VITA 3/16/05



                    DANIEL HENRY GOTTLIEB









EDUCATION



B.S.	University  of California, LA	1959

M.S.	University  of California, LA	1961

Ph.D.	University  of California, LA	1962







PROFESSIONAL EXPERIENCE



Instructor	University of Illinois	1962-64

Mathematician	Institute for Defense Analysis	1964-67

Associate Professor	Purdue University	1967-74

Visiting Professor	Cambridge University	1973-74

Professor	Purdue University	1974-

Visiting Professor	Tel Aviv University	1974

Visiting Professor	University of California, LA	1980

Visiting Professor	Bonn, Sonderforschungsbereich	1981

Visiting Professor	I.H.E.S.	1987-88

Visiting Professor	University of California at Berkeley	1994-95

Member	Newton Institute, Cambridge	November 1994

Member  IPAM at UCLA, Los Angeles       Fall 2001

Visiting Professor      University of California at Los Angeles  2001-2002

Partial retirement    UCLA in Spring



PROFESSIONAL SOCIETIES AND HONORS



AMS

MAA

NDEA Fellow 1959-62





RESEARCH INTERESTS



Algebraic topology

Topology

Robotics

Relativity and Mathematical Physics

History of Mathematics





VITA



Birthdate:  	December 7, 1937

Birthplace:	Hollywood, California

Marital Status	Married, Judith E. Schaper

Children:	Alexander David, Jacob Samuel

Citizenship:	USA



 PUBLICATIONS



  l.	Homotopy and isotopy properties of topological spaces.  Canadian J.

Math. 16 (1964), 561-571.



  2.	(with N. J. Rothman)  Contractibility of certain semigroups.  Bull.

Amer. Math. Soc. 70 (1964), 756-757.



  3.	A new invariant of homotopy type and some diverse applications.

Bull. Amer. Math. Soc. 71 (1965), 517-518.



  4.	A certain subgroup of the fundamental group.  Amer. J. Math. 87

(1965), 840-856.



  5.	A certain class of incidence matrices.  Proc. Amer. Math. Soc. 17

(1966), 1233-1237.



  6.	On fibre spaces and the evaluation map.  Annals of Math. 87 (1968),

42-55.



  7.	Covering transformations and universal fibrations.  Ill. J. Math.

13 (1969), 432-438.



  8.	Evaluation subgroups of homotopy groups.  Amer. J. Math. 91 (1969),

729-756).



  9.	Correction to my paper "On fibre spaces and the evaluation map,"

Annals of Math. 91 (1970), 640-642.



10.	On the construction of G-spaces and applications to homogeneous

spaces.  Cambridge Phil. Soc. 68 (1970), 321-327.



11.	The evaluation map and homology.  Mich. Math. J. 19 (1972), 189-197.



12.	Applications of bundle map theory.  Trans. Amer. Math. Soc. 171

(1972), 23-50.



13.	Homology tangent bundles and universal bundles.  Proc. Amer. Math.

Soc. 36 (1972), 246-252.



14.	Witnesses, transgression, and the evaluation map.  Indiana Math. J.

24 (1975), 825-836.



15.	The total space of universal fibrations.  Pacific J. Math. 46

(1973), 415-417.



16.	(with J. C. Becker)  Coverings of fibrations.  Compositio

Mathematica 26 (1973), 119-128.



17.	Fibre bundles and the Euler characteristic.  J. Differential

Geometry 10 (1975), 39-48.



18.	(with J. C. Becker)  The transfer maps and fibre bundles.  Topology

14 (1975), 1-12.



19.	(with J. C. Becker)  Applications of the evaluation map and

transfer map theorems.  Math.  Ann. 211 (1974), 277-288.

 PUBLICATIONS (CONT.)



20.	(with Andrew Casson)  Fibrations with compact fibres.  Amer. J.

Math. 99 (1977), 159-189.



21.	(with J. C. Becker and Andrew Casson)  The Lefschetz number and

fibre preserving maps.  Bull. Amer. Math. Soc. 81 (1975), 425-427.



22.	(with J. C. Becker)  Transfer for fibrations and duality.

Compositio Mathematica 33 (1976), 107-133.



23.	Fibre bundles with cross-sections and non-collapsing spectral

sequences.  Ill. J. Math. 21 (1977), 176-177.



