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**

email:

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?

RESEARCH

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**:

BOOKS

**Floyd L.Williams**.*Topics in quantum mechanics*, Progress in Mathematical Physics

series, vol.27 (2003), Birkhauser ISBN 0-8176-4311-7**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- 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) **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.** T*he 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.**
T*he 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.

references:

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

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Scott W. Williams

Professor of Mathematics