Floyd L. Williams


Born: September 20, 1939

Birthplace: Kansas City, Missouri

B.S. (1972) Lincoln University (Missouri); M.S. (1975) Washington University (St. Louis)

Ph.D. (1972) Washington University (St. Louis)
thesis: Reduction of Tensor Products of Principle Series Representation of Complex Semi-Simple Lie Groups; Advisor: Ray Kunze

Research Interests: Holomorphic, cohomological, and representation theoretic aspects of Lie theory

Professor of Mathematics, University of Massachusettes at Amherst

URL: http://www.math.umass.edu/Fac_Staff_Students/Faculty/Williams/index.html

Floyd Williams was raised in extreme poverty in Kansas City, Missouri and he had not thought of going to college until his last week in high school when he was offered a music scholarship at Lincoln University in Jefferson City, Missouri.  He became side-tracked by Mathematics and Physics.


In 1962 Floyd L. Williams earned his B.S. in Mathematics from Lincoln University. At Washington University he earned his M.S.(1965) and Ph.D.(1972) in Mathematics. Dr. Floyd L. Williams held the positions of Associate Instructor at the University of California/Irvine (1970-72) and Instructor Massachusetts Institute of Technology (1972-75). At the University of Massachusetts-Amherst, Dr. Williams has been an Assistant Professor (1975-1978), Associate Professor (1978-84), and Professor (1984 -). In 1992 he was the Keynote Speaker at the Forum on Diversity, Excellence, and Motivation, Holyoke Community College. Dr. Williams has given piano recitals overseas. Details can be found on his vita page. Also see the autobiography the SUMMA web site. Also see the web page: Who are the greatest Black Mathematicians?


Dr. Williams has given more than 65 invited lectures , colloquia, and seminar talks at 60 universities and institutes in 14 countries. Dr. Williams publication page for the complete list.

FILM: Williams, Floyd L. An analogue of Hüber's formula for Riemann's zeta function. A lecture presented at the 1991 Annual Meeting of the MAA held in San Francisco, California, January 1991. AMS-MAA Joint Lecture Series. Mathematical Association of America, Washington, DC, 1991. 1 videocassette (NTSC; 1/2 inch; VHS) (45 min.); sd., col.

From 1974 to 1997, Dr. Floyd Williams has published more than 40 research papers and four books:


  1. Floyd L.Williams. Topics in quantum mechanics, Progress in Mathematical Physics
    series, vol.27 (2003), Birkhauser ISBN 0-8176-4311-7
  2. Williams, Floyd L. Lectures on the spectrum of $L\sp 2(\Gamma \backslash G)$. Pitman Research Notes in Mathematics Series, 242. Longman Scientific &Technical, Harlow; copublished in the United States with John Wiley &Sons, Inc., New York, 1991. xiv+348 pp. ISBN: 0-582-06863-0
  3. Andrei A.Bytsenko and Floyd L.Williams (Editors). Mathematical Methods in Physics, Proceeding of the 1999 Londrina Winter School,World Scientific Pub.ISBN 981-02-4284-0, (2000)
  4. Williams, Floyd L. Tensor products of principal series representations. Reduction of tensor products of principal series. Representations of complex semisimple Lie groups. Lecture Notes in Mathematics, Vol. 358. Springer-Verlag, Berlin-New York, 1973. vi+132 pp.

selected papers

44. Bytsenko, A. A.; Gonçalves, A. E.; Williams, F. L. The conformal anomaly in general rank $1$ symmetric spaces and associated operator product. Modern Phys. Lett. A 13 (1998), no. 2, 99--108.

43. Brevik, I.; Bytsenko, A. A.; Gonçalves, A. E.; Williams, F. L. Zeta-function regularization and the thermodynamic potential for quantum fields in symmetric spaces. J. Phys. A 31 (1998), no. 19, 4437--4448.

