science,

University of Cincinnati.

1986--1994: Professor, Dept. of Computer Science

University of Cincinnati.

1979--1986: Associate Professor,

Mathematics Dept., TexasA&MUniversity

College Station, Texas.

1974--1979: Assistant Professor,

Mathematics Dept., TexasA&MUniversity

College Station, Texas.

1972--1974: (Post. Doc.) Research Assistant Professor, Computer Science Dept.

University of Illinois at Urbana-Champaign,

Urbana, Illinois.

1967--1972: Research and Teaching Assistant, Dept. of Mathematics

University of Illinois at Urbana-Champaign,

Urbana, Illinois

Invited Addresses

"Sperner Collections of Rectangles", Special Session on Extremal Problems for Finite Sets, Annual Meeting of the AMS, San Antonio, Texas, Jan 1976.

"Khachian's Algorithm for Linear Programming", University of Wisconsin at Milwaukee, April 1980.

"Software Protection", Sandia Laboratories, July 1981.

"A Scheme for software protection," the Annual IEEE Symposium on Security and Privacy, Oakland, California, March 1982.

"Some Combinatorial Problems in the Plane", New YorkAcademy of Sciences, April 1982.

"Ubiquitous Angles, Distances, and Areas in E4 and E5 , Special Session on Discrete and Computational Geometry, AMS Summer Meeting, Eugene, Oregon, August 1984.

"Ubiquitous angles, distances and areas in Ed", Mathematisches Forschungsinstitut, Oberwohlfach, Germany, October 1984.

"Modular arithmetic, p-adic analysis, and VLSI", SIAM Fall meeting, Tempe, Arizona, Oct. 1985. (One hour talk.)

"Some extremal problems in geometry", Mathematisches Forschungsinstitut, Oberwohlfach, Germany, Feb 1987.

"One-way functions, authentication schemes, and zero knowledge proofs." University of New YorkGraduateCenter, March 1987.

"Points, lines, and zero knowledge proofs", Courant Institute of Math. Sciences, New York city, May 1987.

Workshops Invited to:

The 2006 Snowbird Workshop on Discrete and Computational Geometry, Snowbird Utah.

Conferences Organized:

Special Session on Extremal Problems in Combinatorial Geometry, AMS Summer meeting, Ann Arbor, Michigan, August 1980.

Special Session on the Geometry of Configurations, AMS Summer Meeting, Laramie, Wyoming, August 1985.

Research Publications:

1. Paul T. Bateman, G.Purdy, S.S. Wagstaff, Jr.,"Some numerical results of Fekete polynomials", The Mathematics of Computation, Vol 29, No. 129, pp. 7-23, (1975).

2. Paul Erdos and G.Purdy, "Some extremal problems in geometry", J. Combinatorial Theory, Vol 10, pp. 246-252 (1971).

3. G.Purdy, "The lattice triple packing of spheres in Euclidean Space", Trans. AMS, Vol 181, pp. 457-470 (July 1973).

4. G.Purdy, "Some extremal problems in geometry", Discrete Math, Vol 7, pp. 304-315 (1974).

5. G.Purdy, "A high security log-in procedure", Communications of the ACM, Vol 17, pp. 442-445 (1974).

6. G.Purdy, "Spheres tangent to all the faces of a simplex", J. Combinatorial Theory, Series A,Vol. 17, pp. 131-133 (1974).

7. G.Purdy, "The minimum genus of two-point universal graphs", J. Combinatorial Theory, Series B, pp. 75-77(1979).

8. G.Purdy, "A result on Sperner collections", Utilitas Mathematica 12, pp. 95-99 (1977).

9. Paul Erdos and G.Purdy, "Some extremal problems in Geometry III", Congressus Numerantium XIV, pp. 291-308.

10. G.Purdy, "Planarity of two-point universal graphs", Colloquia Math. Societatis Janos Bolya 10, "Infinite and Finite Sets", Keszthlely, Hungary, Vol III, pp. 1149-1157 (1973).

11. Paul Erdos and G.Purdy, Some Extremal Problems in Geometry IV", Congressus Numerantium XVII, pp. 307-322.

12. G.Purdy, "Polytopes with prescribed contents of (n-1)-facets", Israel J. Math. 30, pp. 54-56 (1978).

13. Paul Erdos and G.Purdy, "Some Combinatorial Problems in the plane", J.Combinatorial Theory--Series A, Vol. 25, No. 2, pp. 201-210 (1978).

14. G.Purdy, "On the number of regions determined by n lines in the projective plane", Geometriae Dedicata 9, pp. 107-109 (1980).

15. Paul Erdos and G.Purdy, "Some extremal problems in geometry V", Congressus Numerantium XIX, pp. 569-578.

16. F.R.K. Chung, P.Erdos, R.L.Graham, D.J. Kleitman, G.Purdy, and D.West, Maximum antichains in rectangular arrays", J. Combinatorial Theory, Series A, 27, pp. 397-400 (1979).

17. G.Purdy, "Triangles in arrangements of lines",Discrete Math. 25, pp. 157-163 (1979).

18. G.R.Burton and G.Purdy, "The directions determined by n points in the plane", J.London Math. Society, (2), pp. 109-114 (1979).

