Floyd Williams

Last updated

Floyd Leroy Williams (born September 20, 1939) is a North American mathematician well known for his work in Lie theory and, most recently, mathematical physics. [1] In addition to Lie theory, his research interests are in homological algebra and the mathematics of quantum mechanics. He received his B.S.(1962) in Mathematics from Lincoln University of Missouri, and later his M.S.(1965) and Ph.D.(1972) from Washington University in St. Louis. [1] Williams was appointed professor of mathematics at the University of Massachusetts Amherst in 1984, and has been professor emeritus since 2005. [1] Williams' accomplishments earned him recognition by Mathematically Gifted & Black as a Black History Month 2019 Honoree. [2]

Contents

Biographical Sketch

Floyd Williams was born on September 20, 1939, and lived in Kansas City, Missouri. He was raised in extreme poverty. His mother told him not to complain about their situation, but rather to have faith in God and work hard. Her advice was taken, and it worked. He eventually was ordained in addition to being a mathematician.

However, it was music, not mathematics, that appealed to him through high school. "In fact," he admits, "mathematics was the only course in which I did not do well." Williams had not thought of going to college until his last week in high school when he was offered a music scholarship at Lincoln University of Missouri in Jefferson City, Missouri.

It was in his sophomore year that he became intrigued by the theory of relativity, which turned out to be his main motivation for studying mathematics. In 1972 he completed his Ph.D. from Washington University where his thesis was in the field of Lie theory. He was an instructor and lecturer at MIT from 1972 to 1975, before moving to the University of Massachusetts Amherst as an assistant professor in 1975. In 1983 he received an MRI grant to continuing researching in this field, ushering him into the mainstream of mathematics.

As an African-American in a field that has had little minority representation, Williams has felt the sting of discrimination during his career. However, he has been a motivation and role model for many young minorities, encouraging them to enter science and engineering. Williams has helped to set up programs that allow pre-college students and undergraduates to meet and talk with mathematicians, scientists and engineers, most notably at a summer camp run at MIT. "All that many of these youngsters see is different courses," he says, "but they want to know what mathematicians do from 8 am to 5 pm. Once minorities commit to graduate work in science or engineering," he continues, "they need extra help and support for what, for many, is the foreign environment of graduate school. Such programs exist at few universities, but we need more of them."

In 2012 he became a fellow of the American Mathematical Society. [3]

Mathematics

Williams' recent contribution to quantum mechanics has been in the area of Nikiforov-Uvarov theory of generalized hypergeometric differential equation, used to solve the Schrödinger equation and to obtain the quantization of energies from a single unified point of view. This theory is developed and is also used to give a uniform approach to the theory of special functions. This study furthers to connect the modern studies of pure mathematics with physics.

Bibliography

Notable works of Floyd Williams include:

He had written over 88 written papers, including four books. Moreover, Floyd L. Williams has been cited 157 times by over 150 authors. Here is a list of some of his most cited works

  1. Kaneyuki, Soji; Williams, Floyd L.Almost paracontact and parahodge structures on manifolds. Nagoya Math. J. 99 (1985), 173–187.
  2. 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.
  3. Perry, Peter A.; Williams, Floyd L. Selberg zeta function and trace formula for the BTZ black hole. Int. J. Pure Appl. Math. 9 (2003), no. 1, 1–21. 11M41
  4. Williams, Floyd L. The n-cohomology of limits of discrete series. J. Funct. Anal. 80 (1988), no. 2, 451–461.
  5. Lectures on the spectrum of L2(Γ\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
  6. Bytsenko, A. A.; Williams, F. L. Asymptotics of the heat kernel on rank-1 locally symmetric spaces. J. Phys. A 32 (1999), no. 31, 5773–5779.
  7. Williams, Floyd L. The cohomology of semisimple Lie algebras with coefficients in a Verma module. Trans. Amer. Math. Soc. 240 (1978), 115–127.
  8. 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.
  9. Williams, F. L. A zeta function for the BTZ black hole. Proceedings of the Second International Winter School on Mathematical Methods in Physics (Londrina, 2002). Internat. J. Modern Phys. A 18 (2003), no. 12, 2205–2209.
  10. Bytsenko, A. A.; Guimarães, M. E. X.; Williams, F. L. Remarks on the spectrum and truncated heat kernel of the BTZ black hole. Lett. Math. Phys. 79 (2007), no. 2, 203–211. 58J90

Related Research Articles

In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. The initial numerical observation was made by John McKay in 1978, and the phrase was coined by John Conway and Simon P. Norton in 1979.

<span class="mw-page-title-main">George Mackey</span> American mathematician

George Whitelaw Mackey was an American mathematician known for his contributions to quantum logic, representation theory, and noncommutative geometry.

