ROBERT S. DORAN

The John William and Helen Stubbs

Potter Professor of Mathematics

Texas Christian University

Fort Worth, Texas 76129

(817) 257-7335

r.doran@tcu.edu

http://www.math.tcu.edu/

Education:

University of Iowa, B. A. (1962); M. S. (1964)

University of Washington, M. S. (1967); Ph.D. (1968)

Ph.D. Thesis: Representations of C*-algebras by uniform CT-bundles and operator theory. Thesis Advisors: Professors R. A. Gangolli and J. M. G. Fell

Military Service:

U. S. Army Special Forces, 82^nd Airborne Division; Instructor, U. S. Army Jungle Survival School, Colón, Panama (1956-1958)

Mathematical Specialties:

Functional Analysis, Banach Algebras & Bundles, Operator Algebras, Abstract Harmonic Analysis, Representations of Locally Compact Groups, Approximate Identities and Factorization in Banach Modules.

Academic Honors:

Phi Beta Kappa

Sigma Xi Scientific Honor Society

Pi Mu Epsilon Mathematics Honor Society

Golden Key Honor society

Academic Appointments: Texas Christian University, August 1969. Assistant professor 1969-72; Associate Professor 1972-79; Professor, since 1979 - ; appointed Potter Professor 1995. Chair, Mathematics Department, since 1990 -

Visiting Academic Appointments:

(a) UNIVERSITY OF OXFORD, Mathematical Institute, Oxford, England (Senior Visiting Scholar, Fall, 1988, Queens College, Oxford).

(b) INSTITUTE FOR ADVANCED STUDY (IAS), Princeton, N.J. (Member, 1981; Director Western Region, 1984; Board of Trustees Association of Members IAS (AMIAS) since 1986; President of the AMIAS Institute Board, 1990 -1999)

(c) MASSACHUSETTS INSTITUTE OF TECHNOLOGY (MIT Scholar, 1981).

(d) UNIVERSITY OF TEXAS, Austin (Visiting Professor 1979; 1980).

Honors and Awards:

CASE-CARNEGIE National Gold Medalist, 1989

CASE-CARNEGIE Texas Professor of the Year, 1989

MAA Texas Professor of the Year, 1992 (Mathematical Association of America)

Minnie Stevens Piper Professor, 1989 (Texas Statewide award)

Chancellor’s Distinguished Teaching Award at TCU, 1988

The TCU Honors Professor of the Year, 1993

Burlington Northern Foundation Faculty Achievement Award 1986

Lester Hook Phi Beta Kappa National Award 1991 (TCU Chapter nominee).

Chancellor’s Award for Distinguished Research 1993 (Natural Science Representative)

Chancellor’s Award for Distinguished Research 1991 (Natural Science Representative)

Teaching Excellence Award, TCU House of Representatives (three times 1987, 1991, 1993)

TCU Top Ten Professor, Teaching Excellence Award (twice, 1986, 1988)

Mortar Board Preferred Professor (six times, 1986, 1987,1994, 1995, 1996, 1998)

Lambda Chi Alpha Professor of the Year (twice, 1992, 1993)

Tom Brown-Jarvis Outstanding Teacher (twice, 1973, 1978)

Minnie Stevens Piper Professor Nominee for TCU (1987)

Natural Science Nominee, Chancellor’s Award for Distinguished Teaching, (three times, 1984, 1986 and 1988)

Tom Brown-Jarvis Outstanding Teacher Award, 1973, 1978

Panhellenic Council Professor, 1996

Brachman Professor, 1975

Mathematics Department Nominee, Chancellor’s Award for Distinguished Research (four times 1985, 1987, 1991 and 1993)

Marquis Who’s Who in the World

Marquis Who’s Who in America

Marquis Who’s Who in the South and Southwest

Marquis Who’s Who in Science and Engineering

Marquis Who’s Who in Education

American Men and Women of Science

Who’s Who Cambridge Biographical Institute

Board of Trustees, Institute for Advanced Study, Princeton, Association of Members, 1986; president of the Board, 1990-1999

President, TCU Chapter Sigma Xi, 1983-1984

Phi Beta Kappa (President of TCU chapter 1989-1992)

Golden Key National Honor society

The John William and Helen Stubbs Potter Professor of Mathematics, since 1995.