24.	Fibering suspensions.  Houston J. of Math. 4 (1978), 49-65.



25.	Partial Transfers, Geometric Applications of Homotopy Theory I.

(1977) Lecture notes in Mathematics, #657, Springer Verlag, 255-266.



26.	Lifting actions in fibrations.  Ibid, pp. 217-254.



27.	Poincare Duality and fibrations.  Proceedings of the American

Mathematical Society 76 (1979), 148-150.



28.	The Lefschetz number and Borsuk Ulam Theorems.  Pac. Journal 103

(1982), 29-37.



29.	Transfers, centers, and group cohomology.  Proc. A.M.S. 40 (1983),

157-162.



30.	(with K. B. Lee and M. Ozaydin)  Compact group actions and maps

into K(º,1)-spaces.  Trans. of A.M.S. 287 (1985), 419-429.



31.	The trace of an action and the degree of a map.  Trans. of A.M.S.

293 (1986), 381-410.



32.	On realizing Nakaoka's coincidence point transfer as an S-map.

Illinois J. of Math. 30 (1986), 689-695.



33.	Robots and fibre bundles.  Bulletin de la Societe Mathematique de

Belgique, 38 (1988), 219-223.



34.	Robots and Topology, Proceedings 1986 IEEE International Conference

on robotics and Automation, Volume 3, pp. 1689-1691.



35.	Topology and the Robot Arm.  Acta Applicandae Mathematicae 11

(1988), 117-121.



36.	A de Moivre formula for fixed Point Theory, ATAS do 5∞ Encontro

Brasiliero de Topologia.  Universidade de Sao Paulo, Sao Carlos, S.P.

Brasil 31 (1988), 59-67.



37.	A de Moivre like formula for fixed point theory.  Proceedings of

the Fixed Point Theory Seminar at the 1986 International Congress of

Mathematicians, R.F. Brown (editor), Contemporary Mathematics, Vol. 72,

99-106, AMS Providence, Rhode Island.



38.	On the index of pullback vector fields.  Proc. of the 2nd Siegen

Topology Symposium, August 1987, Ulrich Koschorke (editor), Lecture Notes

of Mathematics, Vol. 1350, 167-170, Springer Verlag, New York City, NY.

 PUBLICATIONS (CONT.)



39.	Splitting off tori and the evaluation subgroup of the fundamental

group.  Israel J. of Math., 66 (1988), 216-222.



40.	Zeroes of pullback vector fields and fixed point theory for bodies.

Algebraic Topology, Proc. of Intl. Conf. March 21-24, 1988, Contemporary

Mathematics, 96, 163-180.



41.	(with Giora Dula)  Splitting off H-spaces and Conner-Raymond

Splitting Theorem.  J. Fac. Sci. Univ. Tokyo, Sec IA, 37 (1990), 321-334.



42.	(with J.C. Becker)  Vector fields and transfers.  Manuscripta

Mathematica, 72 (1991), 111-130.



43.	Lectures on Vector Fields and the Unity of Mathematics.

Proceedings of the Topology and Geometry Research Center, ed. Jin Suk Pak

and Chan-Young, 3 (1993), 87-114.



44.	(with Murad Ozaydin)  Intersection Numbers, Transfers, and Group

Actions.  Topology and its Applications, 55 (1994), 87-100.



45.	(with Murad Ozaydin)  Group Actions and the Singular Set.  Topology

and its Applications, 52 (1993), 51-59.



46.	Vector Fields and Classical Theorems of Topology.  Rendiconti del

Seminario Matematico e Fisico, Milano, 60 (1990), 193-203.



47.	(with Geetha Samaranayake)  The Index of Discontinuous Vector

Fields.  New York Journal of Mathematics, 1 (1994-95), 130-148.



48.	A Gravitational Lens Need Not Produce an Odd Number of Images.  J.

Mathematical Physics, 35 (1994), 5507-5510.



49.	The Odd Image Theorem, Proceedings of the 7th Marcel Grossman

Relativity Conference on Relativity, Stanford, July 1994, Part B; ed. R. T.

Jantzen and G. Mac Keiser:  World Scientific, New Jersey; 1141-1143.



50.	All the Way with Gauss-Bonnet and the Sociology of Mathematics.

American Mathematical Monthly, 103 (1996), 457-469.