19. G.Purdy, "A proof of a consequence of Diracs conjecture", Geometriae Dedicata 10, pp. 317-321 (1981).

20. P.Erdos, G.Purdy, and E.G.Straus, "On a problem in combinatorial geometry", Discrete Math. 40, pp. 45-52 (1982).

21. G.Purdy, T.Strommer, "The maximal sizes of faces and vertices in an arrangement", Discrete Math. 28, No. 3, pp.331-334(1979).

22. G.Purdy, "Triangles in arrangements of lines II", Proceedings of the AMS 79,pp.77-81(1980).

23. G.Purdy and J.E.Wetzel, "Two-coloring inequalities for Euclidean arrangements in general position", Discrete Math. 31, pp.53-58(1980).

24. G.Purdy, "The independent sets of rank k of a matroid", Discrete Math. 38,pp.87-91(1982).

25. Carla C. Neaderhouser, G.Purdy,"Threshold functions for random hypergraphs", Utilitas Mathematica 17,pp.179-187(1980).

26. Carla C. Neaderhouser, G.Purdy, "On finite sets in Ek in which the diameter is frequently achieved",Periodica Mathematica Hungarica Vol. 13 (3),pp.253-257(1982).

27. G.Purdy, "On three-colored lines in the plane and Ed ", Utilitas Mathematica 19,pp.291-293(1981).

28. R.Entringer and G.Purdy, "How often is a polygon bounded by three sides",Israel J. Math, Vol. 43, No.1, pp.23-27(1982).

29. G.Purdy, G.J.Simmons, and J.Studier,"A scheme for software protection", Proceedings of the 1982 IEEE Symposium on Security and Privacy.

30. G.Purdy, "A carry-free algorithm for finding the greatest common divisor of two integers",Computers and Math. With Applications, Vol. 9 (2),pp.311-316(1983).

31. G.Purdy, "A binary algorithm for solving n by n systems of integer equations",Computers and Math. With Applications Vol. 9 (6), pp.715-719 (1983).

32 G.Purdy, "Some combinatorial problems in the plane.", Discrete Geom. And Convexity (New York, 1982), pp.65-68, Ann. New York Acad. Sci. 440, New York Acad. Science, 440, New York Acad. Sci., New York, (1985).

33. G.Purdy, "Two results about points, lines and planes." Discrete Math. 60, pp. 215-218 (1986).

34. G.R. Blakley, C. Meadows, G.Purdy, "Fingerprinting long forgiving messages", Advances in Cryptology--Crypto '85 (Santa Barbara, Calif., 1985), pp. 180-189, Lecture Notes in Computer Science, 218, (1986), Springer, Berlin.

35. C.Neaderhouser Purdy, G.Purdy, "Integer division in linear time with bounded fan-in", IEEE Trans. On Computers C-36(5),pp.640-644 (1987).

36. G.Purdy, A.Terras, R.Terras, H.Williams, "Graphing L-functions of Kronecker symbols in the real part of the critical strip", Math. Student 47 (1979) no. 2-4, 101-131.

37. C.Purdy and G.Purdy, "Minimal forbidden distance one graphs" Congressus Numerantium 66, pp. 165-171, (1988).

38. G.Purdy and G.J.Simmons, "Zero-knowledge proofs of identity and the veracity of transaction receipts.", Advances in Cryptology--Eurocrypt '88 (Davos, 1988) pp.35-49, Lecture Notes in Computer Science, 330, Springer, Berlin, 1988.

39. Catherine Meadows, G.Purdy, "Summing over a network without revealing summands", BIT 29 no.1,pp 110-125 (1989).

40. Carla N. Purdy, G.Purdy, "The area-time complexity of the greatest common divisor problem: a lower bound." Information Processing Letters 34, no., 1 pp. 43-46, (1990)

41. Paul T.Bateman, A.J..Hildebrand, G.Purdy, "Sums of distinct squares", Acta Arith. 67 no.4,pp.349-380 (1994).

42. Paul Erdos and G.Purdy, "Two combinatorial problems in the plane", Discrete and Computational Geometry, 13 no. 3-4, pp.441-443 (1995).

43. G.Purdy, "A strongly collison-free cryptographic hash function based on factorization", Thirty-Seventh Conference on Combinatorics, Graph Theory and Computing, Boca Raton, March 2006, Congressus Numerantium XLVIII.

44. G. Purdy, C. Purdy, and K.K. Vedantam, "Two binary algorithms for calculating the Jacobi symbol and a fast systolic implementation in hardware", 49th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS 2006), February 2006.

45. P.K.Agarwal, R.Apfelbaum, G.Purdy and M.Sharir, “Similar Simplices in a d-dimensional Point Set,” 23rd Annual ACM Symposium on Computational Geometry, June 6-8, 2007.

Papers Accepted

46. J.W.Smith, G.Purdy, "Bichromatic and Equichromatic Lines in C2 and R2, to appear in the journal: Discrete and Computational Geometry, Springer Verlag, New York.

Papers Submitted

1. G.Purdy, J.W.Smith, "On Finding Ordinary or Monochromatic Intersection Points," available at

2. G.Purdy, J.W Smith, "Lines, Circles, Planes and Spheres," available at

Book Chapters

Paul Erdos and G.Purdy, "Extremal Problems in Combinatorial Geometry", Chapter 17 of Handbook of Combinatorics, Vol I, pp. 809-874, Edited by R.L.Graham, M.Grotschel, L.Lovasz, , North Holland, and MIT Press, 1995.