Research articles and books:

Group representations, ergodic theory, and mathematical physics, Editor with C. C. Moore and R. J. Zimmer, 451 pages, Volume 449, Contemporary Mathematics, American Mathematical Society, Providence, R. I. 2008. (book)

George W. Mackey (1916 – 2006), with Arlan Ramsay, Notices of the American Mathematical Society, 54 (2007), 824 – 850.

Operator algebras, quantization, and non-commutative geometry, Volume 365,

Editor with R. V. Kadison, 422 pages, Contemporary Mathematics, American

Mathematical Society, Providence, R. I. 2004. (book)

The Mathematical Legacy of Harish-Chandra. Editor with V. S. Varadarajan, 551pages, Volume 68, Proceedings of the Symposia for Pure Mathematics, American Mathematical Society, Providence, R. I., 2000. (book)

Automorphic forms, automorphic representations, and arithmetic. I. Editor with Z. Dou and G. Gilbert, 278 pages, Volume 66, Part I, Proceedings of the Symposia for Pure Mathematics, American Mathematical Society, Providence, R. I., 1999. (book)

Automorphic forms, automorphic representations, and arithmetic. II. Editor with Z. Dou and G. Gilbert, 330 pages, Volume. 66, Part II, Proceedings of the Symposia for Pure Mathematics, American Mathematical Society, Providence, R. I., 1999. (book)

C*-algebras: 1943-1993 (A fifty year celebration), Editor, 401 pages, Vol. 167, Contemporary Mathematics, American Mathematical Society, Providence, R. I., 1994. (book)

Self-adjoint and non-selfadjoint operator algebras and operator theory , Editor, 217 pages, Vol. 120, Contemporary Mathematics, American Mathematical Society, Providence, R. I., 1990. (book)

Weak and strong continuity in topological spaces: Generalizations of continuity and preservation of topological properties, J. of Undergraduate Mathematics,

22 (1990), 27-28.

Pure state characterizations of P-commutative Banach *-algebras, Manuscripta Mathematica, 61 (1988), 43-47 (with W. Tiller).

A CARE PACKAGE for undergraduate mathematics students, Mathematics in College, Fall/Winter (1988), 32-37.

Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles, Vol.1 (General representation theory of groups and algebras, 747 pages), Pure and Applied Mathematics #125, Academic Press, New York, 1988 (with J. M. G. Fell). (book)

Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles, Vol. 2 (Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis, 763 pages), Pure and Applied Mathematics #126, Academic Press, New York, 1988 (with J. M. G. Fell). (book)

Characterizations of C*-algebras: The Gelfand-Naimark Theorems, Vol. 101, Pure and Applied Mathematics, (440 pages), Marcel-Dekker Publishing Company, 1986 (with V. A. Belfi). (book)

P-Commutativity of the Banach algebra L1(G)**, Manuscripta Mathematica 43 (1983), 85-89 (with W. Tiller).

History of functional analysis, J. Dieudonné, Bulletin of the American Mathematical Society 7 (1982), 403-409.

Continuity of the involution in a Banach *-algebra, Tamkang Journal of Mathematics 13 (1982), 87-90 (with W. Tiller).

Extensions of pure positive functionals on Banach *-algebras, Proceedings of the American Mathematical Society 82 (1981), 583-586 (with W. Tiller).

Norm and spectral characterizations in Banach algebras, L’Enseignement Mathématique 26 (1980), 103-130 (with V. A. Belfi).

An application of idempotents in the classification of complex algebras, Elemente der Mathematik 35 (1980), 16-17.

Does there exist a Banach *-algebra without identity with no nonzero positive functionals?, American Mathematical Monthly 87 (1980), 474-475.

Approximate identities and factorization of Banach modules, Lecture Notes in Mathematics #768, Springer-Verlag Publishing Company, 305 pages, Heidelberg-New York London, 1979 (with Josef Wichmann). (book)

The Gelfand-Naimark Theorems in C*-algebras, L’Enseignement Mathématique 23 (1977), 153-180 (with Josef Wichmann).