51.	Skew Symmetric Bundle Maps.  Contemporary Mathematics, 220 (1998),

117-141.



52.	(with James C. Becker)  Spaces of Local Vector Fields.  Proceedings

of the Vassar Conference Honoring Stasheff's 60th birthday, January 20,

1997, Comtemporary Mathematics, 227 (1999), 21-28.



53.	(with James C. Becker)  A History of Duality in Algebraic Topology.

Chapter 25 of History of Topology, I. M. James, ed., Elsevier, Amsterdam,

1999, 725-745.



54.	Becker-Gottlieb Transfer, Encyclopedia of Mathematics suppliment,

Volume I, Ed. in chief M. Hasewinkel, Kluwer Acad. Publishers, (1997),

89-90.



55.	Book review of "Poincare and the Three Body Problem" by June

Barrow-Green.  The American Mathematical Monthly, 106 (1999), 977-980.



 PUBLICATIONS (CONT.)



56.	The Sullivan conjecture.  Encyclopedia of Mathematics Supp.,

vol.-2., Ed. in chief M. Hasewinkel, Kluwer Acad. Publishers, (2000),

440-441.



57.	Topology and the Non-existence of Magnetic Monopoles, CUBO

Matematica Educacional, Vol. 2 (May 2000), 101-121.



58.	Fields of Lorentz transformations on Space-Time.  Fixed Point

Conference, Sao Paulo (1999), Topology and its Applications, 116, (2001),

102-122. 

59.  Eigenbundles, Quaternions, and Berry's Phase.
         Preprint:  math.AT/0304281

60. Transfers and Periodic Orbits of Homeomorphisms.Preprint math-AT 0408403 

61. Maxwell's Equations, Preprint:arXiv math-ph 040100162.

62.(with Chen-Farng Benjamin) Fixed point indices and manifolds with 
collars (to appear in Fixed Point Theory and Applications)   





INVITED ADDRESSES



   1.	July 1973.  University of California at Santa Barbara, Topology

Conference. The transfer for fibre bundles.



   2.	October 1973.  Cambridge University, Topology Seminar, The transfer

and the evaluation map.



   3.	October 1973.  Oxford University, Topology Seminar.  The transfer

for fibre bundles.



   4.	March 1974.  University of Manchester, Colloquium.  The transfer

for fibrations for homotopy theorists.



   5.	March 1974.  University of Warwick, Colloquium.  The fibration

transfer for differential topologists.



   6.	March 1974.  University of Paris (Orsay), Larry Siebenmann's

Seminar.  The transfer for fibrations.



   7.	June, 1974.  Tel Aviv University, Israel Mathematical Union.  An

application of topology to group theory.



   8.	August 1974.  University of British Columbia, J. F.  Adams Topology

Seminar at the International Congress of Mathematicians.  The transfer for

group theory.



   9.	March 1975.  Rutgers University, Colloquium.  Transfers and group

theory.



 10.	March 1975.  Rutgers University, Topology Seminar.  Transfers and

transgressons.



 11.	August 1975.  Second Annual Topology Mini-Conference, Ohio State

University.  On the Wang exact sequence.



 12.	May 1, 1976.  Midwest Topology Seminar.  Applications of the Wang

exact sequence.

 13.	February 1976.  Indiana Topology Seminar.  Fibering suspensions.



 14.	September 1976.  Indiana Topology Seminar.  Lifting group actions.



 15.	March 1977.  Rutgers Topology Seminar.  Lifting group actions.



 16.	April 1977.  Northwestern Topology Conference.  Partial transfers.



 INVITED ADDRESSES (CONT.)



 17.	September 1977.  Oberwolfach Fixed Point Conference.

Neilsen-Wecken theory and Cyclic homotopies.



 18.	February 1978.  Topology Seminar Rutgers University.  Lefschetz

numbers and the evaluation map.



 19.	February 1978.  University of Mass.  Colloquium.  Lifting group

actions.



 20.	March 1978.  Univ. of Illinois colloquium.  Transfer and evaluation

maps in Topology.



 21.	April 1978.  Notre Dame U. Colloquium.  Transfer and evaluation

maps in Topology.



 22.	June, 1978.  Canadian Summer School at Waterloo Univ.  Lefshetz

numbers and free actions.