42. Bytsenko, A. A.; Goncalves, A. E.; Williams, F. L. The conformal anomaly associated with an operator product acting in rank $1$ symmetric spaces. JETP Lett. 67 (1998), no. 3, 176--181; translated from Pis\cprime ma Zh. Èksper. Teoret. Fiz. 67 (1998), no. 3, 166--171 (Russian)

41. Williams, Floyd L. The role of Selberg's trace formula in the computation of Casimir energy for certain Clifford-Klein space-times. African Americans in mathematics (Piscataway, NJ, 1996), 69--82, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 34, Amer. Math. Soc., Providence, RI, 1997.

40. Williams, Floyd L. Meromorphic continuation of Minakshisundaram-Pleijel series for semisimple Lie groups. Pacific J. Math. 182 (1998), no. 1, 137--156.

39. Bytsenko, Andrei A.; Williams, Floyd L. Zeta functions on a product of Einstein manifolds, and the multiplicative anomaly. J. Math. Phys. 39 (1998), no. 2, 1075--1086.

38. Williams, Floyd L. Topological Casimir energy for a general class of Clifford-Klein space-times. J. Math. Phys. 38 (1997), no. 2, 796--808.

37. Williams, Floyd L. Spectral zeta series of rank $1$ space forms. Representation theory and harmonic analysis (Cincinnati, OH, 1994), 245--254, Contemp. Math., 191, Amer. Math. Soc., Providence, RI, 1995.

36. Williams, Floyd L. On certain definite integrals which arise in automorphic Lie theory. J. Phys. A 26 (1993), no. 14, 3515--3526.

35. Williams, Floyd L. A factorization of the Selberg zeta function attached to a rank $1$ space form. Manuscripta Math. 77 (1992), no. 1, 17--39.

34. Williams, Floyd L. Some zeta functions attached to $\Gamma\backslash G/K$. New developments in Lie theory and their applications (Córdoba, 1989), 163--177, Progr. Math., 105, Birkhäuser Boston, Boston, MA, 1992.

33. Williams, Floyd L. An analogue of Huber's formula for Riemann's zeta function. Enseign. Math. (2) 38 (1992), no. 1-2, 133--149.

32. Barchini, Leticia; Williams, Floyd L. Periodic zeta functions for rank $1$ space forms of symmetric spaces. Hiroshima Math. J. 22 (1992), no. 1, 33--56.

31. Williams, Floyd L. Spectral multiplicity of derived functor modules. Adv. Math. 85 (1991), no. 2, 145--160.

30. Williams, Floyd L. History and variation on the theme of the Frobenius reciprocity theorem. Math. Intelligencer 13 (1991), no. 3, 68--71.

29. Williams, Floyd L. Unitary representations and a general vanishing theorem for $(0,r)$-cohomology. Osaka J. Math. 25 (1988), no. 3, 599--606.

28. Williams, Floyd L. The $n$-cohomology of limits of discrete series. J. Funct. Anal. 80 (1988), no. 2, 451--461.

27. Williams, Floyd L. On the finiteness of the $L\sp 2$-automorphic cohomology of a flag domain. J. Funct. Anal. 72 (1987), no. 1, 33--43.

26. Williams, Floyd L. Note on a theorem of H. Moscovici. J. Funct. Anal. 72 (1987), no. 1, 28--32.

25. Williams, Floyd L. Finite spaces of nonclassical Poincaré theta series. The Selberg trace formula and related topics (Brunswick, Maine, 1984), 543--554, Contemp. Math., 53, Amer. Math. Soc., Providence, R.I., 1986.

24. Fischer, Hans R.; Williams, Floyd L. The Borel spectral sequence: some remarks and applications. Differential geometry, calculus of variations, and their applications, 255--266, Lecture Notes in Pure and Appl. Math., 100, Dekker, New York, 1985.

23. Williams, Floyd L. A solution of Warner's 3rd problem for representations of holomorphic type. Trans. Amer. Math. Soc. 293 (1986), no. 2, 605--612.

22. Fischer, Hans R.; Jungster, Jerry J.; Williams, Floyd L. The heat kernel on the two-sphere. J. Math. Anal. Appl. 112 (1985), no. 2, 328--334.