A generalization of a theorem of Civin and Yood on Banach *-algebras, Bulletin of the London Mathematical Society 4 (1972), 25-26.

Does there exist more than one Banach *-algebra with discontinuous involution?, American Mathematical Monthly 79 (1972), 762-765.

A theorem which is equivalent to the axiom of choice, Elemente der Mathematik 27 (1972), 127.

An integral inequality, Mathematics Magazine 44 (1971), 267.

If A is a symmetric *-algebra, is Ae symmetric?, American Mathematical Monthly 78 (1971), 178-179.

Representations of C*-algebras by Uniform CT-bundles, Proceedings of the Texas Academy of Science 13 (1970), 147-156.

On the cardinality of the alternating group, Niew Archief (3), 19 (1970), 171.

Commuting elements in a free group, Niew Archief (1), 19 (1970), 78-79.

A noncompact uniform space, American Mathematical Monthly 74 (1967), 89-90.

Harmonic analysis and derivations on P-commutative Banach *-algebras, Notices of the American Mathematical Society 31(1984), January.

An integral representation theorem, Notices of the American Mathematical Society 26 (1979), 471.

Essential subspaces in the dual of a Banach space, Notices of the American Mathematical Society 26 (1979), 100.

Construction of uniform CT-bundles, Notices of the American Mathematical Society 5 (1968), 551.

Representations of C*-algebras by uniform CT-bundles and operator theory,

Ph.D. Dissertation, 1968, University of Washington, Seattle, Washington, 128 Pages.

Technical Reports. TCU Mathematics Department

1. P-commutative Banach *-algebras, (1988), 35 pages.

2. Spectral algebras, (1988), 43 pages.

3. Group algebras of locally compact groups, (1987), 71 pages.

4. Induced representations of locally compact groups, (1986), 130 pages.

5. C*-algebras, (1984), 213 pages.

6. Norm and spectral conditions in Banach algebras, (1980), 64 pages.

7. Lectures on Banach algebras, (1975), 385 pages.

8. Operators in Hilbert space, (1974) 160 pages (dittoed lecture notes).

9. Lectures on functional analysis, (1973), 242 pages.

10. Ergodic theory and group representations, (1972), 116 pages.

11. Characterizations of normed algebras with multiplicative norms, (1972), 33 pages.

12. Lectures on mathematical analysis (1988), 212 pages.

13. Math skills part of formula for success, February 26, 1998.

Papers, participation on panels, etc. at scholarly meetings & colloquia:

Organizer of NSF-CBMS Conference “Topology, C*-algebras, and string duality,” with Greg Friedman, June 2 – 6, 2008. Jonathan Rosenberg, principal lecturer.

Organizer of AMS Special Session: “Group representations, ergodic theory ,and mathematical physics.” (with C. C. Moore and R. J. Zimmer), New Orleans, La., January 7-8, 2007, AMS winter Meeting.

Invited keynote speaker, 2003 Jim Bolen Mathematics Award Ceremony, TCC, The Wonder of Mathematical discovery, April 25, 2003, Fort Worth, Texas.

Institute for Advanced Study Conference and Annual Board Meeting, April 4, 2003, Princeton, New Jersey.

Organizer of AMS Special Session: “Operator Algebras, Quantization, and Non-

commutative Geometry.” (with R. V. Kadison), Baltimore, MD., January 15-16, 2003, AMS winter Meeting.

Institute for Advanced Study conference and Board Meeting, March 2002, Princeton

New Jersey.

Institute for Advanced Study conference and Board Meeting, March 2001, PrincetonNew Jersey.

Mathematics Conference Honoring the Memory of Andre Weil, January 8-9, 1999, Institute for Advanced Study, Princeton, New Jersey.

Conference Director at the Institute for Advanced Study, President, Board of Trustees, Association of Members of the Institute for Advanced Study, March 14-15, 1988, Princeton, New Jersey.

Organizer and Director of “AMS Special Session “Representation Theory and Noncommutative Harmonic Analysis Honoring the Memory of Harish-Chandra”, Baltimore, Maryland, January 9-10, 1998.

Invited Speaker, Baylor Mathematics Colloquium, November 13, 1997 at Baylor University, Waco, Texas.