 23.	July 1978.  Cambridge Univ. Topology Seminar.  Borsuk Ulam type

theorems. Seminar.  Borsuk Ulam type theorems.



 24.	October 1978.  Florida State Topology Seminar.  Borsuk Ulam type

theorems.



 25.	November 1978.  Memorial University of Newfoundland Colloquium.

Lifting of group actions.



 26.	April 1980.  University of Minnesota, Colloquium.  The transfer and

algebraic topology.



 27.	October 8, 1980.  U.C.L.A. Topology Seminar.  Lefschetz numbers and

free actions.



 28.	October 21, 1980.  Southern California Topology Seminar.  The

transfer and coincidence numbers.



 29.	January 30, 1981.  Bonn Topology Seminar.  Fibering suspensions and

the evaluation map.



 30.	February 12, 1981.  Gottingen Colloquium.  Transfers and the

Borsuk-Ulam theorem.



 31.	April 30, 1981.  Bonn University Oberseminar.  The transfer

homomorphism and the evaluation map.



 32.	May 6, 1981.  Swiss Topology Conference.  Lusanne.  The Umkehr map

and fibrations.

 33.	June 4, 1981.  Topology Seminar of Heidelberg.  The Umkehr map and

fibrations.



 34.	May 1982.  Midwest Topology Seminar.  Notre Dame.  An improvement

of the transfer for fibre bundles.



 35.	June 1982.  Rational Homotopy Conference.  Marseille, France.

Localizing transfers.

 INVITED ADDRESSES (CONT.)



 36.	May 28, 1983.  Topology Seminar.  Peking University.  The trace of

an action and the degree of a map.



 37.	May 28, 1983.  Peking Univeristy Colloquium.  Report on M.

Freedman's work on 4-dimensional manifolds.



 38.	June 24, 1983.  Topology Seminar.  Osaka City Univeristy.  The

trace of an action and the degree of a map.



 39.	June 25, 1983.  Colloquium.  Osaka University.  The trace of an

action and the degree of a map.



 40.	June 27, 1983.  Colloquium.  Kyoto University.  The trace of an

action and the degree of a map.



 41.	January 1984.  U.C.L.A. Topology Seminar.  The trace of an action

and the degree of a map.



 42.	April 1984.  I.U.P.U.I. Colloquium.  The trace of an action and the

degree of a map.



 43.	May 1984.  Workshop on Group Actions.  Princeton University.  The

trace of an action and the degree of a map.



 44.	May 1984.  Boston Topology Seminar M.I.T.  The trace of an action

and the degree of a map.



 45.	May 1984.  Topology Seminar (2 lectures).  Pontifica Universidade

Catolica de Rio de Janiero.  The trace of an action and the degree of a map.



 46.	June 1984.  Topology Seminar.  S„o Paulo University.  The Trace of

an action and the degree of a map.



 47.	July 1984.  AMS Conference at Bowdoin, Maine on Group Cohomology.

The transfer and Group Cohomology.



 48.	July 1984.  Conference on Homotopy Theory.  Minnesota Math.

Institute.  The trace of an action and the degree of a map.



 49.	October 3-4, 1984.  J. Clarence Karcher Lecturer, University of

Oklahoma.  Trace of an action, and In search of the best transfer.



 50.	April 1985.  Topology Seminar, University of Wisconsin.  Robots and

fibre bundles.



 51.	June 1985.  Singapore Topology Conference.  Robots and fibre bundles.



 52.	October 25, 1985.  Colloquium, Cleveland State University.  Robots

and fibre bundles.



 53. 	March 10, 1986.  Colloquium, University of Vermont.  Topology and

applied mathematics.

 INVITED ADDRESSES (CONT.)



 54.	April 10, 1986.  I.E.E.E. Robotics Convention, San Francisco.

Topology and Robots.



 55.	June 2, 1986.  Colloquium, University of Sao Paulo at Sao Carlos.

Degree of a map.



 56.	June 18, 1986.  Colloquium, University of Sao Paulo.  Robots and

Topology.



 57.	July 7, 1986.  Inaugural Address, 5th Brazilian topology

Conference, Sao Carlos, Brazil.  A De Moivre formula for fixed point theory.