21. Williams, Floyd L. On the dimension of spaces of automorphic cohomology. Algebraic groups and related topics (Kyoto/Nagoya, 1983), 1--15, Adv. Stud. Pure Math., 6, North-Holland, Amsterdam-New York, 1985.

20. Williams, Floyd L. Formula for the Casimir operator in Iwasawa coordinates. Tokyo J. Math. 8 (1985), no. 1, 99--105.

19. Kaneyuki, Soji; Williams, Floyd L. Almost paracontact and parahodge structures on manifolds. Nagoya Math. J. 99 (1985), 173--187.

18. Kaneyuki, Soji; Williams, Floyd L. On a class of quantizable co-adjoint orbits. Algebras Groups Geom. 2 (1985), no. 1, 70--94.

17. Williams, Floyd L. Discrete series multiplicities in $L\sp 2(\Gamma \backslash G)$. II. Proof of Langlands' conjecture. Amer. J. Math. 107 (1985), no. 2, 367--376.

16. Fischer, Hans R.; Williams, Floyd L. Note on duality on polarized symplectic manifolds. Rep. Math. Phys. 20 (1984), no. 3, 357--363.

15. Fischer, Hans R.; Williams, Floyd L. Borel\mhy LePotier diagrams---calculus of their cohomology bundles. Tôhoku Math. J. (2) 36 (1984), no. 2, 233--251.

14. Fischer, Hans R.; Jungster, Jerry J.; Williams, Floyd L. The heat kernel on the two-sphere. Adv. in Math. 54 (1984), no. 2, 226--232.

13. Williams, Floyd L. Discrete series multiplicities in $L\sp{2}(\Gamma\setminus G)$. Amer. J. Math. 106 (1984), no. 1, 137--148.

12. Williams, Floyd L. Solution of a conjecture of Langlands. Noncommutative harmonic analysis and Lie groups (Marseille, 1982), 179--187, Lecture Notes in Math., 1020, Springer, Berlin-New York, 1983.

11. Williams, Floyd L. Vanishing theorems for type $(0,\,q)$ cohomology of locally symmetric spaces. II. Osaka J. Math. 20 (1983), no. 1, 95--108.

10. Williams, Floyd L. Unitarizable highest weight modules of the conformal group. Adv. in Math. 45 (1982), no. 1, 1--20.

9. Williams, Floyd L. Frobenius reciprocity and Lie group representations on $\bar \partial $ cohomology spaces. Enseign. Math. (2) 28 (1982), no. 1-2, 3--30.

8. Williams, Floyd L. Remarks on the unitary representations appearing in the Matsushima\mhy Murakami formula. Noncommutative harmonic analysis and Lie groups (Marseille, 1980), pp. 536--553, Lecture Notes in Math., 880, Springer, Berlin-New York, 1981.

7. Williams, Floyd L. Vanishing theorems for type $(0,\,q)$ cohomology of locally symmetric spaces. Osaka J. Math. 18 (1981), no. 1, 147--160.

6. Williams, Floyd L. Lie algebra cohomology of infinite-dimensional modules. Adv. in Math. 35 (1980), no. 1, 19--29.

5. Fischer, Hans R.; Williams, Floyd L. Complex-foliated structures. I. Cohomology of the Dolbeault-Kostant complexes. Trans. Amer. Math. Soc. 252 (1979), 163--195.

4. Williams, Floyd L. The cohomology of semisimple Lie algebras with coefficients in a Verma module. Trans. Amer. Math. Soc. 240 (1978), 115--127.

3. Williams, Floyd L. Topological irreducibility of nonunitary representations of group extensions. Trans. Amer. Math. Soc. 233 (1977), 69--84.

2. Williams, Floyd L. Complex homogeneous bundles and finite-dimensional representation theory. Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 2, Williams Coll., Williamstown, Mass., 1975), pp. 317--320. Amer. Math. Soc., Providence, R. I., 1977.

1. Williams, Floyd L. Laplace operators and the ${\germ h}$ module structure of certain cohomology groups. Trans. Amer. Math. Soc. 197 (1974), 1--57.


SUMMA Floyd Williams web site: http://www.maa.org/summa/archive/Willm_FL.htm

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