Director of Biennial Conference of the Institute for Advanced Study, President, Board of Trustees, Association of Members of the Institute for Advanced Study, May 14-15, 1997, Princeton, New Jersey.

Organizer and Director of Mathematics Research Conference, Institute for Advanced Study, Princeton, New Jersey, May 21-22, 1996.

Invited Keynote speaker,"What makes mathematics so special?" MAA conference, Mathematical Association of America, Stephen F. Austin University, October 7, 1994.

Invited speaker, “Solution of a famous unsolved problem,” Parabola meeting, Texas Christian University, September 20, 1994.

Master of Ceremonies, Research Conference Twentieth Anniversary Celebration of the Association of Members of the Institute for Advanced Study, Princeton, N. J., May 20-21, 1994.

Invited speaker, “Reflections of the 1992 MAA Texas Professor of the Year,” Spring meeting, Texas Section of the MAA, Abilene, Texas April 3, 1993.

Invited speaker, “One of America’s great mathematicians: Marshall H. Stone,” Parabola meeting, TCU, March 24, 1993.

Organizer and director of Special Session entitled “C*-algebras 1943-1993 (A fifty year celebration),” combined AMS-MAA winter meeting, San Antonio, Texas, January 13-16, 1993.

American Mathematical Society Library Committee Panel Discussion, “The high cost of periodicals,” AMS meeting, San Antonio, Texas, January 14, 1993.

Invited speaker, “Axioms for C*-algebras, symmetric algebras, and a problem of Kaplansky,” University of Texas, Arlington, November 4, 1992.

MAA meeting, University of Houston, Recipient of 1992 MAA Texas Professor of the Year award, Houston, Texas, April 9-11, 1992.

Program, Deane Montgomery Memorial Service, Institute for Advanced Study, Princeton, New Jersey, October 19, 1992.

Invited speaker, “Marshall H. Stone—Mathematician and Friend of the Institute,” Spring meeting, 9th biennial AMIAS Conference Lectures, Institute for Advanced Study, May 21-22, 1992.

Spring meeting, Institute for Advanced Study, Princeton, May 23-24, 1991,

President of the Board, “Board of Trustees Meeting,” AMIAS, 1991.

Invited One Hour speaker, “M. H. Stone, the man and his mathematics,” Great Plains Operator Theory Conference, Texas A & M University, College Station, May 15-18, 1991.

Invited speaker, “The beauty of Mathematics,” University of Dallas, Irving, Texas, April 23, 1991.

Contributed paper, “Continuity of the involution in Banach *-algebras,” Spring Meeting, Texas Section Mathematical Association of America, April 8, 1991, Nacogdoches, Texas.

Invited speaker, TCJC Cornerstone Honors Program, “Mathematics—its meaning and significance,” February 25, 1991, TCJC, South Campus, Fort Worth, Texas.

Invited speaker, “Adventures into the infinite,” Trinity Valley High School, Fort Worth, November 12, 1990.

Invited speaker, “What do mathematicians do?,” Southwest High School, Fort Worth, November 19, 1990.

Invited speaker, “Varieties of mathematical experience,” Fort Worth Country Day High School, November 28, 1990.

Director and organizer, National Science Foundation, “Coordinates in operator algebra: Groupoids and categories, their representations and applications,” NSF-CBMS Regional Conference, Dr. Paul Muhly, May 20-26, 1990, Texas Christian University, Fort Worth, Texas, Grant Number NSF #524460.

Invited speaker: “Award winning teaching: Reflections of a Piper Professor and CASE Gold Medalist,” Spring Meeting, MAA, April 6, 1990, University of North Texas, Denton, Texas.

Director and Organizer of AMS Special Session, “Group Representations and Operator Algebras,” Louisville, Kentucky, January 17-20, 1990.

Contributed paper, “A survey of the theory of P-commutative Banach *-algebras,” MAA, Texas Section Spring Meeting, April 8, 1989.

Invited speaker, “Axioms for C*-algebras: A solution to a problem of Kaplansky,” Oxford Functional Analysis Seminar, University of Oxford, October 18, 1988.

Invited speaker, “The structure of C*-algebras and symmetric *-algebras,” Seminar, King’s College, University of London, November 3, 1988.