 58.	July 17, 1986.  Colloquium, Campenas University.  Robots and topology.



 59.	July 27, 1986.  Colloquium, University Federal de Sao Carlos.  On

the index formula.



 60.	August 5, 1986.  Fixed Point Session at the International Congress

of Mathematicians.  A de Moivre's formula for fixed point theory.



 61.	January, 1987.  Robots and Topology, hour address AMS-MAA meeting

at San Antonio.



 62.	June 3, 1987.  Topology Seminar UCLA.  A fixed formula.



 63.	July 27, 1987.  Siegen Topology Conference.  Vector field indicies,

coincidence numbers, and normal maps.



 64.	October 19, 1987.  Oxford Topology Seminar.  Vector fields.



 65.	October 22, 1987.  Warwick Colloquium.  Vector fields.



 66.	October 23, 1987.  University of Wales Colloquium.  Topology and

robots.



 67.	October 26, 1987.  University of Liverpool Colloquium.  Vector fields.



 68.	October 27,  1987.  University of Manchester Topology Seminar.

Vector fields.



 69.	October 28, 1987.  London Topology Seminar.  Vector fields.



 70.	October 30, 1987.  Cambridge Topology Seminar.  Vector fields.



 71.	November 10, 1987.  Paris Topology Seminar.  Vector fields.



 72.	November 19, 1987.  University of Nantes Colloquium.  Vector fields

and fixed points for bodies.



 73.	December 10, 1987.  Heidelberg Topology Seminar.  Vector fields.



 74.	December 11, 1987.  Heidelberg Colloquium.  Topology and robots.



 75.	January 15, 1988.  Lille Topology Seminar.  Toral splittings and

the evaluation subgroup.

 INVITED ADDRESSES (CONT.)



 76.	May 29, 1988.  Scottish Topology Seminar.  Vector fields.



 77.	November 19, 1988.  Eastern Pennsylvania and Delaware MAA Sectional

Meeting.  Topology and robots.



 78.	February 15-17, 1989.  Clarence J. Karcher Lecturer, Univ. of

Oklahoma, Vector field law I, II.  Splitting Tori off of spaces.



 79.	October 28, 1989.  Indiana MAA Sectional Meeting.  Topology and Robots.



 80.	May 31, 1990.  OberSeminar Heidelberg.  The Law of Vector Fields

and the Gauss-Bonnet Theorem.



 81.	July 6, 1990.  Colloquium, University of Konstantz:  The Law of

Vector Fields and the Gauss-Bonnet Theorem.



 82.	August 16, 1990.  Hawaii Topology Conference.  Miracles and the Law

of Vector Fields.



 83.	April 18, 1991.  Ohio State University Topology Seminar.  The Law

of Vector Fields.



 84.	May 30, 1991.  University of Milano, Colloquium.  Robots and Topology.



 85.	June 3 1991.  University of Milano Topology Seminar.  Intersection

Numbers, Transfers, and Group Actions.



 86.	June 3, 1991.  University of Milano, Seminar.  Discreteness and

Continuity:  Vector Fields and Their Zeros.



 87.	June 14, 1991.  Univerity of Trieste Colloquium.  Topology and the

Robot Arm.



 88.	June 19, 1991.  University of Napoli Seminar.  Discreteness and

Continuity in Mathematics:  Zeros of Vector Fields.



 89.	June 20, 1991.  University of Salerno, Seminar.  Topology and the

Robot Arm.



 90.	June 21, 1991.  University of Roma, Seminar.  Topology and the

Robot Arm.



 91.	June 26, 1991.  University of Torino, Seminar.  Topology and the

Robot Arm.



 92.	June 28, 1991.  University of Milano, Special Conference Lecture.

Vector Fields and the Classical Theorems of Topology.



 93.	August 12, 1991.  University of Oklahoma, J. Clarence Karcher

Lecture.  Intersection Numbers, Transfers, and Group Actions.



 94.	March 4, 1992.  UCLA, Topology Seminar.  Topological Particles and

Radiation.



 95.	June 15, 1992.  Korea University, Informal Seminar.  Splitting of

Tori, 1hr 30 minutes.

 INVITED ADDRESSES (CONT.)



 96.	June 16, 1992.  Korea University, Informal Seminar.  Vector Fields

and the Evaluation Subgroup.