<span class="mw-page-title-main">Varghese Mathai</span>

Mathai Varghese is a mathematician at the University of Adelaide. His first most influential contribution is the Mathai–Quillen formalism, which he formulated together with Daniel Quillen, and which has since found applications in index theory and topological quantum field theory. He was appointed a full professor in 2006. He was appointed Director of the Institute for Geometry and its Applications in 2009. In 2011, he was elected a Fellow of the Australian Academy of Science. In 2013, he was appointed the Elder Professor of Mathematics at the University of Adelaide, and was elected a Fellow of the Royal Society of South Australia. In 2017, he was awarded an ARC Australian Laureate Fellowship. In 2021, he was awarded the prestigious Hannan Medal and Lecture from the Australian Academy of Science, recognizing an outstanding career in Mathematics. In 2021, he was also awarded the prestigious George Szekeres Medal which is the Australian Mathematical Society’s most prestigious medal, recognising research achievement and an outstanding record of promoting and supporting the discipline.

<span class="mw-page-title-main">Bertram Kostant</span> American Jewish mathematician

Bertram Kostant was an American mathematician who worked in representation theory, differential geometry, and mathematical physics.

<span class="mw-page-title-main">Arthur Jaffe</span> American mathematician

Arthur Michael Jaffe is an American mathematical physicist at Harvard University, where in 1985 he succeeded George Mackey as the Landon T. Clay Professor of Mathematics and Theoretical Science.

Valentine "Valya" Bargmann was a German-American mathematician and theoretical physicist.

In mathematics, secondary calculus is a proposed expansion of classical differential calculus on manifolds, to the "space" of solutions of a (nonlinear) partial differential equation. It is a sophisticated theory at the level of jet spaces and employing algebraic methods.

In mathematics, the Littelmann path model is a combinatorial device due to Peter Littelmann for computing multiplicities without overcounting in the representation theory of symmetrisable Kac–Moody algebras. Its most important application is to complex semisimple Lie algebras or equivalently compact semisimple Lie groups, the case described in this article. Multiplicities in irreducible representations, tensor products and branching rules can be calculated using a coloured directed graph, with labels given by the simple roots of the Lie algebra.

Konrad Osterwalder is a Swiss mathematician and physicist, former Undersecretary-General of the United Nations, former Rector of the United Nations University (UNU), and Rector Emeritus of the Swiss Federal Institute of Technology Zurich. He is known for the Osterwalder–Schrader theorem.

Gennadi Sardanashvily was a theoretical physicist, a principal research scientist of Moscow State University.

<span class="mw-page-title-main">Veeravalli S. Varadarajan</span> Indian mathematician (1937–2019)

Veeravalli Seshadri Varadarajan was an Indian mathematician at the University of California, Los Angeles, who worked in many areas of mathematics, including probability, Lie groups and their representations, quantum mechanics, differential equations, and supersymmetry.

Nolan Russell Wallach is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the two-volume treatise Real Reductive Groups.

<span class="mw-page-title-main">Alexander Varchenko</span>

Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.

<span class="mw-page-title-main">Pierre Bieliavsky</span> Belgian mathematician

Pierre Bieliavsky, is a Belgian mathematician.

Mark Stern is an American mathematician whose focus has been on geometric analysis, Yang–Mills theory, Hodge theory, and string theory.

<span class="mw-page-title-main">Ralph Kaufmann</span> German mathematician

Ralph Martin Kaufmann is a German mathematician working in the United States.

Vadim V. Schechtman is a Russian mathematician who teaches in Toulouse.

<span class="mw-page-title-main">Stanislav Molchanov</span> Soviet American mathematician

Stanislav Alexeyevich Molchanov is a Soviet and American mathematician.

Stephen Albert Fulling is an American mathematician and mathematical physicist, specializing in the mathematics of quantum theory, general relativity, and the spectral and asymptotic theory of differential operators. He is known for preliminary work that led to the discovery of the hypothetical Unruh effect.

<span class="mw-page-title-main">Alexander A. Voronov</span> Russian-American mathematician

Alexander A. Voronov is a Russian-American mathematician specializing in mathematical physics, algebraic topology, and algebraic geometry. He is currently a Professor of Mathematics at the University of Minnesota and a Visiting Senior Scientist at the Kavli Institute for the Physics and Mathematics of the Universe.

References

  1. 1 2 3 "Floyd Williams's Biography". The HistoryMakers. Retrieved 2021-08-13.
  2. ↑ "Floyd Williams". Mathematically Gifted & Black.
  3. ↑ List of Fellows of the American Mathematical Society, retrieved 2013-09-01.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.