Invited speaker, “Characterizations of C*-algebras: From Gelfand-Naimark to Dauns-Hofmann and beyond,” University of Edinburgh, Edinburgh, Scotland, November 28, 1988. (Functional Analysis Seminar).

Invited speaker: “Symmetric *-algebras: Old and new problems,” University of Glasgow, Glasgow, Scotland, November 29, 1988. (Functional Analysis Seminar).

Invited speaker, “Spectral algebras: A new generalization of Banach algebras,” Yorkshire Functional Analysis Group, University of Sheffield, Sheffield, England, December 13, 1988. (Functional Analysis Seminar).

Contributed paper, “The Peter-Weyl Theorem for compact groups,” Spring Meeting, Texas Section Mathematical Association of America, April 15, 1988, Trinity University, San Antonio, Texas.

Parabola Mathematics Club speaker, “The ABC’s of the CBS inequality,” January 19, 1988, TCU Mathematics Club.

Parabola Mathematics Club speaker, “Mathematics made difficult: A look at lines through the origin,” September 20, 1988, TCU Mathematics Club.

Invited participant, Great Plains Operator Theory Seminar, Conference. Topic: “K-Theory in operator algebras,” University of Kansas, Lawrence, Kansas, May 27-30, 1987.

Spring meeting, Institute for Advanced Study, Princeton, May 20-23, 1987. “Board of Trustees of AMIAS,” 1987.

Invited one hour speaker, “Axioms for C*-algebras: Flying by Instruments,” Mathematical Association of America, Annual Spring Meeting, Texas Section, April 2-4, 1987, Tarleton State University, Stephenville, Texas.

INTERNATIONAL CONGRESS OF MATHEMATICIANS, August 2-11, 1986, University of California, Berkeley, California.

Invited participant, Institute for Advanced Study, Princeton, May 14-19, 1986. “Twelfth Anniversary of the Association of Members of the Institute for Advanced Study.”

Invited participant, MATHEMATICAL SCIENCES RESEARCH INSTITUTE, Berkeley, California, May 21-23, 1985. Group Representation Conference in Honor of Professor George W. Mackey of Harvard University.

Contributed paper, American Mathematical Society, Annual Winter Meeting, Louisville, Kentucky, January 28, 1984. “Harmonic Analysis and Derivations of

P-commutative Banach *-Algebras.”

Chairman, “Session on Banach algebras,” Winter Meeting, American Mathematical Society, January 28, 1984, Louisville, Kentucky.

Contributed paper, Mathematical Association of America, Annual Spring Meeting, Texas Section, April 6-7, 1984, University of Texas at Tyler, Tyler, Texas. “Decompositions of Operators with Closed Range.”

Invited speaker, Parabola Mathematics Club, Texas Christian University, March 27, 1984.“Mathematical Axioms: Why do we use them?”

Invited speaker, In-Service Institute for High School Mathematics Teachers, Birdville Independent Public Schools, October 20, 1983. “Optical Illusions and Mathematics.”

Invited participant, Great Plains Operator Theory Seminar, “Recent Developments in Operator Algebras.” Conference Topic: “The theory and applications of completely positive maps and completely bounded maps,” University of Colorado, Boulder, Colorado, June 1-3, 1983.

Contributed paper, Mathematical Association of America, Annual Spring Meeting, Texas Section, April 8, 1983. “Axioms for C*-algebras: A survey from 1943 to 1983.”

Invited speaker, High School Mathematics Club, Irving High School, Irving, Texas, February 8, 1983. “Paradoxes and Infinity: Some surprising results.”

Invited speaker, Institute for Advanced Study, Princeton, (Bi-annual Conference), June 1-3, 1982. Topic: “Problems in Symmetric *-Algebras.”

Invited participant, National Science Foundation (CBMS) Conference on: “Automorphism Groups of von Neumann Algebras and the Structure of Factors,” University of Iowa, Iowa City, Iowa, April 26-30, 1982.

Contributed paper, Mathematical Association of America, Annual Spring Meeting, Texas Section, April 2, 1982, Lamar University, Beaumont, Texas. “The Banach Algebra L1 (G)** is P-commutative.”