 97.	June 17, 1992.  KAISTR, Teajon, Colloquium.  Robots and Topology.



 98.	June 18, 1992.  Hannam University, Teajon, Colloquium.  Vector

Fields and Topology.



 99.	June 19, 1992.  Seoul National University, Seminar.  Vector Fields

and Topology.



100.	June 23, 1992.  Seoul National University, Seminar.  Classical

Invariants of Homotopy Theory.



101.	June 24, 1992.  Seoul National University, Seminar.  Classical

Invariants of Algebraic Topology.



102.	July 6, 7, 8, 1992.  Kyungpook University, Teagu, Korean Topology

and Geometry Conference.  Vector Fields and the Unity of Mathematics.



103.	July 9, 1992.  Keimyung University, Teagu, Colloquium.  Robots and

Topology.



104.	November 7, 1992.  Midwest Relativity Conference, University of

Chicago.  Topology and the Non-Existence of Magnetic Monopoles, 15 minutes.



105.	July 8, 1994.  Middle East Tech. Colloquium.  Gauss-Bonnet:  From

Thales till Today.



106.	June 9, 1994.  Topology and Geometry Conference.  Lehigh

University, 40 minutes.



107.	July 25, 1994.  7th Grossman Conference.  Stanford University, 20

minutes.



108.	November 23, 1994.  Newton Institute Colloquium.  Topology and

Topological Defects, 1 hour.



109.	February 12, 1997. Geometry, Algebra, and Singularities Seminar.

Northeastern University.  Skew-Symmetric Bundle Maps and Electromagnetism,

1 hour.



110.	February 12, 1996  Topology Seminar.  M.I.T.  What Does the Index

of a Vector Field Classify?, 1 hour.



111.	February 14, 1996.  Basic Notions Seminar.  Northeastern

University.  All the Way with Gauss-Bonnet and the Sociology of

Mathematics, 1 hour.



112.	May 14, 1996.  Seoul National University.  All the Way with

Gauss-Bonnet and the Sociology of Mathematics.



113.	May 14, 1996.  Seoul National University.  Skew Symmetric Maps and

Electromagnetism.



114.	May 15, 1996.  Iwha Women's University.  Skew Symmetric Maps and

Electro-Magnetism.

 INVITED ADDRESSES (CONT.)



115.	May 15, 1996.  Yongsei University.  Skew Symmetric Maps and

Electromagnetism.



116.	May 16, 1996.  Seo Gang University.  The History of Mathematics

from the Topological Point of View.



117.	May 17, 1996.  Korea University.  The History of Mathematics from

the Topological Point of View.



118.	May 20, 1996.  Pusan University.  All the Way with Gauss-Bonnet and

the Sociology of Mathematics.



119.	May 21, 1996.  Inje University.  All the Way with Gauss-Bonnet and

the Sociology of Mathematics.



120.	May 21, 1996.  KAIST in Teajon.  On the Index of Vector Fields.



121.	May 22, 1996.  Chombok University.  The History of Mathematics from

the Topological Point of View.



122.	May 22, 1996.  Chosan University.  On the Index of Vector Fields.



123.	May 24, 1996.  Topology Conference, Korea University.  On the Index

of Vector Fields, 1 hour.



124.	June 14, 1996.  Conference on Higher Homotopy Structures in

Topology and Mathematical Physics, Vassar.  The Space of Local Vector

Fields, 20 minutes.



125.	July 10, 1996.  World Congress of Non-Linear Analysts.  Athens,

Greece.  The Degree of a General Map and an Application to Electrodynamics,

40 minutes.



126.	October 29, 1998.  Colloquium, Calvin College.  Robots, Topology,

Mathematics.



127.	April 9, 1999.  Special Quantum Topology Seminar.  Univ. of

Illinois, Chicago Circle.  Exponentials in Physics and Eigenvalues of

Lorentz Transformations, 1 hour.



128.	July 30, 1999.  Fixed Point Conference.  Univ. of Sao Paolo.

Applications of Topology, 1 hour.



129.	October 18, 2000.  Jewish Studies Lunch Series, Purdue.

Mathematics and the Jewish People, 40 minutes.



130.    October 31, 2001. Colloquium. Univ. of Calif at Riverside.

Mathematics and Physics. 1 hour.

131. Robots and Quaternions (1 hour, first talk)
        Conference on Topology and Robotics at ETH, Zurich     
          June 21 Ð29 2003      

132. Transfers and JiangÕs Nielsen Theory for Periodic Points. ((20minutes)
     Special Session for fixed points at AMS winter meeting, Phoenix, 2004   
         
        
133.  Eigenbundles, Quaternions, and BerryÕs Phase (1 hour)
        International Conference on Homotopy Theory and Related Topics 
         Korea University, Seoul Korea, February 3, 2004
          
134. Transfers  and Periodic orbits ala JaingÕs Neilsen Theory (1 hour)
          International Conference on Homotopy Theory and Related Topics
           Hannan University, Teajon, Korea, February 4, 2004

135.  Fixed Points and Fibrations (50 minutes)
          Fixed Point Theory Conference Memorial University of Newfoundland
          July 1, 2004

136.  Fixed Point Indices and Manifolds with Collars (45 minutes)
          International Conference on Homotopy Theory and Related Topics 
          100 year anniversary for
          Korea University, Seoul Korea, February 1 - 4, 2005




ACTIVITIES 1993



A)	Meetings Attended:

		Midwest Topology Seminar, 1/6/93, Chicago Circle

		9th Pacific Coast Relativity Conference, 3/6/93, Santa Barbara

		Midwest Topology Seminar, 5/17/93, Notre Dame

		Caribbean Summer School for Mathematical Physics,

5/30-6/13/93, Guadeloupe

		Georgia Topology Conference, 7/7-7/13/93, University of Georgia

		Midwest Topology Seminar, 11/6/93, Purdue

		A.M.S. Winter Meetings, 1/11-1/14/94, Cincinnati

 ACTIVITIES 1993 (CONT.)



B)	Outside Talks:

		Gauss Bonnet from Thales til Today, Middle East Tech.,

Aukara, Turkey, 1 1/2 Hours



C)	Department Service:

		I designed a course on the History of Mathematics



D)	Graduate Students:

		Geetha Samaranayake



E)	Editorial Work:

		Refereed Papers and Journals





ACTIVITIES 1994



A)	Meetings Attended:

		AMS Winter Meetings, Cincinnati

		Browder Conference, Princeton NJ, March

		Lehigh Conference, June (40 minute talk)

		7th Marcel Grossman Conference on Relativity, Stanford,

July ( 20 minute talk)

		International Congress of Mathematicians, Zurich, August

		Topological Defects, Newton Institute, Cambridge, November

		Southern California Topology Conference, UCLA, Fall



B)	Sabbatical at UC Berkeley in summer and fall





ACTIVITIES 1995



A)	Meetings Attended:

		AMS Winter Meetings, San Francisco, Janaury

		Northern California Topology Conference, Stanford, February 7

		Midwest Topology Seminar, Notre Dame, October 7



B)	Sabbatical at UC Berkeley in spring and summer





ACTIVITIES 1996



A)	Meetings Attended:

		Univ. of Wisconsin meeting honoring Ed Fadell.  April 12-14.

		Symposium on topology and mathematical physics, Toronto,

Fields Institute, April 19-		22.

		Topology meeting, Korea Univ., Seoul, Korea, May 24.

		Higher Homotopy Structure in Topology and Mathematical

Physics.  Vassar College, 		Poughkeepsie, NY.  June 13 - June 15

		World Congress of Non Linear Analysts, (40 minute talk).

Athens, Greece, July 9-11.



B)	Department Service:

		University Senator

		Member of University Resources Committee



C)	17 Invited Addresses



D)	Two papers written.  Another published.





ACTIVITIES 1997



A)	Meetings Attended:

		AMS, San Diego, January 10.

		Midwest Topology Seminar, Evanston, January 25.

		Topology and physics, Evanston, March 24-30, except March 24.

		Mathematics and History, Univ. of Chicago, May 9



B)	Department Service:

		Senate

		Member of University Resources Committee

		Special History reading course for 4 English exchange students



C)	One paper and an encyclopedia article on the Becker-Gottlieb

Transfer , published.

	3 papers accepted.





ACTIVITIES 1998



A)	Meetings Attended:

		AMS, Baltimore, January 6-10.

		Midwest Topology Seminar, Evanston, January 24.

		Midwest Topology Seminar, Chicago Circle, April 18.