Colloquium Speaker, TCU Department of Mathematics, January 21, 1982, “Recent Research on Symmetric and Hermitian *-algebras.”

Invited speaker, Harvard-Massachusetts Institute of Technology Mathematics Colloquium, March 12, 1981, Massachusetts Institute of Technology, Cambridge, Massachusetts. Topic: “Extensions of Pure States.”

Invited Speaker, Texas A & M Mathematics Colloquium, Texas A & M University, College Station, Texas, February 14, 1980. Topic: “Symmetric *-Algebras: A Solution to a Problem of Kaplansky.”

Colloquium Speaker, Texas Christian University, Department of Mathematics, January 24, 1980. Topic: “A Generalized Schwarz Inequality.”

Director & Organizer, by invitation of the American Mathematical Society, of AMS SPECIAL SESSION entitled “C*-Algebras and Operator Theory,” Annual Winter Meeting of the Society, January 3, 1980, San Antonio, Texas.

Invited participant, “Scottish Book (Mathematical) Conference,” May, 1979, North Texas State University, Denton, Texas.

Invited Speaker, Texas Academy of Science, University of Texas, Arlington, Texas, March 10, 1979. Topic: "Polar Decomposition in C*-algebras."

Invited Speaker, Castleberry Mathematics Club, Fort Worth, Texas, October 17, 1979. “Some exciting and remarkable theorems in mathematics.”

Colloquium Speaker, University of Texas, Arlington, 1977, August. Topic: “Automatic Continuity of Positive Linear Functionals on Banach *-Algebras.”

Contributed paper, Mathematical Association of America, Annual Spring Meeting, Texas Section, April, 1976. Topic: “Characterizations of Normed Algebras.”

Colloquium Speaker, University of Texas, Arlington, 1974, March 5. Topic: “The Functional Calculus in Banach Algebras: A Power Package.”

Invited Speaker, University of Texas, Austin, Mathematics Colloquium, February 19, 1973. Topic: “Axioms for C*-Algebras and Related Problems.”

Invited Speaker, Kansas State University Mathematics Colloquium, Manhattan, Kansas, March 29, 1973. Topic: “The Remarkable Gelfand-Naimark Theorems for C*-Algebras.”

Colloquium Speaker, University of Northern Iowa, September, 1973. Topic: “Bundles in Functional Analysis: How They Are Used?”

Colloquium Speaker, University of Texas, Arlington, March 5, 1973. Topic: “Continuity and discontinuity of linear operators.”

Colloquium Speaker, TCU Department of Mathematics, November 22, 1973. Topic:

“Representations in fiber bundles: An Introduction.”

Chairman, “Abstract Harmonic Analysis Session,” American Mathematical Society, Annual Winter Meeting, January, 1973, San Francisco, California.

Colloquium Speaker, TCU Department of Mathematics, February 10, 1972. Topic: “Continuity in Banach Algebras.”

Director and Organizer of Week-long RESEARCH CONFERENCE at TCU. Topic of Conference: “Statistical Mechanics and Ergodic Theory.” June, 1972. Invited Lecturer: Dr. George W. Mackey, Walker Ames and Landon D. Clay Professor of Mathematics, Harvard University. Conference Supported by TCU/RF-Grant #M7121.

Contributed paper, American Mathematical Society, Annual Winter Meeting, January, 1971. Topic: “The Structure of C*-Algebras in Uniform CT-bundles.”

Invited participant, INTERNATIONAL CONFERENCE ON ABSTRACT HARMONIC ANALYSIS, University of Maryland, College Park, Maryland, November 7-12, 1971.

Associate Director of NSF-CBMS Regional Conference, Ten Problems in Hilbert Space, Principal Lecturer: Dr. Paul Halmos, June, 1970, Texas Christian University, Fort Worth, Texas.

Contributed paper, American Mathematical Society, Annual Winter Meeting, January, 1969, New Orleans, Louisiana. Topic: “Construction of Uniform CT-bundles.”

Invited Speaker, Iowa Academy of Science, Iowa Section of the Mathematical Association of America, Cedar Falls, Iowa, April, 1969. Topic: “Representations of C*-Algebras.”