		Arhus Topology and Geometry Conference, August 9-14 (chair

of session).

		International Congress of Math., Berlin, August 17-23

(chair of session).

		CPT and Lorentz Invariance, Bloomington IN, November 7.



B) Department Service:



		Senate

		Member of University Resources Committee

		Visited Calvin College and Hope College to advertise Purdue

		Proposed Undergraduate Topology course (490T- 598T)

		Improved knowledge of History of Math for possible course



C) Outside Talks:



		Robots, Topology, Mathematics; Colloquium Calvin College,

October 29. 1 hour



D) Publications:



		One paper published

		One paper written

		One book review

		One encyclopedia article





ACTIVITIES 1999



A) Meetings Attended:



		Midwest Topology Seminar, Madison, February 13.

		Michael Barrett Conference, Evanston, April 11.

		Mel Rothenberg Conference, Hyde Park, April 25.

		Geometry and Physics, Santa Barbara, July 21-24.

		Fixed Point Conference, S„o Paolo, July 26-30.

 ACTIVITIES 1999 (CONT.)



B) Department Service:



		Senate

		Member of University Resources Committee

		Coordinator of WeBWorK

		Advanced Services Committee



C) Outside Talks



		Univ. of Illinois, Chicago Circle, Special Quantum Topology

Seminar, 1 hour.

		S„o Paolo University, Fixed Point Conference, July 30, 1 hour.



D) Publications:



		Two papers published

		Two papers accepted

		One book review





ACTIVITIES 2000



A)	Meetings Attended:



		A.M.S. Winter Meeting, Washington, D.C., Jan. 19-22.

		Midwest Topology Seminar, Univ. of Chicago, Feb. 26.

		Midwest Topology Seminar, Notre Dame, April 10-13.

		Topology and Geometry Conference, Lehigh, April 10-14.

		Millenium Conference, UCLA, August 6-12.



B)	Department Service:



		Advanced Services Committee

		Ad Hoc Committee

		Head Review Committee

		Colloquium Chair

                Student Cases Committee of SOS



C)	Outside Talks:

		Mathematics and the Jewish People, Oct. 18



D)	Publications:



		One encyclopedia article published

		One paper published

		One paper accepted

		One paper written





ACTIVITIES 2001



A)	Meetings Attended: 



		Workshop on Topology and Algebraic K-theory, IUPUI, Feb. 17, 19

		Midwest Topology Seminar, U. of Illinois, Chicago, Feb. 24

                Conference honoring Sam Gitler, Rochester, April 20-22.

                IPAM workshops on Conformal Field Theory

                Lake Arrowhead CFT Conference.

 ACTIVITIES 2001 (CONT.)



B)	Department Service:



		Advance Services Committee

		Colloquium Chair

                Student Cases Committee of SOS



C)	Outside Talks: Colloquium UC Riverside, Ocotober 31.

                       Two talks at IPAM

                       2 Seminars at UCLA



D)	Publications



E)      Sabbatical leave: IPAM, UCLA, Fall 2001



ACTIVITIES 2002



A)      Meetings Attended:



                American Math. Soc. Winter Meetings in San Diego



B)      Outside Talks: 2 Seminars at UCLA



C)      Publications



D)      Sabbatical leave: UCLA, Spring 2002



PH.D. STUDENTS



	George Lang  (1970), Purdue

	Ryuji Maehara  (1972), Iowa State

	Murad Ozaydin  (1984), Purdue

	Craig Johnson  (1989), Purdue

	Chen Benjamin  (1990), Purdue

	Malhab Keirouz  (1991), Purdue

	Geetha Samaranayake  (1993), Purdue







COMMITTEES:



	Undergraduate Committee	1975-77

	Teacher Evaluation Committee	1975-76

	Graduate Committee	1981-84

	University Grievance Committee	1982-83

	Colloquium Chairman	1983-84

	Academic Senate	1983-86, 1996-1999

	Undergraduate Services Committee	1985-86

	University Resources Committee	1996-1999

	Advanced Services Committee	1999-

	Ad Hoc Subcommittee	2000

	Head Review Committee	2000







MISCELLANEOUS:



	Reviewer of Zentralblatt

	Referee for numerous Journals

	Referee for NSF and other granting organizations

	History of Mathematics Course 1993